Q I 81 GENERAL SCIENCE INSTRUC- V|/4 TION IN THE GRADES PART I. A QUANTITATIVE ANALYSIS OF GENEEUL SCIENCE TEXTS PART II. THE REACTION OF CHILDREN OF THE LAST THREE GRAMMAR GRADES TO SCIENCE ■yV BY HANOR A. WEBB, Ph.D. GEORGE PEABODY COLLEGE FOR TEACHERS CONTRIBUTIONS TO EDUCATION NUMBER FOUR PUBLISHED UNDER THE DIRECTION OF GEORGE PEABODY COLLEGE FOR TEACHERS NASHVILLE, TENNESSEE ALBERT R. MANN LIBRARY New York State Colleges OF Agriculture and Home Economics AT Cornell University n ^„^ ...Cornell University Library U IOI.W4 General science instruction in the grade 3 1924 002 931 586 Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924002931586 GENERAL SCIENCE INSTRUC- TION IN THE GRADES PART I. A QUANTITATIVE ANALYSIS OF GENERAL SCIENCE TEXTS PART II. THE REACTION OF CHILDREN OF THE LAST THREE GRAMMAR GRADES TO SCIENCE BY HANOR A. WEBB, Ph.D. GEORGE PEABODY COLLEGE FOR TEACHERS CONTRIBUTIONS TO EDUCATION NUMBER FOUR PUBLISHED UNDER THE DIRECTION OF GEORGE PEABODY COLLEGE FOR TEACHERS NASHVILLE, TENNESSEE Copyright, 1921, by Hanor A. Webb W4 U] ^ .. .. 0& CULLOM a GHERTNER CO., PRINTERS CONTENTS Chapteb I. Present Status of General Science 5 Chapter II. Method of the Analysis 7 Chaptee III. Subject-Matter of General Science 9 Chapter IV. Acceptability of Topics in General Science 16 Chapter V. Size of Topics in General Science 23 Chapter VI. Distribution of the Sciences in General Science 26 Chapter VII. Correlations Between the Sciences 34 Chapter VIII. Adaptability of General Science : 41 Chapter IX. Test Topics 51 Chapter X. Analysis of the Marks 55 Chapter XI. Analysis of Complete Reaction 72 Chapter XII. The Twenty-Seven Combinations 81 Chapter XIII. Correlations Between Combinations 93 Chapter XIV. The Underlying Type 99 PART 1. CHAPTEK I. THE PRESENT STATUS OF GENERAL SCIENCE. The presentation of General Science may be defined as a method of teaching the laws of Nature and their applications in the inventions of man without considering the boundaries of those groups into which scientific knowledge is usually di- vided: astronomy, botany, chemistry, physics, physiography, zoology. The method is not new, for books treating of natural phenomena in this general manner were published fifty years and more ago as readers for the schools, and at any given date in the last half century one or more such texts have been on the market. In many, if not most, of them the biological phases of science as embodied in Nature Study have predominated. The present tide of interest in the content and method of General Science dates from about 1912, when the publication of texts in rapid sequence was begun. The United States Com- missioner of Education's Report for 1890-1910, published in 1910, had just announced the startling fact that the sciences were rapidly waning in popularity in high schools, as evidenced by the decreasing per cent of enrollment. The school journals had published several articles condemning "university domina- tion" of high-school science, the criticism being largely directed at the types of entrance examinations, and other requirements of college-entrance boards, which seemed to demand that the content and method of high-school science be essentially that of a diluted college course, with emphasis on laws and theories rather than applications and everyday illustrations. If causes are to be judged by results, the psychological mo- ment had arrived for radically altering the methods of teaching science to pupils in early adolescence, for from 1911 to the present date (January 1, 1920) twenty-two texts have been published, also many laboratory manuals, either independent or accompanying texts ; a quarterly journal devoted exclusivelj- to General Science has entered its third volume; departments of General Science have been opened in several educational journals ; committees under the auspices of the National Edu- cational Association, the Association of Science and Mathe- matics Teachers, etc., have had official status and published 6 Science for the Grades reports, and the inclusion of General Science in the eighth and ninth grades has spread rapidly throughout the nation. Of course the new subject has met with strong opposition, and each of its claims has been countered by closely related criticisms." It is unfortunate that but few of the arguments for or against General Science have been based on any accurate examination of texts or manuals. The writer, in 1917," examined the ten textbooks then on the market, page by page, and made a critical analysis of the purpose, subject-matter, and method of treatment found there- in. In the spring of 1919 the list was again brought up to date, and eighteen texts which had been advertised or reviewed in school journals were examined, and an analysis of these texts, greatly amplified and considering many phases not in- cluded in the first analysis, comprises the first portion of this study. ' "A Bibliography of General Science," W. L. Eikenberry, General Science Quarterly, Vol. II., No. 3, p. 406. " "A Quantitative Analysis of General Science," H. A. Webb, School of Science and Mathenjatics, Vol. XVII,, No. 6. pp. 534-545 ; June, 1917. CHAPTEK II. METHOD OF THE ANALYSIS. The eighteen texts contain a total of 6,638 pages of instruc- tion, all tables of contents, introductions, prefaces, general review questions, appendices, and indices excluded. These pages were carefully examined one by one, and an entry made on a card for every half page, labeling each card with the title of the topic, the name of the book, and page number of the topic, to permit future identification. The cards were then arranged under headings of the generally recognized branches of scientific knowledge, then rearranged under the important topics in each of these special sciences. This distribution, and a number of subsequent ones by texts, by size of topics, etc., form the minute data from which the tables of this study are obtained. The topic. The employment of a certain degree of personal judgment was inevitable in these arrangements. It was first necessary to decide upon a title for the subject-matter discussed in a given half page. For example, if the instrument by which the weight of air may be measured was described and illustrat- ed, the word "barometer" was written as the title, especially if the paragraph or page heading gave the hint. The science. It was necessary to judge whether the topic was properly included in any of the several principal divisions of science, and, if so, which one. While the barometer is dis- cussed in several sciences, notably chemistry, physics, meteor- ology, yet its principle is a law of physics fundamental to all the phenomena of the mechanics of fluids. Chemistry and meteorology deal with the applications and interpretations of air pressure after it has been measured, rather than with the workings of the barometer. Texts in physics treat the topic more fully than do texts in the other sciences. The assignment of the topic "barometer" to the science of physics seems just and reasonable from these considerations. In like manner each topic was assigned to some science, or to a purely miscellaneous group, the best possible individual judgment being brought to bear on each decision. The writer has had teaching experience in each and every subject of the high-school science curriculum, and founds these judgments upon the knowledge thus acquired. The unit group. Closely related topics were grouped to re- duce the number of units to be handled. The content of Gen- 8 Science for the Grades eral Science could be far more easily, and almost as accurately, judged from an examination of these groups than from the dis- play of the great mass of minute data. The topic "barometer" thus becomes linked with other topics of air pressure and measurement as considered in physics, under a more general heading, and forms a medium-sized unit of subject-matter neither as small as a paragraph nor as large as a chapter. CHAPTER III THE SUBJECT-MATTER OF GENERAL SCIENCE. It was found that the space devoted to instruction in the eighteen texts examined comprised topics which might be con- sidered as belonging to eight large science groups, which ranked in importance as to space as follows : Pages Pages Physics 2,212.5 Physiography 1,264.5 Biology 908.0 Physiology 885.5 Chemistry 632.0 Househoia Art 343.5 Astronomy 271.5 Miscellaneous 120.5 Table I shows the unit groups of these sciences ranked in the order, first, of the number of texts which include topics of the group; second, the number of pages devoted to the group in these texts. The column headed "Test Topics" will be re- ferred to in the latter portion of this study. If ten texts be considered as a clear majority of the eighteen, it is seen that there is considerable agreement as to the most suitable subject- matter in the principal sciences, the number of unit groups, and the number of pages devoted to topics found in ten or more texts having the following percentage for each science : Science Unit Science Vmt Pages Groups Pages Groups % % % % Physiography 80.5 47.8 Physics 80.3 54.4 Physiology 72.6 33.3 Astronomy 70.2 40.0 Chemistry 64.5 34.2 Biology (Botany) 63.1 43.5 Household Art 56.6 15.4 Zoology 0. 0. Miscellaneous 0. 0. In every science, except zoology, over half of the pages of instruction are devoted to the discussion of topics which are also found in a majority of the other texts. A general con- clusion may certainly be drawn from this condition — that Gen- eral Science is by no means a mass of unrelated subject-matter, and that there is a recognition of the acceptability of a large mass of the subject-matter of the so-called "special sciences" by the authors of these texts. 10 Science for the Grades TABLE 1. The Topics of General Science. In PHYSICS. Number Numher Text Topic of Books of Pages Topics 1. Transfer of Heat. (Radiation, Conduction, Convection, and Applications) 1° '^'if'i i 2 Therniorneters - - — - - o4.o ± 3. Air Pressure and Measurement. Barometers 17 154. 1 4. Energy, Types of. Momentum. Inertia, etc l-i "J- 1 5. Tliree Molecular States of Matter lo o4. 1 6. Quantity of Heat. Specific Heat 1^ f*- 1 7. Levers 1* ■i'i,. ] 8. Magnets, Permanent ig J?-;; ^ 9. Specific Gravity, Buoyancy, etc 13 4.i.u 1 10. Pumps, and Their Uses 13 4d. 1 11. Keflection of Light. Mirrors 13 g9. 1 12. The Inclined Plane 13 3(. 1 13. Mass, or Weight of Matter. Gravity 13 6-i.o 1 14. The Spectrum. Rainbows, etc 13 28.5 1 15. Electromagnets, and Applications 12 36.0 1 16. Boiling and Freezing ■ Points 12 56.5 1 17. Ice Making, Principle of 12 54.5 1 18. Refraction of Light. Lenses, etc 12 45. 1 19. Electrical Cells 12 34. 1 20. Dynamos and Motors 11 48. 1 21. The Steam Engine 11 39. 1 22. Expansion from Heat 11 38. 1 23. Nature of Light 11 38. 1 24. Artificial Lighting, Principles of 10 71. 1 23. Sound 10 58. 1 26. Water and Wind Power 10 .50 27. Electric Heating and Lighting 10 38.5 28. Liquid Pressure, Laws of. Hydraulics 10 38.5 29. Evaporation. Vapor Pressure 10 29. 30. Solutions. Physical Properties of Water 10 24.5 31. Pulleys 10 22 32. Static Electricity 9 29.5 33. Friction Producing Heat 9 18.5 34. Distillation 9 14.0 35. Electroplating 9 13.5 36. Siphons 9 8.5 37. Weights and Measures 8 53. 38. Cohesion and Adhesion. Capillarity 8 21.5 39,. Gasoline Engine 8 21 40. Heat, Theoretical Nature of 8 17.5 41. Machines, and Their Applications '. 7 65. 42. Resolution of Forces. Kites, Airplanes, etc 7 42. 43. Diffusion of Gases. Kinetic Molecular Hypothesis 7 11.5 44. Insolation. Absorption of Heat by Air 6 13.5 45. Units of Electrical Measure 5 11. 46. Color, Theory of 5 11 47. Storage Batteries „ 4 7. 48. Explosions. Energy of Expanding Gases 4 5.."i 49. Electrical Appliances, Fuses, Switches, etc 3 21. 50. Electrical Transformers 3 7. 51. The Pendulum 2 9. 52. Bridges, Construction of 1 8 5 53., Physical Laws, General Definition 1 i.n 54. Angular Measurement 1 i'.-, 55. Hardness of Substances, Scale of 1 i' 56. Absorption of Gases '. 1 ..r, Total pages of topics in Physics. 2,212.5 Subject-Matter of General Science 11 In PHYSIOGRAPHV. Number Number Text Topic of Books of Pages Topics 1. Humidity. Precipitation ot All Kinds 17 181.5 3 2. Winds and Storms. Causes of 17 178. 8 3. Soil Formation. Weathering. Types 16 145.5 3 4. Weatlier Forecasts, and Weatlier Maps 16 93. 2 5. Ground Water, Caves, Springs, etc 14 65.5 2 , 6. Erosion, Deposition, Rivers, Lakes , 13 127.5 2 7. Irrigation, Drainage 13 40.5 . 2 8. Coal, Occurrence, and Formation 13 26. 2 9. Climate, Conditions and Causes 11 62. 2 10. Rocks, Igneous and Sedimentary 10 80.5 2 11. Thunder Storms. Lightning 10 18. 1 12. Tillage of the Soil, Effects of 6 2S..j 13. Oil Wells, Petroleum, Natural Gas, etc 6 23.5 14. Glaciers, Icebergs ., 5 37. 15. Volcanoes, Earthquakes 4 31 16. Mountains, How Formed 4 29.5 17. Land Forms, Coast Lines, Bays, etc 3 55. 18. The Ocean. Currents, etc 3 20 19. The Earth's Crust 3 8 20. Topographical Maps, Rules for Making 2 12.5 21. Mines, Their Construction. Mining 2 3. 22. The Aurora Borealis 2 1.5 Total pages of topics in Physiography 1,264.5 In BIOLOGY. Botany Number Number Text Topic of Books of Pages Topics 1. Photosynthesis 16 68. 2 2. Yeasts and Molds 16 60.5 2 3. Flowers, Structure and Function 15 46.5 2 4. Roots, Structure and Function. Osmosis 14 46.5 2 5. Eugenic Bacteria. Fixation of Nitrogen". 14 31. 2 6. Seeds, Dispersal, Germination 13 39.5 2 7. Stems, Trees as Types.... 12 69.5 2 8. Bacteria, Structure of (not hygiene) 10 33.5 2 9. Leaves, Structure of. 10 27. 2 10. Transpiration 10 24. 2 11. Cells. Protoplasm 8 23.5 12. Fertilizers, and Plant Foods 7 32 13. Plant Life, Miscellaneous Types 7 16.5 14. Distribution and Variety of Plants 6 38.5 15. Artificial Plant Propagation. Budding, Grafting, etc 6 22. 16. Higher Fungi, Toadstools, etc 6 14 17. Heredity. Natural and Artificial Selection 5 49.5 18. Alga? 5 17 19. Gardening, a-nd Cultivation of Plants 4 29. 20. Ferns and Mosses 4 6. 21. Plant Diseases 3 11.5 . — . 22. Sap of Plants. Juices, etc 2 2 Zoology 23. Insects 9 34.5 2 24. Types of Animals. Vertebrates, Invertebrates 6 34. 1 25. Amphibians. Life History of Frog 6 12.5 1 26. Amoeba 6 12. 1 27. Animal Distribution over the Earth 5 28.5 28. Birds 5 16 29. Fish 4 7.5 30. Reproduction in Animals 4 6.5 31. Worms 4 5 32. Mammals - 4 4.5 33. Animals Useful and Harmful to Man 3 12.5 34. Reptiles 3 2 35. Animal Parasites and Pests 2 13 36. Low Forms of Animal Life. Hydra, Coral 2 4.5 37. Crawfish 2 4. 38. Mollusks 2 3. 39. Instinct 2 1 Total pages of topics in Biology 908.(1 12 Science for the Grades In PHYSIOLOGY-HYGIBNB. ^^^^^^ j,„^,,^ rea:t Topic of Book8 of Pages Topics 1. Bacteria, and Contagious Diseases 15 206. 4 2. Pure Water Supply, How Obtained Ij ^J-, ° 3. Insect Carriers of Disease Ij 2*-2 % 4. Respiration , Ig 5U.0 s 5. Digestion 12 T9.S i 6. Tlie Bye 12 ""• S 7. Narcotics and Stimulants 12 52. 3 8. The Circulation 10 4A *5 9. Sewage Disposal J ggg 10. The Nervous System I JJ-" 11. The Bar I Jj- 12. First Aid f °4-5 13. The Sljeleton. Bones 6 ZL.5 14. Excretion _ 5 ^o.o 15. Muscles 5 lo.o 16. Pure Air. Harmfulness of Dust 5 1^- 17. Sanitary Plumbing 4 17.5 18. Hygiene, Miscellaneous Discussion of 3 26.5 19. Animal Parasites, Tapeworm, Hookworm 3 2.5 20. The Special Senses, Miscellaneous 2 3.5 21. Touch 2 2 22. Taste 2 1.5 23. Smell 2 1 24. Ductless Glands 1 2.5 Total pages of topics in Physiology — Hygiene... 885.5 In CHEMISTRY. Number Number Text Topic of Books of Pages Topics 1. Combustion 18 75.5 2 2. Composition of the Atmosphere 16 38. 2 3. Oxygen, Occurrence, Preparation, etc 14 37. 2 4. Carbon Dioxide, Preparation, etc 14 28. 2 5. Composition of Water. Electrolysis 13 20. 2 6. Elements, Mixtures, and Compounds 12 33.5 2 7. Hydrogen, Preparation and Properties 12 23.5 2 8. Hardness of Water 12 14.5 2 9. Physical and Chemical Changes 11 31. 2 10. Nitrogen, Preparation and Properties 11 12.5 1 11. Acids, Bases, and Salts 10 50.5 2 12. Solution and Crystallization 10 24.5 2 13. Phosphorus. Matches 10 19. 2 14. Useful Metals. Metallurgy _ 9 63.5 15. Photography 9 25. 16. Carbon, Its Forms and Uses 9 24 17. Destructive Distillation of Wood and Coal 9 17.5 18. Baking Powders, Chemical Action of 8 17.5 19. Fuels, Chemical Nature of 6 27 20. Sulfur 4 8.5 21. Paints and Oils 4 8 22. Chlorine, Preparation and Properties 4 6. 23. Glass, Manufacture of 3 7 24. Lime, Cement, and Clay 3 6.5 25. Alloys 3 1.5 26. Conservation of Matter, Law of 2 2.5 27. Ammonia, Preparation and Properties 2 2. 28. Fireproofing and Waterproofing 1 2.5 29. Delequescence and Efflorescence 1 1.5 30. Phosphorescence, as in J"ireflies 1 1. 31. Flo~cculation 1 i 32. Distinction between Organic and Inorganic Chemistry.... 1 1 33. Law of Definite Proportions 1 l. Total pages of topics in Chemistry 632.0 Subject-Matter of General Science 13 In HOUSEHOLD ARTS AND SCIENCE. Number Number Text Topic of Books of Pages Topics 1. Composition of Foofls. Carbohydrates, Proteins, Fats.... 15 118 2. Fuel Value of Foods. Dietary 11 76.5 3. Preservation of Foods 7 27.5 4. Cleansing of Textiles 6 28. 5. Textiles and Clothing 6 17. 6. Effect of Cooking on Foods 6 17. 7. Soap Making 5 17.5 8. Food, Adulteration of 3 15. 9. Dyeing 3 5.5 10. Household Management 2 10. 11. Bread Making 2 9.5 12. Flavoring Extracts and Perfumes 2 1.5 13. Paper Making 1 .5 Total pages of topics in Household Arts and Science.. 343.5 In ASTKONOMY. Number Number Text Topic of Books of Pages Topics 1. The Solar System, Sun and Planets 13 2. The Seasons 13 3. The Stars, and Constellations 10 4. The Earth as a Planet 10 5. The Moon. Eclipses 8 6. Time --. 8 7. Latitude and Longitude 6 8. The Tides 4 9. Comets 3 10. Meteors 3 Total pages of topics in Astronomy 271.5 In MISCELLANEOUS TOPICS. Number Number Text Topic of Books of Pages Topics 1. Value and Method of Science Study 8 40.5 2. World Commerce and Transportation 5 41.5 3. Man's Relation to Nature 4 12. 4. Economic Problems, Wages, Industry, etc 1 11.5 5. Prehistoric Man 1 6. 6. Psychology. The Mind 1 3 7. Principles of Civilization 1 3. 8. Economy in the Home, General ■. 1 1.5 9. Drawing, the Art of 1 1.5 67. 36.5 50.5 36.5 30.5 17.5 20. 7. 3.5 2.5 Total pages of Miscellaneous Topics 120.5 Total number of pages classified 6,638.0 Table II. shows the distribution of each of the science groups in each of the eighteen texts, in each case the sciences being ranked in order. This minute data is recorded for reference, but a more comprehensive appreciation of the status of the sciences may be obtained from the summary of this table. The rank of Physics, as most important in the matter of space de- voted to its topics, is indisputable. The deviations of this science from first rank in the texts are almost negligible. The agreement as to the ranks of other sciences is less unanimous, but uniform — that is, the deviations from the median rank are practically the same. Even Physiology, which most greatly varies in the importance assigned to it by diflferent authors, shows a median deviation of only 1.5 ranks either way. 14 Science for the Grades Since the median rank of Biology and Physiograpliy is third in each case, and the deviations are identical, these sciences are tied as to importance. Physiography occurs first in two texts, however, and is recorded above Biology for this reason. Physi- ology and Chemistry have also the same median rank, but the deviation of Physiology is greater, and toward the higher ranks — a difference which is clearly brought out by the calculation of the least sum, which gives that science a slight advantage. The treatment accorded to Household Art and Astronomy is decidedly superficial. As expected, neither of these sciences ranks first or second. The small amount of space devoted to Miscellaneous topics is another contradiction of the claim that much of General Science could not be classified under the head- ings of the more familiar and established bi'anches of scien- tific knowledge. TABLE II. Percentage Composition of General Science Texts. Text A. 588 pages t^cience Pages Physics 2.55.5 Physiography 14.^.5 Physiology 83.5 Household Art 42. Chemistry 25.5 Biology 2,S. Astronomy 7.5 Miscellaneous 0. Unclassified 7.5 Text C. 302 pages Science Paries Physics 74. Physiography 7.S.5 Biology 67.5 Physiology 44. Chemistry 12. Household Art 10. Miscellaneous 6.5 .Astronomy 4. Unclassified 10.5 Text E. 479 pages Science Partes Physics 143. Physiography 71.5 Biology 63.5 Household Art 61. Physiology 58.5 Chemistry 52. Astronomy 4. Miscellaneous 0. Unclassified 25.5 Text G. 283 pages Science Panes Physics 94. Physiography 73.5 Biology 55.5 Chemistry 20.3 Astronomy 10. Household Art 4. Miscellaneous 4. Physiology 2. Unclassified 20. 43.4 24.4 14.2 7.1 4.3 3.9 1.3 0. 1.4 24.6 24.3 22.3 14.6 4.0 3.3 2.2 1.3 3.4 30.0 14.8 13.3 12.7 12.2 10.9 0. % 33.3 25.8 19.5 7.2 3.5 1.4 1.4 .7 7.2 Text B. 370 pages Science Pages % Physiology 63.5 17.0 Biology 58. 15.7 Physics 50. 13.5 Physiography 36.5 9.9 Household Art 24. 6.5 Chemistry 22. 6.0 Astronomy 19.5 5.3 Miscellaneous 15.5 4.2 Unclassified si. 21.9 Text D. 395 pages Science Panes % Physics 107.5 27.3 Biology 69.5 17.5 Physiography 68.5 17.4 Physiology 47.5 12.0 Astronomy 41.5 10.5 Household Art 12. 3.0 Chemistry 11. 2.8 Miscellaneous 6.5 1.6 Unclassified .'.. 31. 7.9 Text v. 294 pages Science Pages % Physics 89.5 30.4 Physiology 49.5 16.9 Chemistry 24.5 8.3 Biology : 17.5 6.0 Astronomy 11.5 3.9 Physiography 8. 2.7 Miscellaneous 3. 1.0 Household Art 0. 0. Unclassified 90.5 30.8 Text H. 418 pages Science Pages % Physics .'.. 169.5 40.5 Biology 62.5 15.0 Physiology 52.5 12.6 Physiography 33. 7 9 Household Art 28.5 6 8 Chemistry 26. 6!2 Astronomy 6. 1.4 Miscellaneous 6' l!4 Unclassified 34. g'2 Subject-Matter of General Science 15 Text I. 378 pages Science Pages Physics 164. Chemistry 87. Physiography 54.5 Miscellaneous 26. Household Art 19. Biology 18. Physiology 3. Astronomy 0. Unclassified 6.5 Text K. 539 pages Science Pages Physics 235. Physiology 98. Household Art 54. Physiography 45.5 Astronomy 35. • Chemistry 26. Biology 5.5 Miscellaneous : 0. Unclassitied 40. Text M. 306 pages Science Pages Physiography 90.5 Physics 61.5 Biology 45. Astronomy 31. Chemistry 26.5 Physiology 11.5 Household Art 2. Miscellaneous 1.5 Unclassified 36.5 Text O. 293 pages Physics Physiography Biology Chemistry Physiology Astronomy Household Art Miscellaneous .. Unclassified .... 91.5 58.5 36.5 35. 26. 22.5 18.5 7.5 0. Text Q. 460 pages Science Pages Physiography 258.5 Biology 70.5 Physics 62.5 Astronomy 33. Physiology 16. Miscellaneous 7. ■ Chemistry 6.5 Household Art 4. Unclassified -. 43.4 23.0 14.5 6.9 5.0 4.7 .8 0. 1.7 43.6 18.2 10.0 8.5 6.5 4.8 1.0 0. 7.4 % 29.6 20.0 14.7 10.1 8.7 3.8 .7 .5 11.9 31.0 19.9 12.4 11.9 8.4 7.6 6.3 2.5 0. % 56.2 15.3 13.6 7.2 3.5 1.5 1.4 .9 .4 Text .1. 468 pages Science Pages Physics 130. Physiology 102.5 Biology 59. Chemistry 47.5 Physiography 46.5 Household Art 18.5 Miscellaneous 3. Astronomy 1. Unclassified 60. Text L. 435 pages Science Pages Physics 139. ."i I'hysiography 64.." Biology 60.5 Chemistry 43.5 Physiology 42. ."1 Household Art 28..j Astronomy - 24. Miscellaneous 6. Unclassified 26. Text N. 193 pages Science Pages Physics 62.5 Biology ■ 25.5 Chemistry 24. .Astronomy .- 19. "> Physiology 14.5 Physiogr;iphy - 9. Household Art 7. Miscellaneous 2.5 Unclassitied 28.5 Text P. 609 pages Scttnee Pages Physics 209.5 Biology - - 89..". Chemistry 77. Physiography 70.5 Physiology 56.5 Miscellaneous - 20.5 Astronomy - 1. Household Art ..- 0. Unclassified 84..-. Text R. 430 pages Science Pages Phvsiolotiv 114.5 Biology 80.5 (^hen)istry 56. Physics — 52.5 Physiography 51. Household Art 10.5 Miscellaneous ...- 5. -\stroDoniy 3. Unclassified 57. TABLE II.— SUMMARY. Rank op the Sciences in Percentage Composition. All Texts Included Nifmbcr of Tej'ts in Which the Physics 14 Physiography 2 Biology Physiology 2 Chemistry Household Art Astronomy ^lisccllaneous - Science Ranks 1st 2d 3d 4th 5th 6th 7th 8th Least Median JUedia-n 26 3 6 4 1 3 4 10 73 83 107 112 131 Rank 1. 3. 3. 4.5 4.5 6. 7. Dev. 1. 1. 1.5 1.5 1. 1. 27.9 21.8 12.6 10.1 10.0 4.0 12.8 % 32.2 14.7 13.9 10.0 9.S 6.6 5.." 1.4 5.9 % 32.4 13.4 12.4 10.1 7.5 4.7 3.6 1.3 14.6 % ?A.r, 14.7 12.7 11.6 9.3 3.4 0." 13.0 20.7 IS.S 13.0 12.2 11.9 2.4 1.2 .7 13.1 Av. Dev. .4 1.2 1.2 1.7 1.3 1.0 .9 CHAPTER IV THE ACCEPTABILITY OF GENERAL SCIENCE TOPICS. The richness of the field of science renders it very unlikely that there will ever be a recognized list of uniformly acceptable topics such as would be found in Latin grammars, histories, and mathematical texts. On the other hand, a text in General Science which was composed of topics found in no other texts would at once be branded as a freak; a science concerning which no two books agreed as to suitable material would be of questionable value for instruction. It has appeared from the previous tables that authors of General Science texts have agreed in a large measure as to the suitability of certain topics in science, rather than indulging in that diversity which the inexhaustible material would permit. This agreement has not been uniform, of course, with the dififerent sciences ; it has been less uniform when the different texts are compared; and even the individual topics are susceptible of quantitative measure- ment as to their suitability, as evidenced by the space devoted to them in one or more of the eighteen texts. In order to de- termine this factor for the topics, and from these data to meas- ure the degree of acceptability which characterizes each science and each text, a method of calculating an Acceptability Factor has been devised. Derivation of the formula fp = Acceptability Factor, TP where t = number of texts in which a topic occurs, T = total number of texts (18 in this study), p = number of pages devoted to the topic in a certain text, P = number of pages devoted to the topic in all texts, these data being recorded in Tables I. and II. The acceptability of a topic included in t texts compared with that of a topic found in T texts is the ratio t : T. The acceptability of a topic to which p pages are devoted in a certain text compared to the average number of pages de- voted to that topic in each of the texts (18 or less) which in- clude it is the ratio p : average, or p : P/t. The real acceptability, all influences being considered, is, therefore, represented by the value t p t tp fp T P T P TP Acceptability of General Science Topics 17 If all texts contained the topic, t/T would equal 1. If all texts containing the topic contained exactly the same space devoted to it, then no text would give excess or deficient attention to the topic, and tp/P would equal 1. A perfect acceptability, therefore, would result in a value of unity, which represents the characteristic treatment received by a topic if all authors were exactly agreed as to its impor- tance. It makes no difference whether the topic receives a large or small amount of space, the value obtained is a true measure of the degree to which the topic is uniformly ac- ceptable to General Science authors. The Acceptability Factor will be^greater than 1 for a topic in a certain text which receives marked prominence as to space, and which is included in all, or nearly all, texts. The Acceptability Factor will be less than 1 for a topic in a certain text which is given little prominence in that text, or which occurs in only a few of the texts. A text with a high average Acceptability Factor in a cer- tain science contains topics in that science which have been considered important by most of the other authors of General Science texts, and these topics have received space above, or at least only slightly below, the average space for those topics. A text with a low average Acceptability Factor in a cer- tain science has emphasized topics not considered important by other authors of General Science texts, and has omitted, or superficially treated, the topics which are generally included by the other authors. Depending on the point of view, such a text would be commended for its originality, or criticized as a freak. It is at least sui generis. If a text ranks high or low in its average Acceptability Factor for all sciences, the corresponding general suitability of its topics, as measured by the composite opinions of all authors of General Science texts upon these topics, is indicated. If a science has a high average Acceptability Factor for the eighteen texts, there is considerable agreement among the au- thors of General Science texts as to the most characteristic and suitable topics of that science. If a science has a low average Acceptability Factor for the eighteen texts, there is a disagreement as to the most suitable topics. Examples. In text K, 13 pages were devoted to a discus- sion of lenses and the refraction of light. This topic occurs in 12 books, and covers a total of 45 pages. Substituting in the formula, 18 Science for the Grades 12 X 12 X 13 = 2.311, the Acceptability Factor, 18 X 45 which indicates that the author of this text considered this topic of over twice the importance assigned to it by the com- bined judgment of all authors of General Science texts. In text L, 4.5 pages were assigned to the topic of water and wind power, the topic being mentioned in 10 texts and cover- ing 50 pages. Then substituting in the formula, 10 X 10 X 4.5 = .500, the Acceptability Factor, 18 X 50 by which it is shown that this author selected a topic not con- sidered acceptable by all authors, and gave it less than the average amount of space, the topic being rated at one-half the standard value it would have possessed if all the authors had agreed upon its use, and assigned a definite and uniform num- ber of pages to its discussion. The Acceptability Factor was calculated for each of the 1,557 unit topics of the eighteen texts of General Science. This minute data, although of interest, is exceedingly bulky, and Table III. contains only the following significant values for each text in each science : 1. The number of topics which exceed the standard Accept- ability Factor of 1, and the average acceptability of these topics. 2. The number of topics which have an Acceptability Factor below the standard of 1, and the average acceptability of these topics. 3. The total number of topics, and the average acceptability. -1. The sciences are listed in the table in the order of the average acceptability of all their topics in all texts. 5. In a summary the texts are ranked in the order of the average acceptability of all their topics in all sciences, the number of which is given. If the judgment of the writer be accepted, that an Accepta- bility Factor of .500 or over indicates a satisfactory agreement as to the suitability of a topic, or if that value as an average for the topics of a text or a science represents a general suita- bility of the topic selected, it then appears that, with the ex- ception of Household Arts and Zoology, there is a fairly well- established agreement among the authors of General Science as to what subject-matter is appropriate. Only six of the texts show a tendency to select their material far afield. This agree- AcceptaMlity of General Science Topics 19 ment is more striking because the judgments of the authors have been made independently over a period of many years. General Science, as a whole, cannot be considered as a hodge- podge of unrelated topics selected by irresponsible whims. Diametric attitudes might be taken as to which type of accepta- bility, high or low, was a characteristic of the best texts — the greater likeness to the more common topics of "special science" in the former case, or the greater freedom from traditional prin- ciples and illustrations of these same "special sciences" in the latter type, being each offered as a desirable qualitj' on a Gen- eral Science text. Whichever argument appeals, the Accepta- bility Factor furnishes a quantitative measure of the true condition. TABLE III. Acceptability Factors PHYSIOGRAPHY. Average of 190 topics in 18 texts, .670 Jledian, .713 Text Excess Deftci ency Total Jiumhcr A rcrage Number A verage l^wmber Average A 6 2.431 5 7>'2~y 11 1.565 B — 12 !.356 12 .356 C .3 1.118 8 .615 11 .753 D 3 1.169 7 .578 10 .755 E 4 1.668 8 .285 12 .746 F — 3 .274 3 .274 G 4 1.374 6 .:i3l 111 .748 H — 9 .311 9 .311 I 1 1.656 7 ..^68 8 .704 J — 13 .387 13 .387 K 2 1.649 3 .641 5 1.044 L 2 1.350 9 .582 11 .722 M ■ — 19 .359 19 ..■!59 N — 4 .248 4 .248 1 1.368 15 .319 16 .38.") P 4 1.247 ,", .688 9 .936 Q 4 2.453 14 .484 18 .924 E — 9 .445 9 .44.-1 PHYSICS. Average of 523 topics in 18 texts, .631 Jleaian, .619 Text Excess Deficiency Total l^uml)er Average Nuvther Average Number Average A 11 2.158 9 .642 20 1.476 B 1 1.333 22 .335 23 .379 C 5 1.097 14 .504 19 .700 D 3 1.160 27 .454 30 .527 E 6 1.486 25 .544 31 .726 P 2 1.160 36 .365 38 .407 G 4 1.271 24 .425 28 .546 - H 10 1.392 25 .438 35 .713 I 10 1.794 16 .551 26 1.029 J 2 1.428 42 .405 44 .4.-.1 K 12 1.535 24 .446 36 .809 L 2 1.420 37 .530 39 .575 M — 33 .316 33 .316 N 3 1.172 16 .444 19 .663 — 40 .377 40 .377 P 14 1.461 16 .425 30 .908 Q 2 1.105 19 .414 21 .480 R 4 1.445 7 .479 11 .s:!0 20 Science for the Grades BOTANY. Average of 194 topics in 18 texts, Text A B C D E F ■ G H I J K L M N O P Q R Excess Number Average 3.052 1.264 1.695 1.451 2.195 1.114 1.053 1.311 1.544 1.149 2.184 1.216 1.532 Deficiency Number Average — 12 .373 12 .371 12 .439 8 .255 7 .251 10 .475 12 .498 4 .593 15 .364 4 .338 13 ,333 9 .482 7 .414 11 .286 7 .440 10 .522 10 .411 Median, -Totalr- Number Average 1 3.052 12 .373 15 .550 14 .618 13 .715 7 .251 11 .631 14 .686 4 .593 15 .364 4 .338 14 .383 11 .633 8 .555 12 .357 12 1.167 13 .682 14 .724 .603 .605 Botany andZoolocty Number Average 1 3.052 17 .344 18 .506 17 .572 18 .604 8 .235 13 .636 22 .535 4 .593 27 .300 4 .338 24 .299 15 .528 9 .513 17 .290 13 1.180 18 .562 18 .657 CHEMISTRY. Average of 243 topics in 18 texts, .601 Median, .578 Text A B C D E F G H I J K L M N O P Q R Number 2 1 1 1 1 2 9 3 1 2 1 2 3 4 1 7 -Excess- Average 1.234 1.173 1.192 1.123 1.194 1.396 1.754 1.164 1.311 1.265 1.073 1.483 1.237 2.365 1.210 1.395 • D efideney Number Average 5 .552 11 .323 5 .584 5 .503 19 .420 14 .328 5 .527 12 .583 11 .434' 20 .393 13 .362 17 .480 16 .244 10 .371 14 .430 12 .482 5 .236 8 .587 Number -Totals 7 11 6 6 20 15 7 12 20 23 14 19 17 12 17 16 6 15 Average .747 .323 .682 .618 .427 .593 .776 .583 1.028 .493 .430 .562 .293 .556 .573 .970 .399 .970 Text A B C D E F G H I J K L M N O P Q R PHYSIOLOGY — HYGIENE. Average of 169 topics in 18 texts, .547. Median, .541 Number 2 2 2 3 2 1 3 5 4 3 4 -Excess- Average 2.265 1.057 1.232 1.157 1.515 1.022 1.256 1.256 1.612 1.555 1.359 Deficiency Number Average 4 .509 11 .363 7 .347 7 .274 8 .398 11 .431 1 .255 6 .502 2 .194 14 .337 6 .347 8 .607 7 .185 6 .292 13 .222 3 .360 10 . .208 14 .428 Number 6 13 9 10 10 12 1 9 2 19 10 -Totals 7 6 13 6 10 18 Average 1.094 .469 .544 .538 .621 .444 .255 .753 .194 .581 .854 .607 .185 .292 .222 .957 .208 .634 Acceptability of General Science Topics 21 ASTR( 3N0MY. Ave rage of 78 t opics in 1 7 texts, .524 Median, .509 "ext p™^^rii7 Defic^f'^f^' : — T Ota I Number Average Number Average Number Average A 1 1.928 — 1 1.928 B — 6 .501 6 .501 C — 2 .455 2 .455 D 3 1.541 2 .612 5 1.170 B 1 1.028 — 1 1.028 P 6 .273 6 .273 G 1 1.217 2 .198 3 .538 H 5 .165 5 .165 I — — — J — 1 .117 1 .117 K 1 1,320 9 .362 10 .458 L 2 1.093 3 .449 5 .717 M 8 .565 8 .565 X 1 1.051 4 .384 5 .517 10 .344 10 .344 P — 1 .140 1 .140 Q 1 1.370 7 ..-)II2 8 .610 R 1 .771 1 .771 HOUSEHOLD ARTS AND SCIENCE. Average of 69 topics in 16 texts, .464 Median, ,260 A B C D E P G H I J K L M N O P Q R Number 2 Average 1.824 1.059 1.067 1.112 3.283 1.138 Defieieney Tota; Number Average Number Ai"eraf7e 1 .495 3 1.216 7 .258 7 .258 — 1 1.059 2 .584 2 .564 4 .487 7 .736 — — 2 .194 2 .194 4 .427 5 .564 2 .516 2 .516 7 .252 7 .252 6 .279 7 .708 3 .554 4 .700 2 .097 2 .097 I-. .120 5 .120 8 .202 8 .202 — — 3 .143 3 .143 4 .262 4 .262 ZOOLOGY. A B C D E P G H I J K L M N O P Q R Number 1 1 1 Average Average of 69 topics in 15 texts, .288 Median, .228 Deficiency- Number 5 3 3 5 1 1 8 12 10 4 1 5 1.304 1.000 verage Number 5 Average .275 .275 .291 3 .291 .364 3 .364 .309 5 .309 .137 1 .137 .294 2 .668 .265 8 .265 — .218 12 10 .218 .183 .183 .237 4 .237 .174 1 .174 .126 5 .126 1 1.304 .248 5 .248 .237 4 .428 Science for the Grades MISCELLANEOUS TOPICS. Average of 22 topics in 15 texts, .280 Median. .170 Text ^Excess D eficiency To tal .V«m6er Average NumTyer Average Number Average A — — B •A .048 3 .048 C 1 .208 1 .208 D 1 .208 1 .208 B — . — F 1 .263 1 .263 G 2 .153 2 .133 H — 2 .246 2 .246 I 1 2.283 — 2 1.283 J 1 .263 1 .263 K . — — — L — 1 .0.35 1 .055 M — 1 .132 1 .132 N 1 .143 1 .143 3 .111 3 .111 P 1 1.927 n 1 1.927 Q 1 .234 1 .234 R — 2 .185 2 1.83 Average Acceptability Factor fob Each Text. (All Topics Included.) Text Number Average Text Number Average A 49 1.371 H 99 .580 P 76 .978 Q 85 .551 I 64 .923 L 111 .536 K 86 .695 N 61 .485 R 78 .678 J 135 .426 E 99 .638 F 83 Alb C 67 .625 B 92 .364 D 81 .610 M 102 .356 G 65 .592 O 124 .356 CHAPTEE V. THE SIZE OF UNDIVIDED TOPICS IN GENERAL SCIENCE TEXTS. One of the charges against which General Science has been compelled to defend itself is that of superficialitj'. The crit- icisms have been met- by alleging a different point of view. If superficiality consists of leaving off the alternate theories, in- ferences, exceptions to rule, qualifying explanations, and other minutife, then perhaps General Science is superficial. But if precise, though brief, explanations of the more important phenomena of Nature, presented in simple, unornamented state- ments easy of comprehension by the adolescent mind, are con- sidered more suitable in the texts to be placed in the hands of children, then General Science is adequately treated. The number of pages devoted continuously to a single topic is available from the cards on which the original entries were made in the examination of the eighteen texts (Chapter II.), and will be in multiples of half pages. In a given text not only is the typical size of the continuously treated topics significant, but also the distribution of these sizes above and below the median. Two texts might show the same value for the median size of their topics ; but the separate measures of one text might conform closely to this central tendency, while those of the other text varied widely from it. Therefore the upper and lower quartiles are given, also the median deviation (P.E.). The.se data are set out in Table IV. These tables show that General Science is presented in the form of small unit topics two or three pages in extent. The highest median is only 7.5 pages, found in the treatment of Physiology in text A. Of the 2,214 continuous topics in the eighteen texts, only 71 are in excess of ten pages and only 14 in excess of twenty pages. The median deviation is rarely over two pages, usually one page or less. Only four texts out of eighteen and only one science (Physiography) contain topics of a median size of three pages or more. It is apparent that the authors of General Science texts are in decided agreement as to this phase of the presentation of their subject-matter. 24 Science for the Grades TABLE IV. The Size of Topics in General Science Texts. (By Pages) Quar- Phys- Pftys- Physiology Chem. Household Astron- Miscel Text tiles ics iography Biology Hygiene istry Arts, etc. omy laneou A 3 Q 8. 6.5 — 9.5 2.5 8. M 3.5 3.5 11.5 7.5 1.5 5. 7.5 1 Q 2. 2. — 2.5 1. 3. P.E. 2. 2. 5.. J 5. 1. 3. B 3 Q 2. 3.5 3.3 5. 2.3 3. 3.5 5. M 1..T 2.5 1.5 3. l._ 1.5 2.5 3. 1 Q .."i 1.5 ~) 1. .it .5 2. 1. P.B. ..-I 1. 1.' 2. .~> 1. .3 2. C 3 Q 3. 5. 3. 6.5 2.5 _ _ _ M 2 ~i 2. 1.5 4.5 1..5 5. 2. 6.5 1 Q 1. 1.' 1. 1.5 .5 P.B. 1. 1..5 1. 2.5 1. 1.5 1. D 3 Q 3.3 7. 3.3 6.5 2. _ 10. _ M 2. 3.5 1.3 3. 1.5 2. 4.5 6.5 1 Q 1. 1.5 1. 2. 1. 2. P.E. 1. 2. 1. 1.5 .5 .5 2.5 B 3 Q 4,0 4.5 3.3 5. 2.5 8. _ M y,. 2. 2.5 3.5 1.5 6.3 1. 1 Q !..-> 1.5 1.5 1.5 1. 4. P.E. 1.-, 1. 1. 2. .5 2. P 3 Q 3. — 2. 4. 2. 3. M 1. 2. 1. 3.5 1. 1. 3. 1 Q .r» — 1. 1.5 .5 .1 P.E. .."» 2. .5 1. .5 .5 G 3 Q 2.-, 4.3 4. _ 3.5 M 1.5 2.3 2. 2. 1. 2. 1. 1. 1 Q 1. 1. 1.5 1. P.E. .-, 1.5 .5 .5 4. H 3 Q i.r> 3.5 3. 7. 2.5 8.5 1.3 M 3. 1.5 2. 4. 1.5 2.5 1.5 3. i^ L.T 1. 1.5 2.5 1. 1. .5 P.E. 1.5 .5 1. 2. .5 1.5 .5 .5 I ^9r 6.3 6.5 4. _ 4.5 7.5 M r,. 3. 3. 1.5 3. 5.5 13. 1 Q O 1. 2.5 1. .3 P.E. 3. 2. 2. .5 1.3 2.5 loT J 3 Q 2.5 5.5 2. 4.5 2. 2. M 1.5 2. 1.5 2.5 1. 1.5 1. 3. 1 Q P.B. 1. 1. 1. 1. .5 .5 1. 1.5 1. .3 .5 1. K "^^ 5. 9. 5. 1. 3. 2.5 M 1 Q 3. 1. 5. 2. 1. 2. 1. 1. .5 2. 3^_ 1.5 1. .5 P.E. 2. 3.5 .5 1. .5 l!3 L 3 Q 4. 7. 2.3 5.5 2. 7. 5.3 M 1 Q P.B. 3. 2. 1..T 2.5 1.5 1. 2. 1. 1. 3.5 2. 2. 1.5 1. .5 4.5 .5 2.5 4. 2. 2. 6. M 3 Q M 1 Q P.E. 2. 1. ..■5 ..■3 4.5 2. 1.5 1. 2.5 1.5 1. .5 2.5 1.5 .5 1. 2. 1. .5 .5 .5 .5 5. 2.5 1. 1.5 1.5 N 3 Q M 1 Q P.E. 3.5 2. 1. 1. 3. 2. 1. 1.5 3.5 1.5 1. .5 2.5 2. 1. 1. 2. 1.5 .5 1. 1.5 1. 1. .5 2.5 1.5 1. .5 1. Size of Topics in General Science Quar. Phys- Phys- Physiology Chem. Household Astron- Miscel- Text tiles ics iography Biology Hygiene istry Arts, etc omy laneous 3 Q 2.5 4.5 1.5 2.5 2. 3.5 2. — M 1.5 1.5 1. 1.5 1.5 2. 1. 3. 1 Q 1. 1. 1. 1. 1. 1. 1. — P.E. .5 .5 .5 .5 .5 1. .5 P 3 Q 7.3 9. 7.5 4.5 4. 6.5 M 4.5 4.5 3. 3.5 3. 1. 4. 1 Q 2. 3. 2. 2.5 1. — 2. P.E. 2.5 2. 2. 3. 2. 2. Q 3 Q 3. 10. 4. 2.5 1. 2.3 . — M 2. 4. 2. 1.5 .3 1. 2.5 7. 1 Q 1. 1.5 1.5 1. .5 — 1.3 — P.E. 1. 2.5 1.5 1. 0.0 1. R 3 Q 4.5 9. 5. 9.5 4. 2.5 — — M 1.5 3.5 4. 3. 3.5 1. 3. 2.3 1 Q 1. 2. 2. 1.5 2. .3 — — P.E. 1. 2.5 2. 2.5 1. .5 1. All Texts 3 Q 3.5 5.5 3. 5. 2.5 5. 3. 5.5 M 2. 3. 1.5 2.3 1.3 2. 2. 3. 1 Q 1. 1.5 1. 1.5 1. 1. 1. 1.5 P.E. 1. 2. .5 1.5 .3 1.5 1. 1.5 All Sciences Text A B C D E F G H I 3 Q 6. 3. 4. 4. 4.5 3. 3. 3.3 6.5 M 3. 1.5 2. 2. 2.5 1.5 1.5 2. 3. 1 Q 1.5 .5 1. 1. 1. 1. 1. 1. 1.5 P.E. 2. 1. 1. 1. 1.5 1. .5 1. 2. Text J K L M N P Q R 3 Q 2.5 5. 4. 2.5 2.5 2.3 6.5 4. 5. M 1.5 2. 2. 1.0 1.3 1.5 4. 2. 3. 1 Q 1. 1. 1. .5 1. 1. 2. 1. 1.3 P.E. .5 1. 1. 1. .5 .5 2. 1. 2. CHAPTER VI. THE DISTRIBUTION OF SCIENCES IN GENERAL SCIENCE TEXTS. To CAREY out the spirit of General Science — to be truly "general" — the special sciences should be fairly evenly dis- tributed over the pages of each General Science text, indicating that as each topic is developed, the related facts from all sciences are linked together into the unit project. Even a superficial examination of the texts reveals the fact that the lines of "special science" are not obliterated — the marks of the old divisions, like ancient shore lines, may be plainly discerned. It seems to have been impossible to pulverize many hard lumps of physics, physiology, etc.; and there are places where a browsing reader, covering a dozen pages, would think that he had picked up a text on chemistry, physiography, biology, etc. To quantitatively measure the evenness of distribution which may be characteristic of each special science in each of the eighteen texts, these texts are divided into ten equal portions. Each portion will contaip from 0% to 100% of the subject- matter of a particular science in that text. An ideal distribu- tion would be found if 10% of the space allotted to the science should occur in each of the ten portions — in fact, this would obviously be 100% distributed — i. e., as widely distributed as possible. On the other extreme, if all of the discussion of a certain science should be concentrated into one of the one-tenth portions where only 10% of it should be found, it is obvious that only 10% of the distribution is correct. The arbitrary selection of ten divisions merely gives a con- venient and appropriate fractional part; any other portion would have been usable. Smaller divisions would give more refined data, but extreme minutiae would have been little, .if any, more instructive in the tables which have been computed. Derivation of the formula 100000 = Per Cent of Distribution, S(%^) in which S(%') represents the sum of the separate per cents of a science in each of the one-tenth portions of a text. The Distribution Per Cent of a science in a certain text is a measure not only of the number of diflferent parts into which the science is divided, but also the size of these parts. The Distribution of the Sciences in General Science 27 further the per cent of a science in a one-tenth portion of a text deviates from an ideal 10%, the poorer the distribution. These differences are brought out in correct proportion by rep- resenting the respective per cents as areas — that is, by plotting the per cents on a line and squaring them. A perfect distribution would.be represented by a line di- vided into ten equal parts, with squares erected on each divi- sion, the resulting rectangle having an area of 1000 per cent units, since the base of each square represented 10%. An imperfect distribution is illustrated by a case chosen at random — the distribution of the science Household Arts in text B. Distribution of Household Arts in Text B. PouTiON OF Text 1 2 3 4 5 6 7 8 9 10 % 2.1 12. .5 7.4 39.0 26.7 12,5 (%)=4.4 156.5 54.8 1521. 712.9 156.5 sum 2606.1 A line is divided in the proportion of the per cent of the science which is found in each of the one-tenth portions of the text. A zero per cent of the science in any portion is, of course, represented by a section of line zero points in length. Squares are erected on each of' the divisions of the line, and the areas of these squares added. The portion of the science which is properly distributed is then compared with this area (2606.1), to which it bears some simple ratio. This fraction is the degree of distribution in re- lation to the ideal distribution of 10% of the science in each one-tenth division of the text. To convert the fraction into percentage, the numerator is multiplied by 100. Substituting in the formula, 100 X 1000 = 37.9%, the Per Cent of Distribution of 2606.1 Household Art in Text B. Proof of the formula. Three other examples will illustrate the working of the formula. Given the distribution of a science 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% in the ten portions of a text. Substituting, 100 000 100 000 = 100% S(%') 1000 The answer is obviously correct, as the distribution is perfect. 28 Science for the Grades Given the distribution of a science as 100% 0% 0% 0% 0% 0% 0% 0% 0% 0% in the ten portions of a text. Substituting 100 000 100 000 = = 10% S(%^) 10000 The answer is obviously correct, as only one-tenth of the science is properly placed in one of the ten portions of the text. Given the distribution of a science as 20% 0% 20% 0% 20% 0% 20% 0% 20% 0% in the ten portions of a text. Substituting, 100 000 100 000 = ^ =50% S(%') 2000 The answer is correct, as the science has obviously been dis- tributed only one-half as efficiently as it might have been. Distribution of less than five pages. Since one-half page is the smallest unit recorded in this study, it is impossible to apply this formula to the few cases where less than five pages is devoted to a certain science in a text. To complete the table, a close approximation of the per cent of distribution in such cases is calculated in the following manner. Just as it is pos- sible to distribute 5 pages into ten divisions of one-half page each, 4.5 pages may be divided into nine such portions, 4 pages into eight portions, etc. If the total amount of a science present in the text is four pages, and is concentrated into one- tenth of the text, when it might have been distributed in eight of these portions (one-half page in each), its distribution is evidently 12.5% of the best that was possible. If the science is found in two of the one-tenth portions, the distribution is 25%, etc. This principle will be illustrated by a table of the full list of possible distributions of a science with two pages, and an- other with two and one-half pages of space in a certain text. Pages 2 2.5 Half-pages 4 5 Half-page value 25% 20% No. of Per Cent of No. of Per Cent of Divisions Distribution Distribution Divisions Distribution Distribution 1 100 25% 1 100 20% 2 7.5-25 50% 2 80-20 40% 2 50-50. 50% 2 60.40 40% .3 50-25-25 75% 3 60-20-20 60% 4 25-25-25-25 100% 3 40-40-20 60% 4 40-20-20-20 80% 5 20-20-20-20-20 100% Distribution of the Sciences in General Science 29 It is apparent that these percentages fairly represent the degree of distribution in comparison with the most perfect dis- tribution possible in each case of from one-half to four and one- half pages of a science in a text. The few Distribution Per Cents in Table V. which it was necessary to calculate by this method are all indicated by a sign (*). The Per Cents of Distribution, and data from which they have been computed, are recorded in Table V. for each science in each text. The texts are ranked in the order of the average Per Cent of Distribution for all the sciences ; the sciences are ranked in each text in the order of their respective Per Cents of Distribution. A summary shows the general rank of the sciences in all texts as to distribution. It appears that the authors of General Science have found it least difficult to scatter the subject-matter of Physics over the pages of their texts, linking the phenomena of that science with the topics of the others. The distribution of Physics in Text K (80.1%) is the highest found for any science in any text. But the average rank for the distribution of Physics (52.4%) greatly exceeds that of the next highest science. Physiography (33.5%), showing that in this and the remaining sciences a condition of real "general" distribution is not even approached. This is not due to any purely accidental value for the averages calculated; for when the distributions for the sciences in each text are averaged, a remarkable uniformity of treatment is disclosed. The extreme range between Text N, 34.8% average distribution, and Text R, 22.8% average distri- bution, is only 12%. The grand average of 29.7%, therefore, closely represents the general distribution in all texts, show- ing that no author has radically departed from the established method of grouping the fields of science under the traditional headings. A widely scattered, "general" distribution may not be the chief desideratum of a General Science text ; it may not be even one of the more important principles in the selection and arrangement of its subject-matter; but claims of the ad- vantages which General Science texts and General Science courses possess over the texts and courses of "special science" due to this wide distribution have been repeatedly made, and it has been interesting to determine to what extent, both in the individual texts and in the sciences of each text, these claims are valid. 30 Science for the Grades TABLE V. The Distbibution of Genebal Science Topics. 1. Text N. 193 pages. Average Distribution, 34.8% Divisions 1. 2. 3. Science : % % % Physics 12. 23.2 Cliemistry 12.5 2.1 Physiology Miscellaneous 40 Biology 4. Household Art 21.4 Physiography Astronomy 71.8 10.3 12.8 % 3.2 29.2 24.1 33.3 % 8.8 22.9 14.1 10. 6. % 8.8 20.8 13.8 17.9 Divisions 2. Text P. 609 pages. Average Distribution, 34.1% 1. 2. 3. 4. 5. 6. Science : % % % % % % Physics 3.4 14.5 17.3 7.9 21.3 24.9 Astronomy 100. Chemistry 3.5 29.8 22.0 Biology Physiology 35.7 Miscellaneous 41.7 9.7 Physiography 61.1 2, 5.6 Household Art 3. Text K. 539 pages. Average Distribution, 33.9% Divisions 1. 2. 3. 4. 5. 6. Science : % % % % % % Physics 7.3 10.9 18.3 4.8 4.1 4.9 Physiology 2. 4.6 13.2 33.3 Chemistry 3.8 42.3 28.8 15.4 1.9 Physiography 48.4 43.9 3.3 Household Art 50.9 42.6 6.5 Biology 27.2 9. 63.8 Astronomy 2.7 Miscellaneous 4. Text H. 418 pages. Average Distribution, 33.3% Divisions 1. 2. 3. 4. 5. 6. Science : % % % % % % Physics 1.7 11.2 15.1 8. 22.6 17.5 Physiology 19.1 19.1 7.5 17.2 Household Art 12.3 40.4 26.3 Biology 7.2 2.8 4. Chemistry 38.5 42.3 11.5 7.7 Miscellaneous 58.1 Physiography 31.8 Astronomy 5. Text E. 479 pages. Average Distribution, 33.2% Divisions 1. 2. 3. 4. 5. 6. Science : % % % % % % Physiology 13.2 22.8 27. 6. Physics 20.3 1.7 24.1 24.5 Chemistry 1.9 24. 17.3 36.6 10.6 Household Art 38.6 30.3 31.1 Physiography 6.7 7.5 Biology 1.6 11.8 1.6 3.2 Astronomy Miscellaneous 7. % 34.6 51.2 7. 10.6 3.4 48.6 13.1 20.4 1.8 18. 17.2 6.9 24.5 2.2 8. % 3.4 13.9 42.9 55.6 42.5 17.9 31.3 8. % 18.4 2. 3.8 4.4 3.5 9.4 8.8 68.2 8. % 16.4 4.2 4.8 44. 29.6 60 10. 14.4 12.5 4. 35.7 11.1 5.1 9. 10. .6 44.7 22.4 9. 10. % 8.8 3.8 84.2 21. 48.8 9. % .7 4S 38.1 12.6 100. 10. 6.9 n 2.2 69.2 0. Distri- bution % 50.8 47.1 40.0 •40.0 30.4 28.0 23.6 18.3 .6 34. 41.9 DistH- bution % 56.5 •50.0 30.5 28.6 28.6 23.8 2.10 % !l.4 24.5 11.3 10. 2.4 10.5 28.5 41.9 100. Distri- bution % SO.l 42.9 .S4.1 23.3 22.4 20.4 13.8 Distri- bution % 62.9 62.4 34.4 29.8 28.8 19.4 17.7 10.0 Distri- bution % 54.8 45.1 ^2 1 29.5 28.6 19.6 •12.5 Distribution of the Sciences in General Hcioice ."ii 6. Text O. 295 pages. Average Distribution, 31.8% Divisiona 1. 2. 3. 4. 5. 6. 7. Science : % % % % % % % Physics 20.3 18.1 9.4 26.3 8.8 8.3 Chemistry 21.4 14.3 8.6 31.4 27.2 1 4 Household Art 13.5 18.9 Physiology 19.2 7.7 Physiography 4.3 23.9 11.1 49.6 Biology 5.9 Astronomy 15.5 73.3 15.5 Miscellaneous 8. 9. 10. Distri- bution % f" % % 4.4 4.4 58.8 5.7 50.9 5.4 18.9 43.3 35.7 28.9 44.2 31.0 11.1 30.3 59.4 34.7 21.0 17.0 100. •10.0 7. Text J. 468 pages. Average Distribution, 31.2% Divisions Science : % Physics 28.4 Astronomy Physiology Household Art .... Chemistry Biology Miscellaneous 100. Physiography 13.1 7." 2.8 30.1 40.6 1.8 .9 10.8 26.2 100. 3.5 1.2 17.4 13.8 2.8 33.3 27. % 2.4 79. 10.1 67.4 .8 16.0 9. 10. % 47.5 24.5 41.5 23.4 30.6 33.3 2.3 Distri- bution % 50.8 •50.0 34.0 31.6 30.6 20.3 •16.7 15.4 8. Te.\t B. 370 pages. Average Distribution, SCSof Divisions 1. 2. 3. 4. 5. 6. Science : % % % % % % Physiography 24.7 34.2 13.7 Physics 16. 28. 29. 13. Household Art 2.1 12.5 7.4 39. Chemistry 11.9 7.1 4.8 28.6 42.8 Biology 6.9 2.6 .9 Physiology 44.3 37.1 7.8 2.3 Miscellaneous 19.4 6.4 Astronomy 7.7 9. 10. Distri- bution % % % % % 12.3 5.5 2.7 6.9 45.5 14. 44.5 26.7 12.5 37.9 4.8 34.8 21.5 22.4 45.7 32.2 8.6 23.7 74.2 16.8 92.3 11.7 9. Text M. 306 pages. Average Distribution, 30.2% Divisions 1. 2. 3. 4. 5. 6. 7. Science : % % % % % % % Household Art Physiography 2.3 14.4 2.3 20.6 23.8 Physics 32.1 37. 19.9 10.2 .8 Miscellaneous 100. Biology 1.1 11.1 Chemistry 7.1 7.1 64.4 21.4 Physiology 21.7 8.7 Astronomy 88.7 9.7 1.6 8. 9. 10. Distri- bution % % % % 75. 25. •50.0 29.9 6.7 46.7 34.4 II (1 • < .< 45.5 42.3 25.1 21.2 69.6 18.5 12.5 10. Text C. 302 pages. Average Distribution, 29.9% Divisions 1. 2. 3. 4. 5. 6. 7. Science : % % % % % % % Physics 20.9 7.4 20.9 20.3 20.3 6.8 Physiography 14.3 25. 15. 28.6 Physiology 11.4 27.3 25. Biology 27.4 1.5 Chemistry 41.6 58.4 Miscellaneous 61.6 38.4 Astronomy 75. button % % % % 3.4 55.2 17.1 50.5 36.3 35.5 23. 4.1 43.9 31.1 19.5 18.9 25. •16.0 32 Science for the Grades 11. Text L. 435 pages. Average Distribution, 28.5% Divisiont 2. 3. 4. 5. 6. 9. 10. Dittrir VutUm % % % % % % % % % % 21 .R 16.2 15.8 19. 14.4 58,4 38?« 15.1 25.5 2.5 31.2 26.7 .8 29.3 17. 1.5 35.5 15.9 37.5 4.9 8.3 52.9 33.1 .8 25.0 15.3 2.4 14.1 1.2 67. 20.2 3.5 45.6 50.9 17.8 10.0 100. 10.0 7. 9. 10. Dlstrir tution % % % % % 20,2 2.7 52.2 27.9 44.1 34.1 4.9 32.6 33.5 44.4 29.7 •25.0 70. 18.5 100. •12.5 •12.5 1. Science : % Physics 12.9 Cliemistry -, Physiography Biology Physiology Household Art .... Astronomy 100. Miscellaneous 12. Text G. 283 pages. Average Distribution, 28.4% Divisiona 1. 2. 3. 4. 5. 6. Science : % % % % % % Physics 6.9 2.7 17. 4.3 28.7 17.5 Physiography 15.3 27.2 8.5 21.1 Chemistry 26.9 34.1 Biology 15,5 6.6 Physiology 100. Astronomy 20. 10. Household Art .... Miscellaneous 100. 13. Text F. 294 pages. Average Distribution, 26.9% Divisions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Distri- Science : iution % % % %%%%%%% % Physics 8.4 21.2 15.1 11.2 9.5 16.2 14.5 4.5 68.7 Chemistry 21.4 7.9 23.5 37.7 6. 3.9 39.3 Physiology 1. 7. 47.5 44.5 23.3 Astronomy 69.5 30.5 17.3 Miscellaneous 100. 000000000 •16.7 Biology 5.7 2.8 91.5 11.8 Physiography 93.8 6.2 11.3 Household Art 0000000000 — 14. Text I. 378 pages. Average Distribution, 26.7% Divisions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Distn- Sclence : iution %%%%%% % % % % % Physics 8.4 2. 10. 22.8 .7 22.9 23.2 56.9, Physiography ...... 9.2 2.7 22. 40.4 23.8 1.8 36.0 Chemistry 1.1 23.6 47.7 4.7 3.5 5.8 12.7 1.1 30.6 Biology 22.2 55.6 13.9 8.3 25.9 Physiology 66.7 33.3 •16.7 Household Art .... 5.3 94.7 11.1 Miscellaneous 100. 000000000 10.0 Astronomy 0000000000 — 15. Text Q. 460 pages. Average Distribution, 26.6% Divisions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Distri- Science : iuUon % % % % % % % % % % % Physiography 8.5 9.5 14.6 2.5 16.3 15.2 18.2 15.2 69.4 Physics 22. 37.2 24.4 14. 2.4 37.6 Biology 1.4 2.8 49.7 37.6 25.2 Household Art 25. 75. *25.0 Physiology 62.5 37.5 18.8 Chemistry 15.4 84.6 13.5 Astronomy 85.1 10.5 4.4 13.5 Miscellaneous 100. 10.0 Distribution of the Sciences in General Science 33 16. Text A. 588 pages. Average Distribution, 26. S% Divisions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Distrl^ Science: hution % % % % % % % % % % % Phpsics 16.9 11. 22.5 9.6 10.2 7.1 22.7 SeTe Physiography 9.7 2.5 21.7 37.6 10.5 12.2 5.8 45.9 Physiology 9. 10.8 41.3 38.9 29.3 Household Art 23.8 64.3 11.9 20 4 Chemistry 98. 2. 10 4 Biology 100. 10.0 Astronomy 0000000000 Miscellaneous 0000000000 17. Text D. 395 pages. Average Distribution, 25.0% Divisions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Distri- Science : button % % % % % % % % % % % Physics 19.6 5. 4.4 16.5 17.4 32. 5. 487 Physiology 35.9 2.1 27.3 21. 13.7 37 5 Physiography 13.9 25.6 16. 1.5 43. 33.9 Biology 1.4 25.9 .7000 4.3 21.6 46.1 30.3 Astronomy 10.8 4.8 78.4 6. 15.9 Miscellaneous 84.6 15.4 13.4 Chemistry 100. 00000000 10.0 Household Art 00000000 100. 10.0 18. Text R. 430 pages. Average Distribution, 22.8% Divisions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Distri- Science : bution % % % % % % % % % % % Physiology 1.3 8.7 25.6 31.9 31.5 35.8 Biology .6 26.7 45.4 27.3 28.4 Physiography 3.8 5.7 53.6 36.9 23.3 Physics 64.5 11.2 6.5 12.2 2.8 2.8 22.3 Chemistry 51.8 48.2 20.0 Household Art 28.6 66.7 4.7 18.9 Miscellaneous 30. 00000 70. 000 17.2 Astronomy 100. 'IS-T TABLE \.— Continued. Rank of the Sciences in Distkibution. All Texts Included Science Number of Texts in Which the Least Median Median Av. Science Ranks Sum Rank Dev. Dev. 1st 2d 3d 4th 5th 6th 7th 8th Physics 13 3 1 1 26 1. .4 Physiology 2 3 5 15 11 65 3. 1.5 1.4 Physiography 2 5 3 12 4 1 71 3.5 1.5 2. Chemistry 4 5 15 2 1 71 3.5 1.5 1.4 Biology 117 3 6 84 4.5 .5 .9 Household Art 1 3 4 1 4 1 4 94 6. 2. 1.8 Astronomy 2 1 1 1 7 6 116 7. 1. 1.2 Miscellaneous 2 1 4 4 7 121 7. 1. 1. Average and Median Distbibtjtions fob the Sciences. All Texts Inclcded ■ — Distribution Per Cent — Scienec Average Median Physics - 52.4% 57.7% Physiography ;....; ; 53.5% 32.1% Physiology - 32.2% 29.7% Chemistry 29.7% 30.6% Household Art 24.8% 21.4% Biology 24.7% 25.2% Astronomy 18.4% 15.1% Miscellaneous 17.9% 15.1% CHAPTEE VII. CORRELATIONS BETWEEN THE SCIENCES AS TO VARIOUS PHASES OF THEIR TREATMENT IN GENERAL SCIENCE. Certain questions now arise in connection with the great inequalities in the treatment which the different sciences re- ceive in General Scienc — for example, the marked predominance of Physics as to space and distribution compared with the decidedly inferior standing of Astronomy, one of the oldest, and Household Arts, one of the newest of sciences. Is there any fundamental connection between any two sciences which causes them to rise and fall together in their ranks? Or do certain sciences receive prominence at the expense of certain others? It has been claimed that Physics and Chemistry are a closely co-ordinated pair — that Biology and Physiology, Physiography and Astronomy, also Household Arts and Physics, show strong relationships. It has likewise been claimed that Physics and Biology, Physiography and Biology, Physiography and House- hold Arts, and possibly some other pairs, are to some extent antagonistic, or competitive, and that where a General Science text might have an adequacy or an excess of one, the other would receive deficient treatment. Such relationships may be most accurately shown by com- puting the correlations between the sciences in pairs, using a formula which takes into account not only the ranks, but also the quantities involved in each measure of a distribution of ranks. Pearson's CoeflScient of Correlation is used to show the relationship set out in the following tables.* Correlation Between the Sciences as to Space IN the Texts In comparing the rank and quantity of each science as to space in the eighteen texts with each other science, 36 co- efficients of correlation may be worked out, eight of them being identities. (Correlation, +!•) Strong positive correlation would indicate a "pairing" of the two sciences, exerting mutual influence over each other's rank. Any author who gave a large space to one would give a proportionally large space to the other, and vice versa. ^Pearson's formula for the Coeffldent of Correlation S(xy) r= ys"(x')". ys(y') In wliich X and y represent the fespective deviations from the median of the dis- tribution. See Alexander. Carter: "School Statistics and Publicity," page 185. Correlations Between the Sciences 35 Strong negative correlation would indicate antagonism be- tween the two sciences, and an inverse ratio as to the space received. Weak correlation would indicate the lack of any funda- mental relationship between the two sciences, the ranks and quantities of each science being independent of the other. In Table VI. there are 36 correlations between pairs of sciences, eight of them identities (+!■), fifteen positive, thir- teen negative. Most of the values are low, only the correla- tions between Physics-Chemistry (+.517) and Physics-House- hold Arts (+.590) being sufficiently strong to indicate a pair- ing — a rise and fall together as to space in the individual texts. In respects to all other pairs, the absence of any gen- eral underlying principles of co-ordination between the sciences in determining the amount of space they are given in General Science texts is demonstrated. TABLE VI. COBKELAHON BETWEEN THE SCIENCES AS TO THE SPACE GiVEN TO EACH IN THE Eighteen Texts. Science Physics Physiography BioUigy Physiology Physics -fl. -I-.091 — .2T7 -i-.341 Physiography -I-.091 -|-1. -|-.1«7 -|-.207 Biology —.277 -|-.167 -|-1. -t-.106 Physiology -I-.341 -I-.207 -f.l06 -fl. Chemistry -I-.517 -t-.185 —.074 —.040 Household Art -I-.590 -I-.234 —.312 -f-.385 Astronomy —.057 —.363 —.252 —.061 Miscellaneous -I-.065 —.115 -I- .123 —.264 Household Bcisnce Chemistry Art Astronomy Miscellaneous Physics .- -f.517 -I- .590 —.057 -f.065 Physiography -f.l85 -H.234 —.363 —.115 Biology —.074 —.312 —.253 -)-.123 Physiology —.040 -I-.385 —.061 —.264 Chemistry -|-1. -(-.173 -.264 +.790 Household Art -I-.173 -1-1. +.061 —.309 Astronomy —.264 +.601 +1. - .i.J Miscellaneous +.790 -.309 —.172 +1. Correlation Between* the Sciences as to Per Cent of Distribution in the Texts. The remarkable uniformity in the average Per Cent of Dis- tribution of the sciences for each of the eighteen texts (29.7%, with average deviation of only 2.9%) may be due either to uni- form distribution of each science throughout aU of the texts, or to widely varying, but compensating, per cents of distribu- tion. The question then arises: Is distribution a quality in- herent in a text — that is, does an author who distributes a cer- tain science widely show proportionally good distribution in the other sciences, or vice versa? Or, comparing the sciences 36 Science for the Grades directly, is the wide distribution of a certain science, such as Physics, usually accompanied by the wide distribution of an- other science, such as Chemistry? If the answers to these questions are affirmative, strong positive values would be obtained in determining the correla- tion of pairs of sciences by Pearson's formula. If, on the other hand, the wide distribution of one science, such as Physics, is obtained in most texts at the expense of the concentration of some other science, such as Biology, strong negative correla- tions would indicate the fact. In Table VII. there are 36 correlations between pairs of sciences — eight identities (+!•)> fifteen positive, and thirteen negative. The only positive value above .4 is in the correlation between Biology-Miscellaneous (+.500) — a relationship with- out significance. A very moderate indication of pairing is shown in the correlation between Physics-Chemistry (-|-.356). Stronger negative correlations are found in the relation of Physiography to several other sciences — Physics ( — .368), Physiology ( — .441 ), Chemistry (—.486), Astronomy ( — .368). It appears that in those texts where the other sciences were widely scattered. Physiography was through some necessity concentrated, and vice versa. The values of these correlations are too low to admit of strong positive interpretations. The close agreement of the averages for the texts is evidently due to compensating values for the diflferent distributions which each science received in the eighteen texts. The present status as to distribution is clearly one of individualism. If in future texts the effective spreading of the topics of each special text throughout all por- tions of the book should become recognized as a necessary principle, the correlations will become positive and significant. If the tendency should favor larger groups of all recognized "special sciences," there would also be strong positive correla- tions. But if it should happen that Chemistry becomes more widely distributed throughout all texts because of its intimate relations to each of the other sciences, while Biology becomes more concentrated for the sake of coherence, then strong nega- tive correlations will be obtained between this pair. Such gen- eral tendencies would be clearly revealed by correlations, but their absence has been demonstrated in the data of Table VII. Correlations Between the Sciences 37 TABLE VII. COEBELATION BETWEEN THE SCIENCES AS TO THE PeE CenT OF DlSTBIBUTIOX I.\ THE EIGHTEEN TEXTS. Science PhyHcs Phyisology Physiography Chemistry Physics +1. +.106 —.368 +.356 Physiology +.106 +1. —.441 +.120 Physiography —.368 —.441 +1. —.486 Chemistry 4-.3o6 +.120 —.486 +1. Biology —.316 +.063 ' +.139 —.051 Househoia Art —.126 +.215 +.184 +.136 Astronomy —.090 +.072 -.368 +.053 Miscellaneous —.373 —.088 —.143 +.107 Science Biology Household Art Astronomy Miscellaneous Physics —.316 —.126 —.090 —.373 Physiology +.063 +.215 +.072 —.088 Physiography +.139 +.184 —.368 —.143 Chemistry —.051 +.136 +.053 +.107 Biology +1. +.072 —.002 +.500 Household Art +.072 +1. —.166 +.178 Astronomy —.002 —.166 +1. +.264 Miscellaneous +.500 +.178 +.264 +1. Correlation Between the Number op Pages and the Per Cent of Distribution of Each Science One of the chief criticisms directed against General Science texts has been that the "hobbies" of the authors were evident — that large sections of some "special" science were included bodily in the text, violating the principles of generalness which is supposed to characterize General Science. The defense has been that if the space devoted to a science was large in the aggregate, it was because numerous topics had been inserted wherever they were worth while — that extensive use of the par- ticular science was due to its broad and varied relationships to the problems of daily life. The exceedingly scant and super- ficial attention paid to other sciences being also criticized, this has been explained on the grounds that adequate treatment of all sciences is impossible — that the author has selected topics from the special fields in the proportion in which they most properly fit into the definite plan of his text, and thus the wisest possible choice from each science has been made. When the total amount of space devoted to the topics .of each science is determined, the amount varies greatly in the differ- ent texts. Are the large totals due to the use of a greater number of small topics, or to larger masses of the "special" science? Is the prominent rank of a certain science as to space in General Science due to more extensive or more intensive treatment? Strong positive correlations between Space and Distribution of a science would indicate that the prominent treatment was characterized by the use of many rather than 38 Science for the Grades large topics, giving possible grounds for the charge of super- ficiality. Strong negative correlations would show that large space was usually poorly distributed, and a basis for the ac- cusation of "hobbies" would be furnished. In Table VIII. the correlations are positive in six sciences, negative in two, all but one being of low value. This excep- tion is in the science Biology (+.536), of which it is charac- teristic that the texts giving the science most space tend to dis- tribute it most thoroughly. This tendency, however, cannot be characteristic of General Science as a whole, or the correla- tions in each science would have been more strongly positive. When the relationship of the sciences in the individual texts is considered by rank alone, it is seen that the science which ranks highest as to space usually is given the highest rank in distribution, and a science treated in a small number of pages is likely to be found in one or two groups. Correlating the ranks of the sciences as to per cent of space occupied and per cent of distribution in each text separately by Spearman's Rank Order Formula,' Table IX. shows perfect agreement in Text A, with positive correlations in all other texts, most of them ex- ceedingly strong. The distribution which a certain science re- ceives in one text is not a function of the importance of that science in General Science as a whole, but to its space in that text only. Neither is there any definite relationship between the actual number of pages a science may include in a text and its distribution; the agreement is in rank only. This further emphasizes the conclusion that no matter how much unity of plan an individual author may embody in his text, his arrange- ment is individual and original, and General Science as a whole is not unified. TABLE VIII. Correlation Between the Numbeb op Pages and Per Cent of Distribution in Each Science. Science Correlation Science Correlation Biology -f.436 Physiology -(-.350 Chemistry -(-.264 Miscellaneous < +.256 Household Art +.249 Physics +.049 Astronomy —.146 Physiography —.202 6S(d=) ^Spearman's Rank Order Formula for Correlation, nCn*— 1) See Alexander, Carter : "School .Statistics and Publicity," page 184. Correlations Between the Sciences 39 TABLE IX. Correlation Between the Ranks of the Sciences as to Per Cent of Space and Per Cent of Distbibution in Each Text. Spearman's Rank Order Formula Used Text Correlation Text Correlation A +1.00 B +.33 C +.88 T> +.81 E +.47 P +.86 G +.83 H +.71 I +.76 J +.28 K +.78 L +.93 M +.09 N +.43 O +.52 P _ +.55 Q +.62 K _ +.90 Correlation Between the Sciences as to AccEPTABiLiTr Factors ix the Texts. Is the proper selection of subject-matter inherent in a text? That is, if an author selects the topics of one science well, does he likewise exercise good discrimination in the case of the other sciences ? If an author decides to be original and uncon- ventional in his choice of the subject-matter he presents in one science, will his tendency be transferred to the other sciences included in his text? Uniformly good selection, uniformly poor selection, or uni- formly mediocre selection of two sciences in all or nearly all texts would be indicated by a strong positive correlation be- tween the ranks of their Acceptability Factors when computed by Pearson's formula. But if good selection in one science was uniformly accompanied by poor selection of another science in all or nearly all texts, a strong negative correlation would be secured. Table X. shows 36 correlations — eight identities (+1.), twenty-flve positive, and three negative. In these negative values the Miscellaneous group constitutes one of the pair; hence these correlations are not significant. Of the twentj'-flve positive values, ten are strongly so, over -|-.500, and five mod- erate, between -f-.400 and +-500. The low positive values are in Miscellaneous and in Chemistry, except where the latter cor- relates fairly high with Physics {-\-A72). These values show a very strong tendency for a conserva- tive text to make equally appropriate selections of the topics of each important science — a poor, or bizarre, text to be uni- formly unconventional. The former tendency is the principal one, for twelve of the eighteen texts have Acceptability Factors abov .500. (Table III.) If General Science were a hodgepodge 40 Science for the Grades of unrelated topics, the Acceptability Factors would be ex- ceedingly low and the correlations close to zero. TABLE X. coreelation between the sciences as to acceptability factors. All Texts Included Science Physiography Physics Biology Chemistry Physiography +1. +.715 +.651 +.171 Physics +.715 +1. +.808 +.472 Biology +.651 +.808 +1. +.327 Chemistry +.171 +.472 +.327 +1. Physiology +.595 +.648 +.566 +.201 Astronomy +.621 +.684 +.716 +.055 • Household Art +.490 +.427 +.485 +.118 MisceUaneouB +.050 +.212 +.171 +.674 Science Physiology Astronomy Bousehold Art Miscellaneoi Physiography +.595 +.621 +.490 +.050 Physics +.643 +.684 +.427 +.212 Biology +.566 +.716 +.485 +.171 Chemistry +.201 +.055 +.118 +.674 Physiology +1. +.379 +.435 -.121 Astronomy +.379 +1. +.581 —.488 Household Art +.435 +.581 +1. —.104 Miscellaneous —.121 —.488 —.104 +1. PART II. CHAPTER VIII. THE ADAPTABILITY OF GENEEAL SCIENCE IN THE LAST THREE GRAMMAR GRADES. TEST TOPICS. With very few exceptions, General Science courses are in- tended for the use of pupils in their first high-school year. Of eighteen General Science texts examined in the spring of 1919, only one was admittedly designed for the grades. It is a fact, however, that in many places a General Science course is given in one of the years which constitute the Junior High School, seventh or eighth grade, one of the simpler texts being pre- sumably used. It is by no means a generally accepted principle that Gen- eral Science should be placed exclusively in the High School — that it is unsuited for the grades. In the great reorganization which world events are forcing upon the methods and curricula of schools, in which the demands for a useful knowledge of en- vironment is drowning out the defensive arguments for courses of abstract and remoter value, more than one voice speaks for an earlier introduction to Nature by instruction in her simpler principles given to children even in the lowest grades. Certain important principles in the selection of subject- matter for science instruction in the grades may only be de- termined by experiment. There is excellent agreement among authors of General Science texts as to the suitability of a large number of topics of the five principal sciences (Table III.) ; but could the same subject-matter be used in the grades, even in simple form ? For example, could the meteorological causes, of winds and storms (17 texts), the types of energy, momentum, inertia, etc. (15 texts), the botany and chemistry of photosyn- thesis (16 texts), the chemical composition of the atmosphere (16 texts), be explained to sixth-grade children in a manner which would really result in their assimilation and understand- ing of the principles involved ? For science instruction in the grades, may topics from the five principal sciences be used in equal amounts ? May they be used in the same proportion as they now occur in General Science, or in some other proportion suggested by experiment? May suggestions be obtained from experimental evidence as to the assimilability, or average amount of possible understand- 42 Science for the Grades ing, which children will show to each of the five principal sciences in the grades, to determine if this assimilability is uni- form? If assimilability is not uniform, which science should pre- dominate in the instruction in each grade? What are the rela- tive amounts of the other sciences which may be acceptably in- cluded in that grade? If a certain science, such as Chemistry, is not suitable for instruction in the sixth grade, in which grade may its topics be profitably included? These and many other questions have prompted the study which follows: I Selection of the Test Topics Table I. shows that the subject-matter of General Science has been principally obtained from five sciences. It was planned to select 25 important and characteristic topics from each of these sciences, choosing only those which occur in a clear majority of the texts. In Physics there are more than 25 topics each of which is found in ten or more texts ; in the other sciences there are less than 25 such topics. The Zoology sec- tion of Biology contains no topic included in ten texts ; but to avoid eliminating the subject altogether, five leading topics were chosen from Zoology, which, added to 20 topics from Botany, fills out the quota for Biology. In choosing the particular fact of science upon which the statements of the "test topic" were to be based, a minute di- vision of each topic was made by examining the half-page cards from which the data of Table I. and others had been compiled. These subtopics were recorded, and ranked according to the number of texts in which each was treated. For example, the first topic of Physics, Transfer of Heat (18 texts), is composed of the subtopics Convection (16 texts), Conduction (15 texts). Types of Furnaces (15 texts), Eadiant Heat (14 texts). Prac- tical Ventilation (11 texts), and nine other items of minor rank. Since but one subtopic is to be selected, and that must be the one most prominently treated, the choice falls upon the principles of Convection, which is discussed in the largest num- ber of texts. In a similar manner the most important subtopic of each of the 25 most highly ranked topics in Physics was selected. In the other sciences, where less than 25 topics were in- cluded in a majority of the texts, it was necessary to select two or more subtopics from the topics which had the greatest num- ber of pages. For example, in Physiography three substopics each were chosen from the first three topics, since these con- Adaptability of General Science 43 tained more pages than the others, and two subtopics from each of the remaining eight topics, making 25 in all. In determining which three subtopics were most prominent in the topic — that of Humidity and Precipitation (17 texts), for example — the component items were found to be General Cause of Humidity (17 texts), Rain (17 texts). Snow (16 texts). Clouds (16 texts), Dew (11 texts), Frost (11 texts), and nine other minor ones. The three subtopics chosen were Rain and Snow, Clouds and Fog, Dew and Frost, since these were clearly predominant and occur in a majority of the 17 texts mentioning Humidity. In a similar manner, all of the 1-5 "test topics," 25 from each of the iive principal sciences, were selected. The number of test topics chosen from each important topic of a science is recorded in a column in Table I. These subtopics are those which rank highest in their respective topics ; the topics are the most important of their respective sciences; all (except five in Biology, from the Zoology division) occur in a clear majority of the eighteen texts. It is believed that this method has resulted in the selection of test topics thoroughly characteristic of each science, each topic representing the most favorable judgment of more than a majority of the authors of General Science texts as to its fitness to be presented as a part of the instruction in his text. Following a special study of the texts as to language and treatment of each selected topic, the test which was to be put into the hands of the children was prepared, consisting of a little folder of four pages fastened together. Page 1. TO EACH BOY AND GIRL : This is a game to see how well you can remember. Here are the rules : 1. DO NOT TURN ANY PAGE OVER, OR LOOK AT IT, UNTIL THE TEACHER TELLS YOU TO DO SO. 2. WHEN THE TEACHER TELLS YOU TO, WRITE ANSWERS TO THE QUESTIONS. 3. ON ONE PAGE THERE IS SOMETHING TO READ. TRY TO REMEMBER IT IF YOU CAN. 4. DO NOT LOOK AHEAD, AND DO NOT LOOK BACK, AT ANY PAGES. Page 2. A question designed to discover whether the child already has a knowledge of the principles of the test topic. This ques- tion was direct, simple, and usually covered one point only. If answered correctly, it would be evident that the child possessed some apperceptive basis for the further consideration of the 44 Science for the Grades particular topic involved. If answered incorrectly, it would appear that the child either had no previous conception of the subject or was unable to express one. The data obtained from the answers to this question were expected to be a measure of the foundation of previous knowledge upon which instruction in General Science in the grades might be built.' Page 3. A direct statement, in which the facts and principles of the test topic were set forth as clearly and simply as possible. While a strict composite of the discussions in the ten or more texts was impossible, the statement was carefully worded after a study of the language of each text. Illustrations accompanied this paragraph in thirty-five instances. Page JfA. One or more direct questions, calling for the specific in- formation given on the preceding page. A correct answer would be evidence that the child has been capable of under- standing the subject matter of the statement ; and the further inference is not unreasonable that similar staements, equally characteristic of the science and of approximately the same de- gree of complexity, might also be assimilated by the child. An incorrect answer, or no answer, might indicate that the topic Was apparently too complicated for the child's understanding, and that he would probably have difficulty, or fail completely, in the assimilation of similar topics in that science. Page IfB. One or more questions, based on the specific information of the statement on page 3, but involving a further step of reason- ing along some closely related line. A correct answer would indicate that the child not only understood the topic, but was able to apply its principles to the solution of another problem . such as might be next propounded by text or teacher in or- dinary recitation. An incorrect answer would warrant the con- clusion that the principles of the statement, even if understood by the child, were in isolated position in his mind, and not sufficiently correlated with his apperceptions to be of practical value. 'For a similar test of certain phases of Chemistry in beginning classes, see Webb, H. A., "A Preliminary Test in Chemistry," Journal of Educational Psy- chology, Vol. X., No. 1, page .36 (January, 1919). Adaptability of General Science 45 Lines for the grade, name, and age of the child headed each sheet, so that they could be identified if separated. Special effort was made to avoid questions which could be answered by mere "yes" or "no," or in which the choice of one alternative without explanation would suffice, the laws of chance predicting correct answers in 50 per cent of such cases. The use of certain words, familiar enough to adults, but pos- sibly strange to the child, such as "explain," "illustrate," "de- scribe," "discuss," etc., was discarded in favor of the simpler phrases, "Tell about it," "What is," "Why is," etc. It is fully realized that in some instances the wording of the statement and questions might have an undue influence for cor- rectness or incorrectness of the answers. This condition is minimized in two directions, however: first, the language, in practically every case, is essentially that of one or more texts, simplified as to words or difficult phrases, or at least is as typical of all texts as a close study was able to determine ; sec- ond, in twenty-five test topics for each science a few statements or questions of more than the average difficulty would probably be compensated by a few of abnormal simplicity. The com- bined results for all twenty-five test topics would thus be a fair measure for the science as a whole. With each package of test topics sent out, letters to teachei's explaining the spirit of the test were inclosed, and also a page of specific directions. The number of minutes which were to be allowed a child for writing answers to each question, and for studying the statement, was determined by some preliminary experiments in the Demonstration School of George Peabody College for Teachers. The object was to give sufficient time for even slow pupils to finish, and the indicated periods were found to be ample. DIRECTIONS TO THE TEACHER. ( This test is for the last three grammar grades only. ) In order that there may be uniformity in the methods by which this test is given, it is requested that the teacher in charge of the pupils use the method and wording below : Step 1. (The teacher should see that each child has a pencil, and that the teacher has a watch or can see a clock.) Teacher (to children) : "Girls and boys, here is a new game. I am going to have placed on each desk some sheets of paper, face downward, and you must not touch or handle them until I tell you to." ( Have the sets, four small pages each ; quietly distributed, face downward.) 46 Science for the Grades step 2. Teacher (to children) : "Now turn the whole thing over, and let us read the rules together." (The reading should be done in concert, or by the teacher plainly and with emphasis, the children reading silently. ) The rules— TO EACH BOY AND GIEL : This is a game to see how well you can remember. Here are the rules : 1. DO NOT TURN ANY PAGE OVER, OR LOOK AT IT, UNTIL THE TEACHER TELLS YOU TO DO SO. 2. WHEN THE TEACHER TELLS YOU TO, WRITE ANSWERS TO THE QUESTIONS. 3. ON ONE PAGE THERE IS SOMETHING TO READ. TRY TO REMEMBER IT IF YOU CAN. 4. DO NOT LOOK AHEAD, AND DO NOT LOOK BACK, AT ANY PAGES. Step 3. Teacher (to children) : "Now turn the first page over. Write your grade, name, and age on the first line. Then answer the question or questions below if you can. I will tell you to stop in just two minutes. If you finish before that time, sit quietly, and do not turn any pages." (Allow exactly two minutes for the writing.) Step 4- Teacher (to children) : "Now turn the page over. You must not turn it back again. Write your grade, name, and age. Read what is written on this page, and try to understand and remember it. Do not turn the page until I tell you to. You will have two minutes to study." (Allow exactly two minutes for study.) Step 5. Teacher (to children) : "Now turn the page, and do not turn it back again. Write your grade, name, and age on the first line. Answer the questions if you can. I will stop you in four minutes ; but if you finish before, sit perfectly still, and do not change what you have written." (Allow exactly four minutes for this writing.) (The papers should now be promptly collected without alteration.) TEST TOPICS IN PHYSICS.' 1. Page 2. Question 1. Why, in winter, is it always colder in a room near the floor than near the ceiling? »A complete set of the test topics in the mimeographed form as sent out may be secured by any Interested person on application to the author. Adaptability of General Science 47 Page 3. CONVECTION CURRENTS. (Illustrated.) Statement : Whenever air becomes warmer, it expands ; and because this makes it lighter, it rises. Cold air contracts, is heavy, and falls. In a room the warm air goes to the ceiling, while cold air comes in along the floor. The same thing is true of water. If a bucket of water is heated, the warm water goes to the top, and cold water to the bottom. This movement of air or water, due to a difference in temperature, is called "convection." Page 4. Question 2. Tell why warm air or water rises, and cold air or water falls. Question 3. Why do the boilers of big factories have such tall chim- neys? Why would not a short chimney do as well? 2. THERMOMETERS. (Illustrated.) 3. a HE PRESSURE OF AIR. (Illustrated.) 4. THE KINDS OF ENERGY. 5. THE THREE STATES OF MATTER. (Illustrated.) 6. HOW HEAT IS MEASURED. 7. THE LEVER. (Illustrated.) 8. MAGNETS. (lUustrated.) 9. SPECIFIC GRAVITY. 10. HOW SUCTION IS CAUSED BY AIR PRESSURE (Illustrated.) 11. HOW LIGHT IS REFLECTED. (Illustrated.) 12. THE INCLINED PLANE. (Illustrated.) 13. THE FORCE OF GRAVITATION. 14. THE SPECTRUM COLORS, OR RAINBOW. (lUustrated.) 15. ELECTROMAGNETS. (Illustrated.) 16. THE BOILING AND FREEZING POINTS OF WATER. 17. HOW ICE IS MADE. IS. THE BENDING OF LIGHT RAYS. (Illustrated.) 19. HOW COAL HAS BEEN MADE. 20. HOW ELECTRIC DYNAMOS AND MOTORS WORK. 21. HOW A STEAM ENGINE WORKS. 22. EXPANSION OP SUBSTANCES WHEN HEATED. 23. THE NATURE OF LIGHT. 24. ARTIFICIAL LIGHTING. 25. THE NATURE OP SOUND. TEST TOPICS IN PHYSIOGRAPHY. 1. Page 2. Question 1. Rain, or snow, is water falling from the sky. How does the water get up into the sky? * * * Page S. RAIN AND SNOW. Statement : As warm air blows across oceans and lakes, it gathers much water vapor from their surfaces. The winds blow this moisture over the land in the form of clouds. The tiny drops of water which form the cloud gradually make larger drops by running together, and fall to the ground as rain. If the moisture in the cloud freezes before it starts to fall, it comes to the ground as snow. 48 Science for the Grades Page 4- Question 2. Where does the water in the sky come from, and how does it turn into rain? Why does the water in the sky sometimes turn to snow instead of rain? Question 3. Why do big clouds sometimes go sailing by without dny rain, and why do they at other times pour rain upon the earth? 2. CLOUDS AND FOG. 3. DEW AND FROST. 4. HIGH AND LOW PRESSURE OF AIR. 5. A "COLD WAVE." 6. WIND BELTS OF THE EARTH. 7. THE KINDS OF SOIL. 8. HOW SOIL HAS BEEN MADE. 9. WHAT SOIL IS MADE OF. 10. FORECASTING THE WEATHER. 11. THE WORK OF THE UNITED STATES WEATHER BUREAU. 12. HOW CAVES HAVE BEEN FORMED. 13. SPRINGS AND WELLS. 14. HOW A STREAM SORTS OUT ROCKS OF DIFFERENT. SIZES. 15. THE CUTTING OF VALLEYS. (Illustrated.) 16. DELTAS AND FLOOD PLAINS. (Illustrated.) 17. THE IRRIGATION OF DESERT LANDS. 13. SWAMPS AND DRAINAGE. 19. HOW COAL HAS BEEN MADE. 20. WHAT COAL IS MADE OF. 21. CLIMATE. 22. THE EFFECT OF LAKES AND OCEANS ON CLIMATE. 23. IGNEOUS ROCKS, ROCKS THAT HAVE BEEN MELTED. 24. HOW LIMESTONE IS FORMED. 25. THE CAUSE OF LIGHTNING AND THUNDER. TEST TOPICS IN BIOLOGY. 1. Page 2. Question 1. Where do trees get the materia] to make wood out of while they are growing? * * * Page 3. THE FORMATION OF STARCH IN PLANT LEAVES. Statement: Leaves are the food makers for the plant. Two sub- stances unite in the leaves: (1) The carbon dioxide gas from the air; (2) water coming through the roots and up the stem. These two substances unite in the leaves to form starch. This can only happen while the sun is shining. At night the starch which has been made during the day is carried to all parts of the plant. This it what makes the plant grow. * * * Page 4- Question 2. Tell how a plant manufactures starch in its leaves. What becomes of the starch after it is made? Question 3. If a plant is placed in a dark cellar, will it grow much' '.Tell exactly why. 2. THE GREEN SUBSTANCE IN LEAVES. :3. THE FUNGUS PLANTS. MOLDS. 4. THE YEAST PLANT. (Illustrated.) Adaptability of General Science 49 5. HOW FLOWERS MAKE FRUITS. (Illustrated.) 6. THE PARTS OF A FLOWER. (Illustrated.) 7.' THE PURPOSE OF ROOTS. (Illustrated.) s. THE FORMS OF ROOTS. (Illustrated.) 9. THE NITRIFYING BACTERIA. (lUustrated.) 10. GOOD AND BAD GERMS. 11. HOW SEEDS ARE SCATTERED. 12. HOW SEEDS GROW. (Illustrated.) 13. THE STEMS OF TREES. (Illustrated.) 14. TREES AND THEIR USES. (Illustrated.) 15. GERMS, OR BACTERIA. (Illustrated.) 16. HOW GERMS, OR BACTERIA, REPRODUCE. (Illustrated.) 17. THE PURPOSE OF LEAVES. 18. HOW LEAVES HELP THE PLANT. 19. HOW PLANTS USE THE AIR. 20. HOW PLANTS USB WATER. 21. THE LIFE HISTORY OF INSECTS. 22. THE BODY OF A TRUE INSECT. (Illustrated.) 23. THE KINDS OP ANIMALS. 24. THE LIFE HISTORY OF A FROG. (Illustrated.) 25. THE SIMPLEST ANIMAL, AN AMEBA. (Illustrated.) TEST TOPICS IN PHYSIOLOGY. '\ .. >• I. Page 2. Question 1. How do catching diseases, like measles, get from one person to another? Page 3. THE CAUSE OF DISEASE. Statement: All catching diseases are due to tiny germs, which may live in our nose, our throat, our lungs, our intestines, our blood, and in other parts of our body. These germs get into our body when we do various things which are not healthy, such as drinking impure water, eating food on which flies have walked, drinking from cups that other people use, etc. In fact, if we carelessly handle anything that sick peo- ple have used, the germs from these sick persons may get into our bodies and give us the disease. Page 4. Question 2. How does one person catch a disease from another? What are the best ways to keep from catching diseases? Question ?. Do flies ever do us any harm? Why should we try to keep flies away from our food? 2. WHERE GERMS ARE FOUND IN THE BODY. 3. TOXINS AND ANTITOXINS. 4. HOW GERMS MAY BE KILLED. 5. HOW WATER IS PURIFIED. 6. THE IMPURITIES IN WATER. 7. PURE WATER TO DRINK. 8. INSECTS WHICH CARRY DISEASE. 9. FLIES AND TYPHOID FEVER. 10. THE CAUSE OF MALARIA. II. THE GASES IN OUR LUNGS. 12. HOW WE BREATHE. (Illustrated.) 13. THE STRUCTURE OF OUR LUNGS. (Illustrated.) 14. THE DIGESTION OF FOOD IN THE MOUTH. 15. HOW FOOD IS DIGESTED IN OUR INTESTINES. 16. HOW FOOD IS DIGESTED IN OUR STOMACH. 50 Science for the Grades 17. DEFECTS OF THE EYE. FAR-SIGHT AND NEAR-SIGHT. 18. HOW POOR LIGHT HURTS THE EYES. 19. HOW THE EYES SEE. (Illustrated.) 20. THE HARMFULNESS OF ALCOHOL. 21. THE HARM OF PATENT MEDICINES. 22. HOW TOBACCO HARMS THE BODY. 23. OUR HEART (Illustrated.) 24. WHAT THE BLOOD IS MADE OF. 25. THE BLOOD VESSELS. TEST TOPICS IN CHEMISTRY. I. Page 2. Question 1. Why must Are in a stove have plenty of air before it will burn? Page S. Statement : Whenever anything- burns, it unites with oxygen gas from the air. Since only about one-fifth of the air is oxygen, a sub- stance would burn more vigorously in a bottle of pure oxygen than It would in air. Some substances, such as paper, wood, coal, etc., unite with oxygen very rapidly. These burn easily, and with much flame. Other things, such as iron, lead, and other metals, unite with the oxygen of the air very slowly, and become covered with rust. Rusting and burning are similar processes, except that burning is a more rapid union with oxygen than rusting. In pure oxygen a hot iron wire would not rust but would catch fire and burn. Page 4- Question 2. In what way is the burning of wood and the rusting of iron alike? In what ways are burning and rusting different? Question 3. ' Does the oxygen which we breath from the air have anything to do with the warmth of our skin? Tell about it. 2. FLAMES. KINDLING POINTS. 3. THE GASES OF THE AIR. 4. THE AIR IS A MIXTURE. 5. THE PROPERTIES OF OXYGEN. 6. THE PREPARATION AND PROPERTIES OF OXYGEN. 7. CARBON DIOXIDE GAS. 8. CARBON DIOXIDE AS A FIRE EXTINGUISHER. 9. WHAT WATER IS MADE OF. 10. THE COMPOSITION OF WATER. II. ATOMS AND MOLECULES. 12. ELEMENTS, MIXTURES, AND COMPOUNDS. 13. THE PROPERTIES OF HYDROGEN. 14. PREPARATION AND PROPERTIES OP HYDROGEN 15. THE HARDNESS OP WATER. 16. HOW WASHING SODA HELPS IN WASHING. 17. PHYSICAL AND CHEMICAL' CHANGES. 18. PHYSICAL AND CHEMICAL ACTIONS. 19. HOW NITROGEN IS PREPARED FROM THE AIR. 20. ACIDS, BASES, AND SALTS IN THE HOME. 21. ACIDS, BASES, AND SALTS. 22. HOW CRYSTALS ARE FORMED. (lUusrated ) 23. HOW THINGS DISSOLVE IN WATER. 24. THE PROPERTIES OP PHOSPHORUS. 25. HOW MATCHES ARE MADE. CHAPTER IX. DISTRIBUTION AND SAMPLING OF THE TEST TOPICS. The value of a study such as the one here undertaken in- creases with the number of individuals to whom the test is ap- plied. In the present instance, circumstances made it neces- sary that all the grading, tabulating, etc., be done by the writer ; consequently the number of tests had to be confined within reasonable limits. On the other hand, it was realized that a suflScient number must be used to insure fair sampling. A goal of ten thousand replies was decided upon, which, if fairly distributed among the five sciences, would give approximately 2,000 tests for each. Letters were sent to 120 Superintendents of Schools in towns of not more than 10,000 or less than 5,000 population, as given in the Educational Directory for 1918. Sixty-two su- perintendents agreed to distribute the material to their teachers for use. The supply of test pamphlets, 125 different kinds, was thoroughly mixed and mingled, and approximately 19,000 of them sent to these superintendents. Forty of them returned a total of 9,819 sets. The names of the cities and of the superin- tendents, to each of whom the writer feels personally indebted, follow : City and State — Superintendent Number of Pupils in Each Grade Alabama .5th 6th 7th 8th Bessemer, L. L. Vann 149 164 103 Florence, F. T. Appleby 40 56 86 Gadsden, W. C. Dodson 148 97 147 Huntsville, K. C. Johnston 47 52 30 38 Talladega, D. A. McNeil 51 51 45 Arkansas Helena, E. B. Tucker 55 49 28 Jonesboro, J. P. Womack 21 14 10 Florida Miami, R. B. Hall 92 164 81 Georgia Albany, R. E. Brooks 73 73 72 Americus, J. E. Mathis 76 67 40 Illinois Carbondale. A. R. Boone 40 59 29 Granite City, L. P. Frohardt 115 116 113 Normal, C. F. Miller 40 45 49 Indiana Alexandria, F. W. Stoler 65 57 34 Bedford, E. W. Montgomery 96 80 67 Goshen, James Wilkinson 101 80 91 Kentucky Paducah, Ralph Yakel 343 398 336 Paris, Lee Kirkpatrick 65 45 33 Richmond, W. D. Bridges. 35 40 8 52 Science for the Grades City and State — Superintendent Number of Pupils in Each Orade Louisiana 5th 6th 7th Sth Alexandria, C. C. Hensen 142 194 146 Morgan City, L. A. Law 61 46 Maryland Sykesville, Miss Adda Mai Cummings ll 12 15 Mississippi Yazoo City, H. M. Ivy 31 24 36 Missouri Carthage, W. C. Barnes 40 138 81 NouTH Carolina Concord, A. S. Webb 144 113 80 Greensboro, Frederick Archer 28 26 30 Ohio Barberton, U. L. Light 91 98 74 Troy, C. W. Cookson 80 86 68 Oklahoma Alva. Albert W. Fanning 69 71 30 Chickasha, William F. Ramsey 106 102 103 Shawnee, H. G. Faust 126 124 210 Tennessee Bristol, R. B. Rubins 80 73 49 Clarksville, A. J. Smith 96 93 44 Columbia, B. F. Harris 52 44 27 Nashville (Glenn School), H. C. Weber 21 26 35 Peabody Demonstration School, J. B. Tippett... 67 60 22 Texas Tyler, T. H. Shelby 141 125 159 Virginia Charlottesville, James G. Johnson 172 131 119 Fredericksburg, B. F. Birkhead 73 81 53 West Virginia Morgantown, F. T. Pyle 37 134 165 In several of the States the "last three grammar grades" are numbered Sth, 6th, and 7th ; in others, 6th, Sth, and Sth. Two methods of grouping their answers are possible — either con- sidering the 5th, 6th, 7th grades in one set of schools as equiva- lent to the 6th, 7th, 8th grades of the other schools, or con- sidering the 6th and 7th grades of both groups as equivalent and treating the Sth and Sth grades separately. An attempt was made to ascertain whether the curricula of the two types of schools would indicate which of the two methods was most appropriate, but expressions on the point were conflicting and largely a matter of opinion. It was decided, therefore, to avoid the responsibility of assuming either side of the argument to be correct, and to record both sets of the last three grammar grades separately. It will not be difficult, if any one so desires, to combine the data of a table for any two grades considered equivalent. Test Topics 53 For purposes of identification, the 6th and 7th grades in the 0-6-7 grouping will be followed by the letter "x" in all future references ; the 6th and 7th grades in the 6-7-8 grouping will be followed by the letter "r." These letters were derived from the words "xtra" and "regular," which were first used to keep the records of the two tj'pes separate. Analysis of the Sampling The 9,819 test sets returned represented exceedingly fair sampling, as indicated by the following tables : Grand Total, hy Grades •J 1239 6r 2072 6x 1201 7r 2305 7x 1122 8 1880 The higher grades in each group show slightly fewer replies, as expected. Grand Total, by Sciences If the distribution had been perfect, each science would be represented by 1,964 answers. The number of answers received, and the deviation from this average, is recorded : Science No. Answers Dev. Physiology 2032 +68. Physiography 2001 +37. Physics 1957 —7. Chemistry 1933 —31. Biology 1896 —68. The count shows a remarkable uniformitj-. The slight devia- tion is almost perfectly symmetrical. The extreme range out of nearly two thousand answers is only 136. The various devia- tions from the average of 1,964 average only 43, or '2.2% Totals in Each Science, by Grades Science 5 6a; 7a! Science 6r 7r 8 Physiology 291 229 214 Physiology 439 486 373 Physiography 321 245 235 Physiography 433 466 391 Physics 257 239 224 Physics 421 446 370 Chemistry 230 260 218 Chemistry 384 464 377 Biology 230 228 231 Biology 395 443 369 Average 248 240 224 Average 414 461 376 Av. Deviation 21 10 7 Av. Deviation 20 15 6 These data show that the tests were distributed with great uniformity to the separate grades, and that there is no marked excess or deficiency of answers in any science or in any grade. The fairness of the sampling seems to be thoroughly demon- strated. 54 Science for the Chrades Answers to Individual Test Topics In each one pf the six grade groups, children answered ques- tions related to five sciences, which were presented under twen- ty-five test topics. Thus there are 6 X 5 X 25 = 750 separate and distinct question groups under which the results are re- corded. Each of these 750 units constitutes the number of an- swers received for one test topic of one science in one grade. There is no reason to expect that each unit group would con- tain the same number of answers; on the other hand, by the laws of probability, there should be a normal distribution curve for the number of unit groups which would successively con- tain answers ranked in order from zero on upward. That the normal distribution is closely approximated is shown by the data in Table XI. The five divisions of the curve show the following distribution : Question groups answered by — 5 Students 6-10 11-15 lS-20 20 or More or Less Sttuients Students Students Students Total 96 184 226 144 100 750 12.80% 24.53% 30.13% 19.20% 13.33% 99.99% The curve is slightly skewed toward the left, or zero end. The median number of answers is 13 — that is, half the unit groups include 13 or less answers and half include 13 or more answers. The quartiles are in the 8 and 16 group, which again calls attention to the slight skew toward the lower ranks. The curve shows three mildly prominent modes at the 9, 12, and 15 groups. The efforts to secure a perfectly random distribution seem to have been entirely successful. TABLE XI. DiSTRIBU TION OF ' r50 Unit Question Geoups According [ TO THE NUMBBB OF Students Answebing, Them. JJurnber Unit Uurnber Unit JJumber Unit Jiumher Unit of Groups ot Groups of Groups of Groups Answers 1 Involved 4 4 Answers Involved Answers Involved Answers lu vol red 11 35 21 25 31 4 2 15 12 52 22 20 32 1 3 25 13 46 23 16 SH 2 4 20 14 45 24 7 34 2 5 28 15 48 25 6 35 1 6 28 16 43 26 4 36 1 7 27 17 28 27 4 37 1 8 38 18 29 28 4 above 37 9 50 19 22 29 1 10 41 20 22 30 1 CHAPTEE X. ANALYSIS OF THE MAKKS. The letters A, B, and C were used in marking the tests. "A" represents a correct answer in which the student displays a reasonable understanding of the topic, and expresses the idea in a manner which would be acceptable to the average teacher. "B" represents a decidedly inferior answer, a hazy conception evidenced by faulty or incomplete expression, leaving doubt as to whether there is really an appreciable understanding. The germ of the idea is recognizable, however. "C" represents an incorrect answer, or no answer at all. Since the time allowed for writing the test was proved to be generous, the lack of an attempt is reasonably interpreted as inability on the part of the student to answer. In a few cases, where, in spite of strict prohibitions found in the instructions, the answers were ob- viously copied from the statement on page 3 of the pamphlet, a mark of "C" was given. Method of Grading Each of the 29,457 questions were individually marked by the writer. They were taken in the unsorted order, just as re- ceived from the superintendents. In this way the possibility of the mind getting into a certain "track" in marking a large num- ber of identical questions was avoided — a condition in which reasonable variations in answers might not be properly judged. Each mark was of necessity a matter of separate decision. Admitting the unquestioned fact that in a certain per cent of the cases a mark of A would be given where a mark of B or C was better justified, the laws of probability would equalize the matter in the large number of judgments involved with the compensating error of substituting B or C for A in an approxi- mately equal number of cases. Further, the conclusions of this study are not based upon the minute data such as would be in- fluenced by a small per cent of erroneous judgments. The grading was done almost continuously day after day, and thus the point of view remained reasonably constant throughout the entire time. No tabulations of any kind were made until after all the grading was completed. Thus it was impossible to tell the tendencies which were developing or to receive any informa- tion which might bias the judgments in any way. The question had been asked of each superintendent as to whether the children had received any previous instruction in General Science, the object being to discover whether any 56 Science for the Grades schools in which the subject was taught had been accidentally included in the list. Only one small group of 30 pupils in the eighth grade of one school had elected such a course under an option. The answers of these pupils were compared with the marks of 30 others in the same school and grade, and no ap- preciable difference was noted. These test papers were then included in the general distribution. Numerical Count of Marks The numerical count of the marks for each of the three ques- tions, the objects of which have been previously explained, is recorded in Table XII. Certain general tendencies are roughly indicated by these results — that the number of A's and C's are approximately equal, and either is more than one and one-half times the number of B's. The A's are more numerous in the higher grades, the C's more numerous in the lower grades, as expected. Question 1, on Previous Knowledge, receives roughly 21/2 times as many C's as A's, while Question 2, on Direct As- similation, has about 2% times as many A's as C's. In Ques- tion 3, on the Power of Application, the C's predominate, but are only 20% in excess. As to the separate sciences, the most noticeable feature is the decided difficulty which was experienced with Chemistry which in all three questions is markedly deficient in A's and received C's in excess. In all sciences the reactions of the children were least fav- orable toward Question 1, Previous Knowledge, which received fewest A's and most C's ; and most favorable toward Question 2, Direct Assimilation, with most A's and fewest C's. TABLE XII. Numerical Count of the Marks A'a B's C's Question Question Question Orade 1 2 S Total 12 3 Total 12 3 Total 5 164 312 281 857 223 376 264 863 852 451 694 1997 6r 351 961 614 1926 452 619 441 1512 1296 492 1017 1778 6x 231 578 3S5 1194 223 350 259 832 747 273 557 1577 Tr 558 1375 920 1853 538 575 433 1546 1209 355 952 1516 7x 294 704 469 1467 278 278 248 804 550 140 405 1095 8 608 1370 944 2922 491 355 349 1195 781 155 587 1523 Total 2206 5400 3613 11219 2205 2553 1994 6752 5408 1866 4212 11486 A's B's C's Question Question Question Science 12 3 Total 12 3 Total 12 3 Total Physiology .T.ll 1306 1117 3014 ,",74 440 456 1470 867 286 459 1612 Physinsraphy 4!1S 1232 734 2464 434 442 349 122r, 1069 327 918 2314 Biology 492 1068 737 2297 462 522 461 1445 942 306 698 1946 Physics 413 960 581 1954 400 497 332 1229 1144 500 1044 2688 Chemistry 212 834 444 1490 335 652 396 1383 1386 447 1093 2926 Total 2206 5400 3613 11219 2205 2553 1994 6752 5408 1866 4212 11486 Grand total, 294.')7 marks Analysis of the Marks 57 Only the most roughly approximate conclusions may be drawn from these gross totals, however. The marks must be classified more minutely; and percentages, instead of absolute figures, used in order to equalize the difiierences in the number of answers received from each grade, or for each science. Percentage Tables of the Marks The first assembling of the indivdual test papers for pur- poses of classification is by ''unit groups" into which the papers of one grade, one science, and one test topic are collected. There are 750 such groups. In each test paper there are three questions marked, the significance of which has been previously explained. The median number of answers included in each unit group is 13, with variations from zero to 37, with prac- tically normal distribution. The per cent of A's, B's, and C's for each of the three ques- tions was calculated for each unit group. Then the 25 groups which comprise all of the questions in one science answered by the children of one grade were ranked, and the quartiles, median, and average determined. These figures, therefore, rep- resent the characteristic reaction of the children in each sep- arate grade to each separate science. This data is set out in Table XIII. The use of the per cent instead of the actual numerical count of A's, B's, and C's in these answers equalized the varia- tions in the number of answers in the different topics, the dif- ferent sciences, and the different grades. For example, 100 A's in a group of 200 is a much larger proportion than 100 A's in a group of 300, although the numerical count is the same; a percentage alone expresses the true relation. The use of the median in recording the central characteristic value for these per cents neutralizes another possible source of error which might affect the conclusions. Suppose certain questions have been grossly unfair, and not characteristic of the sciences they were supposed to represent. The replies would contain an abnormal per cent of correct or incorrect an- swers, depending on the unnatural ease or difficulty of the question. Each of these would greatly influence the average, but would simply form an extreme case where the median is used, not affecting its value more than one step at the utmost and having no greater effect on the nearest quartilc. In the table the average is included for each case, and will show, by its deviation from the median, whether such uncom- pensated extreme cases exist. From the upper and lower quar- 58 Science for the Grades tiles those groups in which the cases are concentrated in the higher or lower ranks, or those cases in which the distribution is more uniform, may be discerned. The most significant figures, however, are the respective medians, which record the reactions of the children in each science. TABLE XIII. Peecentagb Table of the Makks. Fifth Grade Physiology Physiography Biology Physics Chemistry A's. B's. C's. A's. C'a. A's. B's. % % % % % Question 1. PreTious Knowledge 3 Q M 1 Q Av. 20. 5.88 13.14 38.88 18.49 23.61 13.83 20. 11.06 3.11 3 Q M 1 Q Av. 40.68 25. 9.58 28.85 24.03 11.11 15.18 24.03 15.50 32.05 7.17 17.45 20.48 11.03 3 Q M 1 Q At. 87.87 60. 32.29 58.01 100. 71.43 38.89 66.33 100. 72.11 45.39 70.67 92.58 80.90 56.30 71.49 100. 93.75 75.55 85.86 Question 2. Direct Assimilation. 3 Q M 1 Q At. 69.05 35.71 19.09 42.06 63.34 30.78 34.17 53.57 25. 14.83 32.51 36.10 16.78 19.22 27.21 16.67 18.36 3Q M 1 Q At. 40. 28.57 14.28 28.27 61.91 31.25 20.83 37.88 48.19 26.38 20. 31.55 88.25 25. 14.37 25.97 50. 37.50 18.34 34.39 3 Q M \'^ Av. 45.56 22.73 16.53 29.67 41.88 28.57 9.40 27.99 50. 25. 21.82 34.14 69.05 51.32 39.23 54.81 66.67 44.45 23.61 47.25 Question 3. Power of Application 3 Q M 1 Q At. 58.57 36.36 12.91 34.72 35.41 14.29 24.27 42.22 24.11 3.33 27.15 26.97 11.11 14.59 25. 10.36 3 Q M \"^ At. 38.18 28.57 16.67 28.01 25.96 11.11 16.59 40. 26.78 3.33 25.69 19.09 6.48 11.03 33.33 8.33 15.76 3 Q M 1 Q At. 51.67 33.33 20.56 37.27 87.30 62.5 35.89 59.14 73.21 , 42.22 24.11 47.16 100. 76.92 58.33 74.38 100. 75. 55.83 73.88 Analysis of the Marks 59 Sixth X Grade C's. A's. B's. C's. A's. B's. C's. Physiology f % *hy8iograph % y Biology % Physics % Chemistry % 3 Q M 1 Q Av. Question 1. 51.09 12.5 2.78 28.75 Previous .-.0. 16.67 25.12 Knowledge MS 18 7.69 21.83 8.39 18.34 27.14 9.25 3Q M 1 Q Av. 33.33 21.43 12.23 23.88 30.95 17.65 20.39 33.33 21.43 3.57 24.14 33.24 13.33 21.15 14.58 9.36 3 Q M 1 Q Av. 66.67 50. 26.78 79.09 55.55 25. 54.49 85.17 50. 25. 54.03 90.20 65.87 41.43 60.51 100. 91.67 70.83 81.39 Question 2. Direct Assimilation 3 Q M 1 Q Av. 94.45 75. 30.95 64.87 81.05 55.55 50. 60.07 86.43 50. 35.68 54.62 57.24 39.28 14.08 39.59 62.01 40. 12.5 40.66 3 Q M 1 Q Av. 36.60 • 20. 3.84 23. 33.33 18.75 3.34 20.28 43.07 25. 8.57 26.50 50. 29.67 20.91 35.73 53.57 28.07 13.94 34.65 3 Q M 1 Q Av. 26.67 12.13 42.73 12.5 19.65 29.28 28. 18.88 40. 18.46 2.94 24.68 38.46 20. 7.70 24.69 Question 3. Power of Application 3 Q M 1 Q At. 84.53 50. 30.56 56.06 66.52 30.77 14.58 39.34 50. . 33.33 17.14 36.54 42.26 30. 2.94 26.17 34.13 15.38 17.27 3 Q M 1 Q Av. 33.33 2S. 3.57 21.08 22.71 14.28 15.15 39.23 25. 17.14 27.01 25.38 10.26 13.55 37.98 25. 1.78 22.16 3 Q M 1 Q Av. 38.19 18.19 3.57 22.88 74.82 41.67 25. 45.51 60. 29.41 15.00 36.45 87.5 51.92 39.23 60.28 73.21 66.67 43.75 60.57 60 Science for the Grades Sixth R Gbadb A's. B's. C's. A's. B'S. C's. B's. C's. Physiology Physiography Biology Physics Chemistry % % % % % Question 1. PreTious Knowledge 3 Q M 1 Q Av. 31.37- 15.38 18.77 25.66 17.78 20.05 33.80 12.5 5.15 22.17 28.28 4.76 15.63 15. 8.39 3 Q M At. 41.27 23.81 13.80 28.29 33.30 21.12 10.53 23. 33.81 23.07 8.42 23.57 36.47 13.33 7.69 18.46 23.61 8.33 12.73 3 Q M 1 Q Av. 73.51 61.54 26.49 52.94 75.96 57.77 31.58 56.95 73.46 60. 26.68 54.26 85.84 64.28 51.19 65.91 100. 88.89 66.44 78.88 Question 2. Direct Assimilation 3 Q M 1 Q Ar. 75.30 55.56 28.57 54.22 71.85 60. 30.38 52. 64.97 46.15 30.30 48.27 55.49 40.91 16.67 39.59 47.22 25. 20.53 34.39 3 Q M 1 Q At. 42.02 23.08 17.16 27.62 39.23 22.87 13.48 25.99 45.23 37.5 20.83 32.61 38.13 26.32 14.83 26.28 57.73 40. 23.01 37.03 3 Q M \^ At. 35.50 8.76 1.97 18.16 28.83 12.91 9.55 22.01 30.30 18.75 4.56 19.12 50. 29.41 15.58 34.13 42.78 23.53 9.16 28.58 Question 3. Power of Application 3 Q M 1 Q At. 61.71 . 40. 23.27 42.32 43.91 30.49 12.41 31.65 46.41 33.33 18.07 32.35 39.28 25. 5.84 23.87 31.66 11.11 2.5 19.18 3 Q M 1 Q At. 33.56 26.67 . 18.75 26.84 27.96 19.90 5.57 17.53 37.98 26.92 13.39 26.92 27.63 14.29 7.41 16.87 30.95 16.67 8.71 20.26 3 Q M 1 Q At. 46.03 23.08 12.13 30.84 73.57 49.87 29.70 50.82 57.36 33.33 21.64 40.73 82.44 58.33 37.85 59.26 82.84 64.92 38.19 60.56 C's. B's. C's. Analysis of the Marks 61 Seventh X Grade Physiology I % Question 1. 'hysiograpl % Previons "ly Biology % Knowledge Physics % Chemistry % 3 Q M 1 Q Av. 60.38 33.33 11.11 36.21 61.25 20. 29.46 50. 25. 6. 29.75 45. 20. 26.67 19.64 10.80 3 Q M 1 Q Av. 49.71 28.57 27.62 31.66 20. 4.16 23.69 50. 30.77 32.96 28.57 12.5 23.11 45.83 15.38 23.92 3 Q M 1 Q Av. 57.78 33.33 10.8 36.11 68.33 36.36 21.67 46.85 52.78 33.33 18.33 37.29 77.35 55.56 12.14 50.22 96.67 83.33 38.88 65.28 Question 2. Direct Assimilation 3 Q M 1 Q Av. 95.4 81.82 53.57 70.94 85.72 77.78 51.92 67.75 88.75 66.67 44.15 62.98 77.5 50. 33.33 53.65 66.67 50. 34.84 51.48 3 Q M 1 Q Av. 30.95 14.28 18.31 35.89 15.38 8.71 15.38 41.93 27.27 5. 26.62 36.67 23.87 16.67 27.29 50. 26.62 15.48 32.88 3 Q M 1 Q Av. 12.96 10.77 17.42 11.11 12.24 13.76 10.40 32.05 16.67 19.06 24.74 12.5 15.64 Question 3. Power of Application 3 Q M 1 Q Av. 87.86 72.72 50. 64.48 72.11 50. 17.42 47.78 51.66 33.33 18.33 37.49 53.57 28.57 5.55 31.41 39.58 28.57 13.39 30.1 3 Q M 1 Q Av. 30.3 15.39 19.36 24.74 10. 14.35 48.07 18.18 9.57 27.02 39.18 16.67 20.53 38.59 16.67 20.84 3 Q M 1 Q Av. 16.78 16.16 56.35 33.33 21.11 37.87 69.05 20. 4.55 35.49 73.86 47.62 25. 48.06 75. 50. 21.82 49.06 6)2 Science for the Chrades Seventh R Grade A's C'B. A'S. B's. C's. A's. B's. C's. 3 Q M 1 Q Av. Physiology F % Question 1. 48.42 31.17 13.64 31.17 'hysiograpl % Previous 48.68 29.96 5.44 29.96 'ly Biology % Knowledge 35.41 13.64 7.14 24.24 Physics % 43.91 21.43 25.02 Chemistry % 18.33 9.52 12.08 1 Q Av. 42.22 29.41 19.47 31. 26.50 20. 12.40 21. 37.71 23.54 14.89 26.67 37.98 21.43 6.45 24.06 31.64 10. 4.65 18.6 1 Q Av. 53.93 36.36 16.23 37.83 75.5 50. 21.5 49.04 72.24 50. 33.27 49.1 77.38 47.06 28.85 50.92 92.51 73.68 49.81 69.32 Question 2. Direct Assimilation 3 Q H 1 Q Av. 82.24 73.34 50. 67.08 87.59 73.34 51.47 68.9 79.28 60. 41.88 59.93 75.49 58.14 35.12 56.2 57.78 44.45 27.67 45.35 3 Q M 1 Q Av. 27.28 18.18 9.52 20.02 28.04 11.77 5.28 17.75 45.31 23.54 13.58 27.07 30.21 23.81 14.64 24.06 50. 37.5 18.6 35.32 3 Q M 1 Q Av. 23.02 9.52 12.9 17.42 11.77 3.97 13.35 18. 13.33 5.88 13. 32.05 14.29 6.25 19.74 26.05 18.18 7.1 19.33 Question 3. Power of Application a Q M 1 Q Av. 81.8 63.64 48.33 60.74 66.83 29.41 16.23 38.35 55.08 42.86 30=95 41.44 50. 35. 10.26 33.44 43.74 22.22 10.1 25.18 3 Q M 1 Q Av. 27.52 15. 6.66 19.48 28.22 16. 5.44 16.87 34.31 20. 10.43 22.37 23.52 14.29 6.07 15.66 32.66 16.67 9.55 19.94 3 Q M 1 Q Av. 28.59 13.63 6.66 19.78 63.86 45.45 27.21 44.78 48.81 33.33 23.02 36.19 82.29 45. 26.68 50.9 75.49 52.94 28.66 54.88 Analysis of the Marks 63 B's C's. A's B's. C's. A's. B's. C's. Eighth Gbadb Physiology Physiography Biology % % % Question 1. PreTlous Knowledge Physics % Chemistry % 3 Q M 1 Q Av. 66.67 40.91 25.39 45.69 53.75 18.18 29.90 63.33 26.67 11.11 37.76 43.21 25. 15.34 30.21 22.64 6.67 15.75 3 Q M 1 Q At. 48.44 27.28 10.55 30.36 36.93 22.22 8.01 23.76 38.75 33.33 10.55 27.34 37.64 25. 10.55 26.84 41.25 23.07 6.9 25. 3 Q M 1 Q At. 43.33 18.18 23.95 71.19 45.46 23.61 46.34 55.05 33.33 9.41 34.9 66.67 35.71 17.5 43.02 85.63 60. 40. 59.25 Question 2. Direct Assimilation 3 Q M 1 Q At. 100. 80. 73.89 80.97 97.92 78.57 61.82 77.23 93.33 ■77.77 59.92 75.64 86.39 62.5 50. 64.03 73.61 62.5 51.66 60.44 19.37 10. 12.1 32.05 15.38 16.33 32.76 15.38 6.11 17.84 39.28 22.22 10. 23.34 35.43 25. 18.18 25. 3 Q M 1 Q- At. 15.55 6.93 9 6.44 10.76 5.56 6.52 23.61 6.66 12.63 15.85 7.7 14.43 Question 3. Power of Application 3 Q M 1 Q At. 90.69 66.67 60. 71.73 75.6 32.18 27.18 50.8 69. 60. 35.08 51.8 63.75 42.86 20.71 41.56 50. 35. 12.91 33.86 3 Q M 1 Q At. 25.83 12.5 5.41 16.85 28.87 15.39 4.95 17.11 26.59 14.28 7.88 17.5 23.61 16.67 7.73 17.73 27.92 10.52 3.12 18.34 1 Q At. 18.74 10. 11.42 48.08 30.77 17.42 32.09 43.05 28.57 11.27 30.7 54.25 35.29 23.21 40.7 72.38 45.46 23.21 47.8 Examination of the medians reveals that in most cases the grades may be ranked according to the general ability of chil- dren to assimilate the facts of science in the order: 5, 6r, 6x, 7r, 7x, 8. That this ranking is thoroughly characteristic is shown when the averages of the medians of all sciences in a particular grade are recorded and ranked. The increments, or differences from grade to grade, will show any exceptions to the general 64 Science for the Grade* tendency for the average per cents to progress from grade to grade in the typical order. These averages, and increments, are recorded in Table XIV. With one exception of very small value (6r-6x, Question 1), the increments in the A's from the fifth to eighth grades are positive for all three questions. The increments in the C's are negative for all questions. Those in the B's vary from positive to negative by small amounts. The rank order of the grades as given above seems firmly established. TABLE XIV. Averages fob the Median Pee Cents in Each Grade. ALL Sciences Included A's. Grades 5 6r 6x 7r 7x 8 Question 1 1.17 10.08 9.05 17.25 19.67 23.48 Question 2 24.95 45.52 51.96 61.85 65.25 72.27 Question 3 17.17 27.99 31.90 38.63 42.64 51.34 A's. Increments between — Grades 5 and 6r and 6x and 7r and 7x and 8 Question 1 +8.91 —1.03 +8.20 +2.42 +3.81 Question 2 +20.57 +6.44 +9.89 +3.40 +7.02 Question 3 +10.82 +3.91 +6.73 +4.01 +8.70 Sum of increments +40.30 +9.32 +24.82 +9.83 +19.53 Average of ineieiiients 13.4a 3.7;) 8.27 3.28 6.31 B's. Averages. Grades 5 6r 6x 7r 7x 8 .Question 1 8.65 17.93 14.77 20.88 21.44 26.18 Question 2 29.74 25.95 24.3 22.96 22.81 17.60 Question 3 16.25 20.89 19.91 16.39 15.38 13.87 B's. Increments between — Grades 5 and 6r and 6x and 7r and 7i and 8 Question 1 +9.28 —3.16 +6.11 +.56 +4.74 Question 2 — 3.79 —1.65 —1.34 —.15 —5.21 Question 3 +4.64 —.92 —3.52 —1.01 —1.51 Sum of increments +10.13 —5.73 +1.25 —.60 —1.98 Average of increments 5.90 1.91 3.66 .57 3.82 C's. Averages. Grades 5 6r 6x 7r 7x 8 Question 1 75.62 66.49 62.62 51.7 48.38 38.54 Question 2 34.41 18.67 15.79 13.42 8.06 3.98 Question 3 57.95 45.90 41.57 38.07 30.19 30.02 C's. Increments between — Grades 5 and 6r and 6x and 7r and 7x and 8 Question 1 —9.13 —3.87 —10.92 —3.32 —9.84 Question 2 —15.74 —2.88 —2.37 —5.37 —4.08 Question 3 — 12.05 —4.33 —3.50 —7.88 —.17 Sum of increments —36.92 —11.08 —16.79 —16.57 —14.09 Average of increments 12.31 3.69 5.60 5.51 4.70 Examination of the medians reveals that in most cases the sciences may be ranked according to the general ability of chil- dren to assimilate their characteristic facts in the order — Physiology, Physiography, Biology, Physics, Chemistry. That this ranking is typical is shown when the average of the medians of all grades in each particular science are record- Analysis of the Marks 65 ed and ranked. The increments, or differences from science to science, will show any exceptions to the general tendency for the average per cents to progress from science to science in the typical order. These averages and increments are recorded in Table XV. With one small exception (Physiography-Biology in Ques- tion 3), the increments of the A's in the sciences ranked from Physiology to Chemistry are negative. With three exceptions, only one of consequence (Physiography-Biology, Question 3), the increments in the C's are positive. The B's vary in sign. In comparing Physiography and Biology, it is seen that the latter possesses a large excess of B's, which explains the ex- ceptions noted above. In all other respects the rank order of the sciences as given above seems to be thoroughly charac- teristic. TABLE XV. Average for the Median Per Cents in Each Science. All Grades Included ; A's. Averages. Scienoe Physiology Physiography Biology Physics Chemistry Question 1 22.59 14.67 14.25 13.26 2.69 Question 2 66.90 62.67 54.26 44.89 39.77 Question 3 54.90 34.52 37.83 28.76 18.71 A's. Increments between — Physiology and Physiography and Biology and Physics and Chemistry Question 1 -7.92 -.42 -.99 -10.57 Question 2 -4.23 -8.41 -9.37 -5.02 Question 3 -20.38 -f3.31 -9.07 -10.05 Sum of Increments -32.53 -5.52 -19.43 -^g-g* Average of Increments 10.84 3.05 6.48 8.55 B's. Averages. Science Physiology Physiography Biology Physics Chemistry Question 1 . . 25.92 18.70 22.02 15.46 9.46 QSestioS 2 ::::;;;;.... 19.02 19.23 25.85 25.14 33.58 Question 3 20.52 14.45 21.86 13.11 15.64 B's. Increments between — Physiology and Physiography and Biology and Physics and Chemistry Question 1 -7.22 4-3.32 -6.56 -6.00 Question 2 -1-21 -|- 6.62 -71. -j-8.44 Question 3 -5.93 -f7.41 -8.75 4-2.53 Sum of increments -12.94 +17.35 -^^g? 4-4.97 Average of increments 4.45 5.78 5.34 3. too C's. Averages. Science Physiology Physiography Biology Physics Chemistry Question 1 43.24 52.76 49.80 58.23 81.89 Question 2 6.84 12.81 15.11 22.64 21.06 Question 3 16.37 43.93 31.14 52.51 59.17 C's. Increments between — Physiology and Physiography and Biology and Physics and Chemistr]/ Question 1 4- -952 -2.96 4-8.43 4-23.66 Question 2 4-5.97 4-2.30 4-7.53 —1.58 Question 3 4-27.56 -12.79 4-21.37 4-6.66 Sum of increments 4-43.05 -13.45 4-37.33 4-28.74 Average of increments 14.35 5.28 12.44 10.11 ^IG Science for the Grades Interi'kbtation or the Eeactions. Gbxeral Characteristics ix the Grades Question 1. The Previous Kitoirledge of Children. Children of the fifth grade have very little information con- cerning even the simplest phenomena of science. The median per cent of correct answers received to questions ^^'hich were designed to probe their minds for knowledge already possessed was zero for all sciences except Physiology-Hygiene, and less than 6% in that instance. There is an exceedingly small ap- perceptive foundation upon which to build General Science in- struction in the fifth grade. In the sixth grades, information concerning the body, and health (Phj'siology), also land forms and the weather (Physio- graphy), have become appreciably more familiar; but the phe- nomena of Physics and Chemistry still are not matters of com- mon knowledge. In the seventh grade, all of the sciences except Chemistry show reasonable medians, which, in the eighth grade, are slightly increased, with the exception of Physiography, which remains practically the same. Physiology-Hygiene is decidedly in the lead in these two grades, probably due, in many cases, to some definite instruction which has begun in that subject. It is difficult to arbitrarily determine the amount of pre- vious knowledge which could furnish a sufficient basis for be- ginning instruction in a particular science. Certainly it would seem unwise from this data to place ordinary topics of the five sciences before children of the fifth grade and expect them to really understand. The possibility of learning rules concern- ing any science by rote is, of course, admitted ; but this is not the type of instruction under discussion. There are also the elementary types of "Nature Primers" and "Natural Science Readers" which have been often used in the fifth and lower grades; but this extremely simple treatment would hardly en- title the topics to be classed with the characteristic subject- matter of Physics, Physiography, etc., in General Science texts. If, for illustration, 15% be taken as a reasonable median, representing the per cent of a class of students which avouM 3iaye previous knowledge of a science, then the standard topics ■of Physiology-Hygiene and Physiography might be given in the sixth grade, and Physics and Biology added in the seventh grade. It is doubtful whether the almost total ignorance of Chemistry would permit a recommendation that it be included in even the eighth grade. As a general principle, there should be a modicum of apperception upon which to build a child's Analysis of the Markv 67 knowledge in a science by instruction, and, under the circum- stances, the expediency of chemical instruction is seriously to be questioned in the grades. In all sciences the median per cents of C\s progi-esslvely de- crease, with two slight exceptions, from the fifth to the eightli grade. They tend to confirm the inferences draA\-u from the distribution of the A's, representing as they do the approxi- mate reciprocals of the percentages of the A's. Question 2. The power of Direct Assiiinlation possessed hij children. It is believed that the child's state of mind when answering Question 2 of the test topic immediately after haviug studied a direct statement of some scientific fact closely approximates his state of miud when reciting to a teacher, or engaging in a written exercise, concerning toiDics which have been previously studied from a textbook. The advantage of recency, and of having but one topic to hold in mind, lies with this test ; the dis- advantage of dealing with an isolated topic, not linked with any project or lesson plan, is also a factor, which may com- pensate the advantage of recency. It is the belief of the writer that the conditions of the test favor as good, or possibly better, reactions from the children in the form of correct answers as would be found in the ordinary recitation or written exerci.se. If this be true, a reasonably high standard of median per cents for A's in the answers of Question 2 may be set to indicate a satisfactory performance. Can any median for Question 2 in the fifth grade be consid- ered satisfactory? Would not a written test in any subject which 3G% or less of a class of normal children could pass be considered unreasonable? And if the pupils had just given diligent study to the points covered by the test, would not the subject-matter which had been assigned to them which could be assimilated by only 36% or less of the class be considered above their mental grasp ? In the fifth grade, Physiology ranks highest v.'ith most A's and fewest C's, but the median is very low in comparison with other grades. Physics and Chemistry rank lowest in A's, and the per cent of C's is correspondingly high, showing that the inability of children to assimilate these topics is definite and positive. It does not appear that in the fifth grade the children are capable of really understanding any reasonable proportion of truly representative topics of the principal sciences. Here, again, the possibility of learning by rote or becoming interested in childish primers is admitted; but this study refers to the real subject-matter and principles of science, expressed with simplicity, but based upon the topics 68 Science for the Grades which a majority of the authors of General Science texts con- sidered indispensable. As a basis of discussion, let approximately 60% be designat- ed as a satisfactory median. If it is reasonable to expect that 60% of a class should pass the average test, then values less than this per cent would indicate subject-matter too diflacult for their comprehension. It would then appear that the first definite science instruction would be properly given in the sixth grade, and would include the topics of Physiology-Hygiene and Physiography. The fields of Biology, and possibly Physics, could be drawn upon for characteristic information in the seventh grade. Physics is appropriate for the eighth grade, and Chemistry is barely over the line. The rank of Physics and Chemistry in this grade compared with the other sciences shows that they present far greater difficulties to children in the as- similation of their subject-matter. Any outline of simplified topics which pupils in grades below the eighth could pass over with high marks would probably have to eliminate some of the most definite and characteristic principles of these two sciences. Again, the C's consistently decrease from the fifth to the eighth grades, coming to a vanishing point in Physiology, Physiography, and Biology. The low per cent of C's in Physics and Chemistry encourage consideration for these sciences in the eighth grade, since the failures, in large proportion, are only partial. The excess of B's in the eighth grade for each of these two sciences over the B's for the other sciences is very marked. Question 3. The power of Application possessed ty children. The surest test for a statement learned by rote is to attempt to use it as a basis for further questioning. There is no promi- nent fact of science that is not co-ordinated' with many other topics, usually in simple and obvious relationships. Question 3 of the test topic involved a step beyond the mere understand- ing of the statement presented to the child ; it tested the genuine- ness of the child's assimilation. In a good recitation a teacher follows the expressions of one pupil with a logically related question addressed to the same or another pupil, and each, in- dividual student, in his response, is supposed to reason from the statements of his predecessor. While an increase in the power of application from the fifth to the eighth grade is shown, it is not characterized by the regularity found in the answers from questions based on pre- vious knowledge and direct assimilation. In the fifth grade the median per cents of A's are low for Question 3, except in Analysis of the Marks 69 Physiology, this power of application being probably due to the greater amount of previous knowledge possessed in that subject. In the sixth and seventh grades a fair proportion of the children appear to be able to apply their knowledge in all sciences except Chemistry. The per cents for Physics and Biology remain practically stationary for these grades, while Physiography shows a serious inconsistency between the median per cents in the 7r and 7x grades which has been verified, but not explained. The per cent of A's for Chemistry does not reach acceptable proportions. Physiology-Hygiene alone has increased steadily, and has the highest rank at all times. In the eighth grade, Physiology still leads in A's, although the pupils who are to be graduated in the 7x grade seem to have reasoned slightly better than those who will graduate in the eighth. Physiography has about the same status as in the seventh grade, while Biology has suddenly attained a satisfac- tory rank. Physics has also shown a marked improvement, though still ranking low. Chemistry still presents insuperable obstacles to the use of logical reason. The C's show the same general decrease in the higher grades, while the B's posses a uniformity which largely neutralizes their possible influence on the conclusions. The general results obtained from the ques- tion designed to show powers of application are nowhere in- consistent with the interpretations from the data on previous knowledge and direct assimilation. Comparison op the R and X Grades Since the "last three grammar grades" comprise two dis- tinct groups — the 5th, 6th, 7th, and the 6th, 7th, 8th — in dif- ferent schools, it is of interest to determine whether there is any appreciable difference in the reaction of children who have the same number of years to go before graduation. Using the tabulation of the median per cents of A's from Table XIV., it is shown that better reactions are given by the children of the 6x and 7x grades in comparison to those of the similarly num- bered 6r and 7r grades. They do not rank as high as the cor- responding grades measured backward from graduation, the 7r and the 8th grades, the difference being greater in this com- parison than in the first — that is, there is less difference be- tween the grades numbered 6 (6r and 6x), also the grades num- bered 7 (7r and 7x), than between the grades taken the year before graduation (6x and 7r) and the grades taken the year of graduation (7x and 8). Those who are graduating in the seventh grade are better able to understand the principles of science than the seventh-grade pupils of the other gi'oup, but 70 Science for the Grades are not as capable as those who are graduating in the eighth grade. The conclusions based upon the A's are confirmed by the percentages of the C's. The differences between the two sixth grades, also the two seventh grades, appear even less when the B's are considered ; for while the 6x grade has more A's, the 6r grade has more B's; the 7x grade has more A's, the 7r grade more B's. While it was appropriate to tabulate the results for the six grades separately, yet if a combination had been made, the grouping by numerical grades — i. e., 5, 6r-6x, 7r-7x,8 — would have more correctly represented the similar ability of children. General Cojitarison of the Percentages in the Sciences Examination of the average percentages for each science, all grades included, reveals two outstanding points. First, the decided ability of children above the fifth grade to master the characteristic topic of Physiology-Hygiene — a tribute, no doubt, to the efforts which have been made for many years to spread the gospel of health and sanitation to evety one who is able to read. This fact, coupled with the definite personal relation which health has to the individual and the references concern- ing disease and its cause which are constantly made in every home, may account for the large amount of previous knowledge, the high assimilability, and the satisfactory response to further questioning shown in the grades studied. Second, the apparent inability of the same group of children, even in the eighth grade, to assimilate the typical facts of Chemistry, is equally stiiking. Tlie previous knowledge which children in the grades studied may liave of Cliemistry is only one-eleventh that of Hieir knowledge of Physiology. Their power of assimilation is only one-half, and their power of application is only one-third in the same connection. In these same three particulars the sciences of Physiog- ra|)liy, Biol()<;y, and Physics rank in the order mentioned. In l)revious knowledge their differences are very moderate, the typical ])er cent being approxinuitely two-thir(is that of Physi- oloijy. in direct assimilation. Physiography is almost as suit- able as piiysiology. Biology ranks considerably lower, while Physics is but little more appropriate than Chemistry. In the power of ap])lication. Physiography and Biology are almost identical in rank, while Physics again present serious diffl- cnlties. Analysis of the Marks 71 Summary op Interpretations 1. A representative list of the principles of science cannot be effectively presented to children of the fifth grade and belo\\-. They lack a sufficient apperceptive foundation of previous ex- perience ; they are not able to directly assimilate any reasonable number of characteristic ideas of science and express them again; their minds have not suflSciently developed so that pow- ers of logical reasoning might be expected. 2. In the sixth grade, Physiology and Physiography alone seem to be suitable for science instruction. There is a reason- able amount of previous knowledge possessed by children in this grade, and the characteristic and fundamental topics of these sciences seem to be satisfactorily assimilated and logical- ly applied according to the standards suggested. 3. In the seventh grade. Biology, and possibly a most ele- mentary treatment of Physics, becomes appropriate according to similar standards, J:. In the eighth grade, Physics is acceptable for instruction according to .similar standards. 5. That Chemistry is of doubtful value for instruction in any of the grammar grades, since its percentaf^es in previous knowledge, direct assimilation, and power of apjilication, all fall below the suggested standards, which are efisily attained by children of some grade or grades in the other sciences. CHAPTER XI. AN ANALYSIS OF THE COMPLETE REACTION OP CHILDREN TO SCIENCE. A STUDY of these data is not complete when the mere re- sults are tabulated. The psychological aspect of the problem — the "reaction" of children of the last three grammar grades toward the presentation of the charactertistic truths of science — involves not only how well they learn, but how they learn. Three successive steps have been considered as factors in the true assimilation of the principles of science. 1. Prvious knowledge, upon, which to build the new concep- tions. This necessity is fundamental to all learning, formal or informal, at all ages, and with every type of mind. 2. Ability to assimilate plain statements, which involves as- sociation of the ideas contained therein with previous knowl- edge. The power to re-express the statement is also an integral part of this ability. 3. The power to apply the information — to reason from the combined knowledge of the first two steps. This does not necessarily involve the development of further principles; if may simply be a recognition of the same principle as applying to the new phenomenon or illustration. The data of the preceding pages show each of these factors separately for each science and each grade. The mark of A, B, or C which a child received on his response to the test of previous knowledge had its proportional influence on the final tabulations for that particular phase ; each A, B, or received in the other two factors functioned in a similar manner. But by separately recording the three marks received for each child, his reaction has been split into three sections. With the total reaction of the child as a unit, three distinct marks in the possible rankings from best to worst are imme- diately obvious. A child who received three A's on his test paper could not possibly have done better ; a child who received three C's could not possibly have done worse. Three B's would have been an exactly medium response. But there are twenty- seven combinations of the marks of A, B, and in groups of three; and by the laws of chance, under no guiding influence, the marks of the 9,819 children should have been equally di- Analysis of Complete Reaction 73 vided among all twenty-seven combinations, and all shades of excellence should have been equally represented. But there were guiding influences, and strong ones, on the reactions of these children ! An overwhelming number of these three-mark sets come under certain combinations. To find out what these influences are, and to interpret their cause and pos- sible significance, is the purpose of this further study. Bank of the Combinations The number of test papers marked under each of the 27 combinations is recorded in Table XVI. The combinations are ranked for each science in each grade; and to emphasize the upper measures, all combinations above the median are written in capital letters, those below the median in small letters. Medians and quartiles are indicated. TABLE XVI. DiSTBIBUTION OP THE AnSWEBS IN THE TWENTY-SeVEN COMBINATIONS. Fifth Grade Physiology Physiography Biology Physics Chemistry CCC 48 CCC 45 CCC 47 3 QCCC 83 3 Q CCC 83 ; QCBB 29 3 Q CBC 31 3 Q CBC 26 CBC 40 M CBC 38 BAA 26 CAC 29 CBB 19 M CAC 19 CAA 24 M AAA 17 CAA 17 cae 21 M AAA 23 M AAA 14 bcc 16 ebb 19 caa 13 ebb 12 1 Q caa 12 ccb 20 aac 11 cac 13 caa 11 cba 15 ebb 10 cab 11 aaa 6 cab 10 cac 13 bac 8 ccb 11 1 Q aac 6 bbc 8 cbc 13 cba 8 bba 8 ccb 8 1 Q bab 12 1 Q bbb 6 1 Q bcc 8 beb cca 6 6 cba bac 5 4 bbb 10 bbc 6 baa 7 baa 5 bcc 4 cab 10 abc 5 aab 5 bac 5 aac 2 bac 9 baa 5 aac S bbc it abc 2 aab 6 cca 5 abb 5 ccb 5 bba 2 bcc 6 aab 4 bcb 5 aba 4 bbb 2 aac 5 aba 4 cba 5 bba 4 bca 2 aba 5 bab 4 ace 4 cab 4 cca 2 bba 5 bcc 4 bbc 4 aca 3 aaa abb 3 ccb 4 abc 3 ace 3 aab bbc 2 bcb 3 bab 3 bab 3 aba bca 2 abb 2 bac 3 bca 3 ace cca 2 ace 2 acb 2 aab 2 baa abc 1 cab 2 cca 2 abc 2 bcb ace 1 acb 1 aba 1 cba 2 abb bcb 1 bba 1 bbb 1 abb 1 aca aca bca 1 bca 1 bbb 1 acb acb aca aca acb bab Total, 291 Total, 231 Total, 230 Total, 257 Total, 230 Scirnce for the Grades Sixth E Grade Physiology Physiography Biology Physics Chemistry CCC 51 CCC 58 CBC 43 CCC 95 CCC . 80 CAA 50 3 QCBC 54 CAC 37 3 Q CBC 46 3 Q CBC 68 Q AAA 48 3 Q CCC 37 CAC 46 CAC 44 M CAC 50 BAA 45 AAA 41 AAA 32 M CAA 29 M CAB 27 JI CAA 36 BAA 21 caa 28 CAB 21 aaa 23 ebb 23 ebb 27 baa 20 M CBA 20 cab 21 bbc 19 bab 23 cab 24 bbc 16 cab 16 cac 23 bac 21 caa 19 ebb 16 1 Q cba 14 cbc 23 1 Q aac 18 aab 18 aac 15 1 Q cba IS ebb 16 1 Q baa 13 ccb 13 bbb 12 aac 15 baa 12 bba 14 bba 11 bab 15 ccb 12 abc 10 bbc 14 ccb 11 1 Q bac 15 cba- 11 bac 9 bbb 13 bab 111 bac 111 bcc 7 jiab 10 bcc 10 bbb 13 bbb 10 aac 6 bac 10 cba 9 ccb 11 abc 8 cca 6 ccb 1(1 aab 7 bba 1(1 ace 7 aaa 4 abb fi bbc 6 bbc S aab 6 aba 4 bcb 6 ebb 6 . bcc 7 bab 6 ace 3 aba r, aba 4 aba 6 bee 6 bab 3 cca 5 abc 4 abb 6 eea 6 bba 3 aac 4 aca 4 cca 6 aba 5 abb 2 abc 3 abb 3 bcb 5 bea 5 bbb 2 ace 2 ace 3 abc 4 bba 4 aab 1 aca 1 cca 3 aca 4 aca 3 bcb 1 bea 1 bcb 2 aeb 2 bcb 3 aca .-eh neb 1 ace 2 aeb 1 aeb bcc bca bca 2 iibh (1 bca Tov.il. 43;) , Total, i:v.'. Total, 3115 T otal. 421 Total. ?,R4 Sixth X Grade Physioi '.ogy Pliy.'iiof/raijhfi Biology Pliysics Cheiniatry AAA 45 AAA 36 CBC 26 CCC 47 CBC 52 Q CAA 30 :; Q CCC 33 CCC 3 Q CAA 24 18 3 Q CBC Mil 3 Q CCC 45 BAA 27 CBC 29 CAC 2.S CAB 2.S M 1 '(.'( ' 19 11 CAA Uli AAA CAC 17 IB M CCA 17 M CAC 2S ebb 13 eac 25 M CBA 15 aaa 15 caa 21 cbc 13 bae 14 ebb 14 ebb 11 bab 10 aac 10 aab 12 aae 10 1 Q bbc 10 cac 9 1 Q baa 10 # cab 12 baa 7 1 Q cab 8 ebb 12 bba 7 cba 10 cab 7 baa 11 1 Q cab 7 ccb 11 I'ha N ecb 1 1 Q bab 10 . a be 6 aab 7 aab i; bbc (i aab 4 bba (J lio Analysis of Complete Reaction 75 Seventh R Grade Physiology Physiography Biology Physics Chemif !fr,/ AAA 113 AAA 67 AAA .54 CAC 51 1 CBC 70 3 Q CAA 70 3 Q CAC .17 BAA 3 Q CAA 44 44 3 Q CCC 54 3 Q CAC 5.S M BAA 66 CAA .".1 AAA 45 CCA 45 CBC 41 CAC 34 CBC 3.S CCC 37 ccc 2.^ M CCC 36 CAB 33 M CAA 33 M CAB i; 5 cbc 25 M CCC 31 cba 22 baa 32 aac 30 bbc 20 aab 20 bac 31 cbc 30 baa 2!) ebb 25 bab 16 aac 2fl eba 18 bac 27 cba 211 1 Q cac 15 1 Q cab IS bac ebb 17 16 1 Q cab 10 bac 1 Q ccb I'l 10 bac 14 aab l.-i bba 15 ebb l.s bba 14 bab 13 bbc 14 aaa 14 bbb 12 ebb 13 aab 14 cca 10 baa 13 ebb '.) ccb 12 aba 14 ccb 1(1 bee 12 ccb n bbc 10 aac 13 aba s cca 12 aac R cba s bab 13 ' abc .s aab 111 cab S bba 6 bbc 10 bab ■S abc ,s aba H bcc ,~, abc n bcc 7 ace ■S abb ,""► abc 4 bbb 6 aab 6 aac bca ") bbb 4 bcc 6 cba 5 bab I'l bcb 4 ace 3 ccb 6 ace 4 aba 5 acb 3 aca 2 abb 4 bba 4 bba 5 bbc 3 acb 2 bcb 4 bbb 3 abb 4 bcc 3 aba 1 cca 4 abb 2 bbb 4 cca 3 abb 1 ace 2 bea 2 acb abc 2 bca 1 acb 1 aca 1 bca 2 aca 2 beb (t bca 1 acb 1 bcb 1 ace i ■ cca aca (1 bcb 1 aca Total, 4S6 Total, 466 Total, 443 Total, 440 Total, 464 Seventh X Grade Physiol ogy Physiography Biol 'ogy Physics Ccmi^ !tru 3 Q AAA 60 AAA 40 AAA 33 CCC 20 CBC 35 3 Q CAA 25 3 Q BAA 26 3 Q CAA 27 3 Q CAA 31 CAA 3.3 J[ BAA CAC •-,- AAB 10 CAC 10 CAB 25 BAA is CAA 19 AAA IS JI CAC 2] bab 17 31 AAC 15 CBC 17 AAC 15 cba 10 JI CAC 15 JI CBB 15 ecc IS ea e s cbc 14 baa 12 1 Q aab 7 CCC 13 cab 11 baa 14 bbe 11 cab 11 ebb 11 cbc 11 1 Q ebb 11 lah 7 bab 10 ccc 11 cab aba 1 Q bac 10 aac 9 bac S bac !) CCC 1 Q bab S 1 Q bab 7 aaa 7 bbc ,", ebb n abc 5 bac 4 eba 7 bbb s bbc 7 bab 5 ebb 4 bbb 1', bbc s aab (i bcc 4 cbc 4 bbc ('■ bac 7 bab i; eba 4 bba 3 abc ."i eba 7 bba 5 ceb 4 bbb bee ,-, bee 6 eba .", aab abb 2 aab 4 abb 4 bcc 4 aac :'. aca 2 cca 4 abc 4 ccb 4 beb bcb 2 bba 2 bba 3 abc 3 aba 2 abc ceb 2 ceb 2 cca 3 abb 2 ace aba i aba 1 abb 2 cca 2 bea aca 1 acb 1 ace 2 aca 1 bcc ace 1 bca 1 bbb 2 acb cca bca 1 aca II acb 1 ace II ccb abb II ace bca 1 bba II aac acb beb bcb 1 bbb II acb II beb cca aca u bca II Total, 214 Total. 235 Total, 231 Total, 224 Total, ■2\s 76 Science for the Grades Eighth Geadb Physiology Physiography Biology Physics Chemistry Q AAA 135 AAA 72 AAA 81 AAA 71 CAA 58 3 Q 1 CAA 47 3 Q BAA 50 3 Q CAA 39 3 Q CAC 51 M BAA 69 CAC 45 CAA 47 CAC 30 CBC 37 caa 30 M BAA 37 M CAC 24 BAA 29 BAA 28 aab 18 M BAC 28 M AAA 23 bab 16 cbc 23 aac 18 1 Q bac 12 cab 23 cbc 17 cab 24 cab 2" aab 22 cab 16 cbc 23 bac 18 cba 12 bac 21 bab 15 aac 21 cec 18 cab 10 1 Q ccc 16 1 Q aab 14 1 Q ccc 16 aac 17 aac 8 1 Q bbc 16 bba 8 aac 15 bac 12 bbc 12 cac 8 cba 14 ccc 12 ebb 11 ebb 12 ccc 8 bab 11 aba 10 aab 9 bab 10 bbb 7 ebb 9 cba 7 bba S aab 9 cbc 7 bbb 7 abb 6 bab 7 bee 9 ccb 7 bba 6 abc 6 cba 6 cba 8 aba 4 ccb 6 bbc 6 ccb 6 abb 6 cca 3 aba 4 ebb 6 abc 5 bba 6 bbc 2 bbc 4 bba 5 aba 4 bbb 6 bcc 2 bcb 2 bbb 4 abb 4 abc 5 ebb 2 cca 2 cca 4 bca 4 acb 5 abb 1 abc 1 ccb 3 bcc 4 ccb 4 aca 1 ace 1 bcb 2 bbb 3 aba 3 acb 1 bcc 1 aea 1 cca 3 cca 3 cca 1 abb acb 1 ace 2 aec 2 bcb 1 aca aec 1 acb 1 bca 1 abc acb bcc 1 aca aca ace bea bca bcb bcb Total, 373 Total, 391 Total, 369 Total, 370 Total, 377 There are three principal points to observe in each of these distributions. 1. The amount of concentration of marks under a few com- binations — a condition indicated by the height of the upper quartile and median. The ranks of the combinations below the median are not of much significance. 2. The predominance of A's, B's, or C's in the combinations above the median, and their occurrence in connection with the questions on previous knowledge, direct assimilation, or power of application. 3. The rank of the perfect mark (AAA) and of complete failure (CCC). Rank of the 27 combinations in the Fifth Grade. The concentration above the median is extreme, 51.3% of the answers (658 out of 1,239) being grouped in 14.1% (19 out of 135) of the combinations. In Chemistry, two combinations, and in Physics, three combinations, contain over half the an- swers. The C's overwhelmingly predominate in the marks for previous knowledge and for ability to apply, while A's have a slight lead in direct assimilation. Total failure (CCC) leads in all sciences, and CBC, which is obviously only one step higher than total failure, ranks second except in Physiology. The Analysis of Complete Reaction 77 children of this grade who are above the average intelligence are barely numerous enough to bring the perfect combination (AAA) above the median, its rank being fourth or fifth, except in Physics and Chemistry, where its rank is 8.5 and 20.5, re- spectively. These subjects are in no sense suitable for fifth- grade instruction. It appears that the extremely poor reaction of fifth-grade children to the presentation of characteristic topics of science is largely due to a lack of previous experience which might be utilized as an apperceptive basis. Rank of the 27 comMnations in the Sixth R Grade. The concentration above the median is great, 52.1% (1,079 out of 2,072) of the answers being grouped under 17.8% of the combinations. The principal congestion is again in Chemistry and Physics. Questions on previous knowledge receive prac- tically nothing but C's, while the A's have considerably in- creased their lead in direct assimilation, and are much more highly ranked, but do not predominate, in the power of applica- tion. The B's above the median are surprisingly few. Total failure (CCC) ranks highest, except in Biology, where it has given place to two better combinations. OBC has a prominent rank, either first or second, except in Physiology. Perfect re- sponse (AAA) has advanced its rank in all sciences — has al- most reached the median in Physics (rank 5), but is still far away in Chemistry (rank 16.5). The improvement over the fifth grade is decided. In Physi- ology the very slight excess which CCC has over CAA and AAA indicates that perfection has practically caught up with failure. In Physiography and Biology the good combinations are not far behind the poor ones. In Physics and Chemistry the failures still greatly predominate. Children of the Sixth R Grade give satisfactory response only to Physiology-Hygiene and Physiography, except as to their previous knowledge, in which they are still deficient. The other sciences cannot be considered suitable for instruction in this grade. Rank of the 21 combinations in the Sixth X Grade. The concentration above the median is still great 52.9% of the answers (636 out of 1,201) being grouped under 16.3% of the combinations. Previous knowledge still shows practically nothing but C's ; but the A's are greatly in excess in direct as- similation, and are almost equal to the C's in power of applica- tion. The B's are still very scarce. In these respects the Sixth X Grade is but little different from the Sixth R Grade, but a 78 Science for the Grades decided advantage appears in the sciences of Physiology-Hy- giene and Physiography, where perfection (AAA) has taken first place by a wide margin over failure (CCC) in the former and by a bare three answers in the latter science. In fact, Physiology-Hygiene shows three of the best possible combina- tions in the three highest ranks. Perfection has not yet ap- peared above the median in Physics or Chemistry; only the slightest improvement in the first rank of Chemistry is to be observed. The children of the Sixth X Grade, in the two sciences which seem to be most suitable for study (Physiology-Hygiene and Physiography), are slightly more proficient than the chil- dren of the Sixth R Grade. Their responses are otherwise very similar. Rank of the 27 comhinutiom^ in the Seventh R Grade. Concentration above the median is still high, 52.8% of the answers (1,219 out of 2,305) being included in 17.8% of the combinations. C's predominate in previous knowledge, but not to the extent that they do in the sixth grades. The A's are in large excess in direct assimilation, and have become equal to the C's in power of application. Practically no B's are included in the upper half of the marks. Biology joins the group of the sciences in which perfect marks (AAA) lead, and perfection (AAA) for the first time appears above the median in Physics. It is below the median only in Chemistry, ranking eleventh. In Physiology-Hygiene, complete failure (CCC) has fallen below the median for the first time in any science, and it is barely above the median in Physiography and Biology. The only three combinations above the median in Physiology are the best pos- sible ones, the whole upper 50% t>f the answers being concen- trated in them. Biology also contains the same best three com- binations, but the upper half of the answers is not confined to them. Rank of the 21 combinations in the Seventh X Grade. Concentration above the median is still high, 53.9% of the answers (605 out of 1,122) being grouped in 17.8% of the com- binations. Previous knowledge is very slightly better in Phys- ics, Biology, and Physiography than it was in the Seventh E Grade, and much better than in the sixth grades. The A's predominate in all stiences in direct assimilation, and are in plurality in the power of application in all sciences except Physics and Chemistry. The perfect group (AAA) leads in all sciences except Physics and Chemistry, and is absent from above the median in Chemistry only, ranking tenth. Absolute failure (CCC) has fallen below the median in all sciences except Phys- Analysis of Complete Reaction 79 ics, where it again ranks first by a very narrow margin of two answers over the quite acceptable combination CAA whicli holds second place. Again the B's are very scarce. Other con- ditions vary only slightly from the Seventh K Grade. Children of the seventh grades give satisfactory responses in all sciences except Chemistry, although Physics still pre- sents serious difBculties. In Physiography, Biologj', and Phys- ics the good showing is made in spite of the small amount of previous knowledge, which is but little, if any, greater than that possessed by children of the sixth grades. The ability to make applications has con.siderably increased in the Seventh Grade. Sank of the 27 coiiihiiiatioHS in the Eifjhth Grade. There is extreme concentration above the median, the great- est found in any grade, TuM'/r of the answers (1,077 out of 1,880), being included in only 11.8% of the combinations. For the first time the predominance of C"s in previous knowledge is not excessive. In direct assimilation the groups are exclusively A's, except for one B in Chemistry, The C's are completely eliminated. There, are twice as many A's in power of applica tion as there are C's, with no B's. Perfection (AAA) leads in all sciences except Chemistry, but is found above the median for the first time in that subject. Failure (CCC) has completely disappeared from the upper 50%, ranking 7.5 in Chemistry and about 10 in the other groups. BAA, an almost perfect combination, and CAA, but little less so, rank high in all sciences. In Physiology the response is almost iDerfect, with only the two best combinations above the median. Children of the Eighth Grade give satisfactory reactions to all sciences except Chemistry. The children have not yet ac- quired, however, or have been unable to classify, the amount of previous experience which would seem desirable for best re- sults in learning a science; but the condition is far better in the eighth grade than in any previous one. Characteristics of the sciences ahovc the median ; Physi- ology. The reaction to Physiology-Hygiene is good except in the fifth grade. Perfection (AAA) is always included as one of the combinations above the median, and leads in rank from the Sixth X Grade up, the excess being yvy marked in the seventh and eighth grades. Failure (CCC) leads strongly in the fifth grade, has a plurality of only one answer in the Sixth E Grade, is displaced in the Sixth X Grade, and disappears from the upper 50% in the seventh and eighth grades. 80 Science for the Grades Previous knowledge is fair only in the seventh and eighth grades. Direct assimilation and power of application rank perfect above the median in the seventh and eighth grades and almost perfect in the fifth and sixth grades. Physiology-Hy- giene is obviously the most suitable of any science for instruc- tion in the grades. Characteristics of the sciences above the median: Phys- iography. The response in Physiography becomes good in the Sixth X Grade, only the presence of a rather large group of failures (CCC) lowering the suitability. In the Sixth E Grade the condition is not quite so good, as the failures (CCO) outrank the perfect marks (AAA). With the elimination of the fail- ures from above the median in the seventh grades, the reaction becomes excellent. Characteristics of the sciences above the median: Biology. This subject in the fifth and sixth grades is less satisfac- tory than Physiography. The upper 50% of the answers are distributed over more different combinations, and there is a lower rank for perfection (AAA) and other more satisfactory combinations. These differences practically disappear in the seventh and eighth grades, in which perfection takes first rank, the science being obviously suitable as a source of topics for instruction in these grades. Characteristics of the sciences above the median: Physics. In Physics even a fair reaction cannot be claimed until the seventh grade, when perfection (AAA) becomes one of the groups above the median; but the high per cent of failures (CCC) neutralizes a large part of this good influence. The A's are plentiful in direct assimilation, however. In the eighth grade the general condition is good, the O's having been prac- tically eliminated from the direct assimilation and power of application groups. The topics of Physics seem, therefore, to be appropriate for instruction in the eighth grade. Characteristics of the sciences above the median: Chem- istry. The reaction to Chemistry is poor in every grade. It can hardly be called fair even in the eighth grade, where perfec- tion (AAA) first receives a rank higher than tenth. Of the 1,026 test papers in the groups above the median, answers in previous knowledge receive only 23 A's and 28 B's. The C's are three times as numerous as the A's in the power of applica- tion. The low rank .of the better combinations rather dis- courages the inclusion of chemical topics for instruction in any grade. OHAPTEK XII. RANK AND SCATTER OF THE TWENTY-SEVEN COMBINATIONS. It is instructive to know, in the case of any one of the triple mark combinations, how uniform its rank has been in the different grades in one science or in the different sciences in one grade. For example, CCC ranks first in all sciences of the fifth grade, but its relative rank is tenth in the eighth grade. AAA ranks highest in Physiology, Physiography, and Biology, but occupies the fourteenth place in Chemistry. The marked concentration of the answers under the head of certain combinations leaves other combinations with few, if any, answers. What these combinations are, and whether they are the same in different grades and different sciences, must be determined if the cause and significance of this uneven dis- tribution is to be studied. If the ranks of a combination as it occurs in one science throughout all grades is averaged, a typical measure of the im- portance of that combination in the particular science is ob- tained. The average rank of a combination as it occurs in one grade, but including each science, is also a typical measure of the importance of that combination in the particular grade. The average is chosen rather than the median, because of the small number of cases— six and five, respectively, in each sci- ence and grade — and the possible range of 27 units in rank. The data of these ranks are recorded in Table XVII. When orders of rank are assigned in this manner for each combination, either from average or median figures, it is im- portant to know whether the position is a result of the com- bination occurring uniformly in that rank (as where CCC ranks first in all sciences in the fifth grade), or whether it is merely the position determined by calculation from varying ranks (as where AAA in the Sixth X Grade occupies the fifth position, with an average rank of 6.4, which has been calculated from two first ranks, one fourth, one fifth, and one twenty-first rank in the five sciences). The dispersion of the ranks from which the average is calculated is of value as an auxiliary to this definite average. The story of the man who was drowned while crossing a stream with a.n.average depth of two feet is a simple illustration of the point. Ordinary measures of dispersion do not appropriately apply here because of the small number of cases — five sciences, six grades. Extreme range only shows two of the number; and if 82 Science for the Grades these ranks were 1 and 27, respectively, no hint of the location of the other three or four ranks would be disclosed. It is use- less to calculate a quartile deviation from only five or six cases ; the median deviation, the standard deviation, and the average deviation are of doubtful value for the same reason. The formula 100 -Sid) -ysTdT = % of Scattering (n-1)^ has been derived, in which d represents the differences in the successive ranks when in rank order. The steps in the deriva- tion of this formula are as follows : 1. In two or more series where the sum of the differences of the ranks in order is the same, but the size of these individual differences is unequal and the scattering obviously not the same, if the differences are squared, added, and the square root extracted, the inequality is brought out. Example : Series 1, 3, 5, 7, 9; differences, 2, 2, 2, 2; Sd = 8; yS(d') = 4. Series 1, 2, 3, 6, 9; differences, 1, 1, 3, 3; Sd = 8; yS(d^) = 4.47 Larger gaps in the ranks indicate a higher scatter, and the value yS(d') varies in direct proportion to the size of these gaps. 2. Obviously the series 5, 6, 7, 8, 9, in which S(d) ^4, has less scatter than the series 1, 7, 14, 20, 27, in which S (d) =26. The larger sum of the differences represents a larger scatter ; therefore the quantity S (d) is a direct measure of the propor- tion of scattering. These two values, S(d) •y(Sd") represent a rectangle which, when plotted, would have as one dimension the side of the square which would contain the sum of the areas of the squared differences, and as the other dimension the total range of the ranks. This area is a measure of the actual extent of scatter- ing. 3. This area may now be compared with the total possible area of scattering, so that the scatter of any given set of ranks may be recorded as a proportion (fraction) or as a per cent. With 27 ranks, the largest possible sum of differences is 26, or n — 1, where n = the number of ranks. The area which would represent this scatter is (n — 1)'', and is the largest possible rectangle which could be constructed by any application of these differences. The ratio wliich the dispersal of any certain case bears to the largest possible scattering is the quantity Sfd) -ViM) [n-iy The Twenty-Seven Combinations 83 i. To convert this ratio into per cent, multiply the numera- tor by 100. The formula, therefore, becomes 100-S(d)-yS(d') = Per Cent of Scattering of Eanks. (n-1)^ In a given set of tables with the same number of ranks the 100 quantity is a constant. With 27 ranks, 100/676 = (n-r) .146. For 25 ranks the constant is .174; for 20 ranks, .277; etc. Graphic Proof of the Formula 1. Given a series, such as 5, 5, 5, 5, 5, with no scattering. S(d) is zero; therefore the formula gives a zero per cent of scatter. 2. Given a series 1, 1, 27, 27, 27, where the ranks would have the greatest possible scatter from the average as calculated. 100X26X26 Substituting, = 100% Scatter. 676 3. Given a series of ranks 1, 7.5, 14, 20.5, 27, in which the extreme range of 26 ranks has been divided into four equal parts — i. e., four equal steps of 6.5. It is obvious that this dis- persal is symmetrical to the average, which is 14, and is the exact median scatter for five ranks in 27 cases. Plotting the rectangle for the scattering to scale will indicate the actual area of scattering; another rectangle may indicate the largest possible area of scatter with 27 ranks. If these areas be super- imposed, the ratio of rectangle 1 to rectangle 2 is 50%. This value is also given by calculation from the formula. The per cent of scatter from the average has been calculated for the ranks of each combination in the separate grades, all sciences included, and for each combination in the separate sciences, all grades included. The values are recorded in Table XVII. In connection with either the median or the average, the per cent of scatter gives a measure of the degree to which the cen- tral tendency is truly representative. The per cent may be used where the number of cases is too small to permit the use of the customary measures of deviation. Even in a large num- ber of cases the per cent of scatter may in certain instances be 84 Science for the Grades more instructive than these measures, since it presents a ratio rather than an absolute quantity — that is, it measures the amount of scattering in comparison with the largest possible scatter, rather than merely computing a value for it, which value is either an average or a median itself, and subject to all inaccuracies and disadvantages of these central tendencies. The gaps, whether located near the extremes or close to the central tendency, are measured with perfect equality, which is not true of any of the other measures of deviation, the average deviation being unduly influenced by the cases near the ex- treme range, and the median deviation and the quartile range ignoring them. TABL E XVII. Rank and Scatter OF THE Twenty-Seven Combinations. Fifth Grade ,Q (}n,e> 1/1 f* p. Average Pt Combi- Phys- Phys- fcj \JV%J tvv \f^ sr Ct. of nation iology iography Biology Physics Chemistry Bank Dispersal CCC 1 1 1 1 1 1. CBC 8.5 2 2 2 2 3.3 5.33 CBB 2 7 3 5 4 4.2 1.96 CAC 8.5 3 6 3 3 4.7 3.18 CAA 4 5 4 6 5 4.8 .42 AAA 5 4 4 8.5 20.5 8.5 30.64 CCB 6 17 7.5 12.5 7.5 10.1 11.21 BCC 14.5 17 9.5 4 10.5 11.1 14.07 BBA 17 25 9.5 16 14.5 11.9 22.03 AAC 17 6 14 8.5 14.5 12. 11.10 CBA 7 8.5 14 23 9 12.3 24.66 BAA 3 13 14 12.5 20.5 12.6 29.94 CAB 11.5 22 7.5 16 6 12.8 20.43 BAC 13 8.5 20 12.5 10.5 12.9 12.84 BBC 21 10.5 17.5 12.5 7.5 13.8 14.16 CCA 21 13 22.5 8.5 14.5 15.9 16.95 BBB 11.5 10.5 25 25.5 14.5 17.4 27.33 BCB 24 20 14 8.5 20.5 17.4 20.38 AAB 14.5 17 14 23 20.5 17.9 6.97 BAB 10 17 20 19.5 25.5 18.4 19.91 ABC 24 13 20 23 14.5 18.9 10.61 ABA ACC BCA 17 17 25 16 20.5 19.1 7.71 24 22 17.5 19.5 20.5 20.7 3.19 21 25 25 19.5 14.5 21. 10.22 ABB ACA 19 26.5 22 27 14 27 25.5 19.5 25.5 25.5 21.5 25.1 10.67 6.75 ACB 26.5 25 22.5 27 25.5 25.3 1.85 The Twenty-Seven Cambinations 85 Sixth R Geade W /^ ^^j^P Average Comftt- Phys- Phys- fj %j frt tv\j\/^ t Per Ct. 0) nation iology iography Biology Physics Chemistry Rank Dispersal CCC 1 1 2.5 1 1 1.2 .33 CBC 8 2 1 2 2 3. 6.30 CAC 8 3 2.5 3 3 3.9 4.09 CAA 2 5 8 4 4 4.6 3.32 CAB 5.5 7 5.5 6 7 6.2 .25 AAA 3 4 4 5 16.5 6.5 23.12 BAA 4 6 5.5 10 10 7.1 3.82 CBB 5.5 17.5 10 7.5 5 9.1 15.11 CBA 10 15 7 12 8 10.4 4.91 BBC 11.5 17.5 17 7.5 6 11.9 11.88 BAC 15 8 12 13.5 12 12.1 4.74 CCB 15 11.5 15 11 9 12.3 3.60 AAC 21 9 12 9 14.5 13.1 11.91 BAB 8 13.5 12 18.5 19 14.2 10.74 BBB 13 10 14 13.5 21.5 14.4 13.79 BBA 11.5 11.5 16 23 19 16.2 11.44 AAB 15 16 9 18.5 23.5 16.4 19.02 BCC 26.5 13.5 18 18.5 13 17.9 18.39 CCA 19.5 23 20 18.5 14.5 19.1 6.59 ABC 22 20 23.5 15 11 19.3 12.71 ABA 19.5 20 20 21.5 16.5 19.5 2.51 ACC 23 23 26 16 19 21.4 8.62 ABB 17.5 23 20 27 21.5 21.8 7.27 BCB 17.5 25 22 24.5 23.5 22.5 5.40 ACA 24.5 20 23.5 24.5 26 24.5 3.26 BCA 24.5 27 26 21.5 26 25. 2.73 ACB 26.5 26 26 26 26 26.1 .04 Sixth X Gkadb fl' /iS ain nc Average Comtt- Phys- Phys- — O Lilfilltj C Per Ct. oi nation iology iography Biology . Physics Chemistry Rank Dispersal CCC 4 2 2 1 2 2.2 .99 CBC 5.5 3 1 2 1 2.5 1.91 CAA 2 4 3 4 5 3.6 .77 CAC 8 5 5 3 3.5 4.9 2.51 AAA 1 1 4 5 21 6.4 50.95 CAB 9.5 9.5 8 9 3.5 7.9 4.92 CBB 5.5 15 8 6 6 8.1 10.25 BAA 3 7.5 10 9 17 9.3 17.63 CBA 9.5 15 6 11.5 7.5 9.9 6.31 AAC 10.5 7.5 17 7 21 10.6 21.02 CCB IS 9.5 14.5 14 9 12. 3.02 BAB 7 12 11 11 17 12.2 8.10 AAB 11 11 8 20.5 13 12.7 13.98 BBC 17.5 15 17 11.5 7.5 13.7 8.43 BAC 17.5 6 14.5 18 13 13.8 13.81 BBB 13 19 12.5 18 21 16.7 6.91 CCA 17.5 19 12.5 22 13 16.8 7.80 BBA 13 15 22 9 26 17. 22.91 ABC 20.5 19 24.5 14 10 17.4 15.04 BCC 17.5 26 17 14 13 17.5 18.47 ACC 22.5 26 19.5 20.5 13 20.3 13.53 ABA 15 26 19.5 25 21 21.3 10.23 BCB 22.5 22.5 22 27 21.5 21.8 7.27 ABB 25.5 24 24.5 18 24 23.2 6.77 ACB 25.5 22.5 22 25 21 23.2 1.85 BCA 25.5 15.5 26.5 22.5 26 23.2 13.58 ACA 25.5 19 26.5 27 26 24.8 7.25 86 Science for the Grades Seventhh E Grade Combi- Phys- Phys- —Science — Average Per Ct. of nation iology iography Biology Physics Chemistry Bank Dispersal CAA 2 3 2.5 ■5 3 3.1 .94 AAA 1 1 1 3 11 3.4 12.20 CAC 9 2 4 1 2 3.6 6.48 CBC 5 4 7 4 1 4.2 3.32 CCC 4 5 6 2 4 4.2 1.45 BAA 3 6 2.5 7 12 6.1 8.34 BAC 10.5 7 9 8 9 8.7 1.07 CAB 15.5 9 5 9 5 ,8.7 11.85 CBB 13.5 11.5 10 10 7 10.4 3.75 CBA 6 15 8 19 8 11.2 15.97 AAB 7 10 12.5 18 15 12.5 8.98 AAC 15.5 8 14.5 6 18.5 12.5 13.89 BAB 8 . 11.5 14.5 15 18.5 13.5 9.02 CCB 13.5 13 19 12.5 10 13.6 8.10 BBC 22 14 16 11 6 13.3 20.36 BBA 10.5 16 11 20.5 20.5 15.7 9.53 BCC 22 17 19 17 13.5 17.7 6.32 ABA 17 24 12.5 15 20.5 17.8 10.02 ABC 25.5 18.5 17 15 16.5 18.5 11.39 BBB 12 18.5 19 22 22.5 18.8 11.18 CCA 22 26.5 22 12.5 13.5 19.3 19.99 ACC 27 20 24 20.5 16.5 21.6 9.02 ABB 18.5 24 22 23.5 22.5 22.1 3.82 BCA 18.5 24 25.5 23.5 25 23.3 5.33 ACB 22 21.5 25.5 26 24 23.8 1.95 BCB 20 26.5 22 26 26 24.1 4.33 ACA 25.5 21.5 27 Seventh 26 X Gkadb 27 25.4 4.11 Comti- Phys- Phys- O Vl/fjilW Average Per Ct. of nation iology iography Biology Physics Chemistry Bank Dispersal CCA 2 2 3.5 2 2 2.3 .33 AAA 1 1 1 4 10 3.4 8.93 BAA 3 4 2 7 6 3.8 1.96 CCC 9.5 7 8 1 . 5 6.1 6.06 CAC 6 3 6 3 4 6.4 .99 CBC 13 6 5 8 1 6.6 12.04 SAB 7.5 8 8 9 3 " 7.1 4.12 CBB 13 11 8 . 5.5 7.5 9. 4.61 BAB 4 9.5 12 13.5 11.5 10.1 8.52 BBC 11 13.5 12 11.5 7.5 11.1 3.82 BAC 13 9.5 14.5 10 9 11.2 2.79 AAB 7.5 17.5 3.5 13.5 17 11.8 16.60 AAC 16.5 5 10 5.5 17 11.8 40.20 CBA 5 12 14.5 15.5 14 12.2 11.44 ABA 9.5 22 22 11.5 20 17. 16.57 BCC 22.5 15.5 16 17.5 14 17.1 6.80 ABC 22.5 15.5 17.5 19.5 11.5 17.3 9.35 BBB 15.5 13.5 12 23 25 17.8 15.68 CCB 22.0 19.5 20 17.5 14 18.7 6.00 BBA 15.5 19.5 19 15.5 25 18.9 9.19 ABB 18 26 17.5 21.5 20 20.6 4.21 CCA 22.5 17.5 25 19.5 20 20.9 4.54 BCB 18 26 25 25 17 22.2 9.51 ACA 18 22 25 27 22 22.8 7.17 ACC 22.5 22 25 21 25 23.2 1.34 BCA 22.5 22 22 25 25 23.3 1.13 ACB 26.5 26 22 25 25 24.9 2.13 The Twenty-Seven ComMnations 87 Eighth Geade IS^a^y,^ Combi- Phys- Phys- ll/V^ftUi Average Per Ct. of tuition iology iography Biology Physics i Chemistry Bank Dispersal AAA 1 1 1 1 5 1.8 2.37 CAA 3 2 3 2 1 2.2 .42 BAA 2 4 2 4 4 3.2 .59 CAC 10.5 3 4 3 2 4.5 8.36 CAB 8 6 7 6 6 6.6 .42 CBC 14 5 6 7 3 7. 12.07 BAC 6 8 10.5 5 7.5 7.6 2.54 AAC 10.5 10 5 8 9 8.5 2.73 AAB 4 7 9 12 13.5 9.1 6.92 CCC 10.5 9 10.5 9 7.5 9.3 .94 BAC 5 12 8 14 12 10.2 7.17 CBA 7 11 13 15.5 15 10.9 6.19 CBB 19 13 15.5 11 11 13.9 5.80 BBC 19 17.5 15.5 10 10 14.4 7.17 BBA 10.5 15.5 18 13 17 14.8 4.40 BBB 14 14 19.5 22. 5 17 17.4 6.19 CCB 14 15.5 21 15.5 21 17.4 5.88 ABA 16 17.5 12 19.5 22.5 17.5 8.69 BCC 19 22 24.5 19. 5 13.5 19.7 10.67 ABB 23 25.5 15.5 19. 5 17 20.1 7.69 ABC 26.5 22 15.5 17 19.5 20.1 9.63 CCA 17 19.5 19.5 22.5 22.5 20.2 3.18 BCB 23 19.5 22 26. 5 26.5 23.1 4.57 ACB 23 25.5 24.5 25 19.5 23.5 3.44 BCA 23 25.5 27 19.5 25 24. 4.80 ACC 26.5 22 24.5 24 24 24.2 1.51 ACA 23 25.5 24.3 26.5 26.5 25.2 1.07 Physics Per Comtir Qrades Average Cent of nation 5 6r ex 7r 73) 8 Rank Dispersal CCC 1 1 1 2 1 9 2.5 8.37 CAC 3 3 3 1 3 3 2.7 .59 CAA 6 4 4 5 2 2 3.8 1.45 CBC 2 2 2 4 8 7 4.2 3.32 AAA 8.5 5 5 3 4 1 4.4 4.74 AAC 8.5 9 7 6 5.5 8 7.4 .86 CBB 5 7.5 6 10 5.5 11 7.5 2.81 BAA 12-1 10 9 7 7 4 8.3 5.66 CAB 16 6 9 9 9 6 9.2 11.27 BBC 12.5 T.S- 11.5 11 11.5 10 10.7 2.16 BAC 12.5 13.5 18 8 10 5 11.2 12.24 CCB 12.5 11 14 12.5 17..^ 15.5 13.9 3.15 BCC 4 18.5 14 17 17.5 19.5 14.4 24.18 BAB 19.5 18.5 14 15 13.5 14 15.8 3.38 CBA 23 12 11.5 19 15.5 15.5 16.1 10.86 BBA 16 23 9 20.5 15.5 13 16.2 14.50 ABC 23 15 14 15 19.5 17 17.3 6.45 CCA 8.5 18.5 22.5 12.5 19.5 22.5 17.3 16.3* AAB 23 18.5 20.5 18 13.5 12 17.6 9.S3: ABA 16 21.5 25 15 11.5 19.5 18.1 12.90-' ACC 19.5 16 20.5 20.5 21.5 24 20.3 .J.3C-. BBB 25.5 13.5 18 22 23 22.5 20.8 11.64 BCA 19.5 21.5 22.5 2.3.5 25 19.5 21.9 2.34'- ABB 25.5 27 18 23.5 21.5 19.5 22.5 5.53: BCB 8.5 24.5 25 26 25 26.5 22.6 42.74 ACA 19.5 24.5 27 26 27 26.5 25.1 5.84 ACB 27 26 25 26 25 25 25.7 .42 88 Science for the Grades Biology Per Comil- nation Average Cent of Rank Dispersal 5 fir Gruaco fix 7r ItD 8 AAA 5 4 4 1 1 1 2.7 1.87 CBC 2 1 1 7 5 6 3.7 3.07 CAA 4 8 3 2.5 3.5 3 4. 3.33 CAC 6 2.5 5 4 6 4 4.6 1.07 CCC 1 2.5 2 6 8 10.5 5. 6.67 BAA 14 5.5 10 2.5 2 2 6. 11.98 CAB 7.5 5.5 8 5 8 7 6.8 .76 CBB 3 10 8 10 8 15.5 9.1 14.23 AAB 14 9 8 12.5 3.5 9 9.3 ■9.29 CBA 14 7 6 8 14.5 13 10.4 6.68 AAC 14 12 17 14.5 10.5 5 12.2 11.64 BAB 20 12 11 14.5 12 S 12.9 12.11 BAC 20 12 14.5 9 14.5 10.5 13.4 10.42 BBA 9.5 16 22 11 19 18 15.9 13.44 BBC 17.5 17 17 16 12 15.5 15.9 3.02 CCB 7.5 15 14.5 19 20 21 16.2 16.38 BBB 25 14 12.5 19 12 19.5 17. 14.64 BCC 9.5 18 17 19 16 24.5 17.3 19.28 ABA 25 20 19.5 12.5 22 12 18.5 12.86 ABB 14 20 24.5 22 17.5 15.5 18.9 7.45 ABC 20 23.5 24.5 17 17.5 15.5 19.7 6.24 CCA 22.5 20 12.5 22 25 19.5 20.3 14.30 BCB 14 22 22 22 25 .22 21.2 14.00 ACC 17.5 26 19.5 24 25 24.5 22.7 6.38 ACB 22.5 26 22 25.5 22 24.5 23.7 1.32 BCA 25 26 26.5 25.5 22 27 25.3 2.67 ACA 27 23.5 26.5 27 Chemistry 25 24.5 25.6 .96 Combi- Qytn^nn Average Per Cent of nation 5 fir 6x 7r 7® 8 Rank . Dispersal CBC 2 2 1 1 1 3 1.7 .42 CAC 3 3 3.5 2 4 2 2.9 .36 CAA 5 4 5 3 2 1 3.3 1.18 CCC 1 1 2 4 5 7.5 3.4 3.36 CAB 6 7 3.5 5 3 6 5.1 1.25 CBB 4 5 6 7 7.5 11 6.8 1.08 BBC 7.5 6 7.5 6 7.5 10 7.4 1.72 BAC 10.5 12 13 9 9 7.5 10.2 2.26 CBA 9 8.5 7.5 8 14 IS 10.3 5.74 BAA 20.5 10 17 12 6 4 11.6 19.12 CCB 7.5 9 9 10 14 21 11.8 16.50 BCC 10.5 13 13 13.5 14" 13.5 12.9 1.34 ABC 14.5 11 10 16.5 11.5 19.5 13.8 8.54 AAA 20.5 16.5 21 11 10 5 14.0 20.15 AAC 14.5 14.5 21 18.5 17 9 15.8 11.91 CCA 14.5 14.5 13 13 20 22.5 16.3 8.75 AAB 20.5 23.5 13 15 17 13.5 17.1 8.18 BAB 25.5 19 17 18.5 11.5 12 17.3 15.88 ACC 20.5 19 13 16.5 25 24 19.7 10.35 ABA 20.5 16.5 21 20.5 20 22.5 20.2 3.44 BBA 14.5 19 26 20 25 17 20.3 10.39 BBB 14.5 21.5 21 22.5 25 17 20.3 8.47 BCB 20.5 23 17 26 17 26.5 21.7 7.40 ABB 25.5 21.5 24 22.5 20 17 21.8 5.14 ACB 25.5 26 21 24 25 19.5 23.5 4.40 BCA 14.5 26 26 25 25 25 23.5 5.37 ACA 25.5 26 26 27 22 26.5 25.5 2.67 The Twenty-Seven ComMnations 89 Physiography Per Combi- Qrn^oo Average Cent of nation 5 er fix 1r 7x 8 Ranh 1 dispersal AAA 4 4 1 1 1 1 2. 1.33 CAC 3 3 5 2 3 3 3.2 .99 CAA 5 5 4 3 2 2 3.5 !77 CBC 2 2 3 4 6 5 3.7 1.18 CCC 1 1 2 5 7 9 4. 5.02 BAA 13 6 7.5 6 4 4 6.8 8.04 AAC 6 9 7.5 8 5 10 7.6 1.73 BAC 8.5 8 6 7 9.5 8 7.9 .70 CAB 22 7 9.5 9 8 6 10.3 29.89 CBB 7 17.3 . 15 11.5 11 13 12.5 9.35 BAB 17 13.3 12 11.5 9.5 12 12.6 5.42 CBA 8.3 13 15 15 12 11 12.8 3.88 AAB 17 16 11 10 17.5 7 13.1 10.66 BBB lO.u 10 19 18.3 13.5 14 14,3 7.29 CCB 17 11.5 9.3 13 19.5 13.5 14.3 6.08 BBC 10.5 17.5 13 14 13.5 17.5 14.7 4.21 BBA 23 11.5 15 16 19.5 15.5 17.1 14.88 ABC 13 20 19 18.5 15.5 22 18. 6.03 BCC 17 13.3 26 17 15.5 22 18.5 7.98 CCA 13 23. 19 26.5 17.5 19.5 19.8 13.73 ABA 17 20 26 24 22 17.5 21.1 5.73 ACA 27 20 19 21.5 22 23.5 22.3 5.02 ACC 22 23 26 20 22 22 22.5 3.32 BCA 25 27 15 24 22 25.5 23.1 13.46 BCB 20 25.3 22.5 26.5 26 19.5 23.2 4.26 ABB 22 23 24 24 26 25.5 24.1 1.23 ACB 25 26 22.3 21.5 26 25.5 24.4 1.83 Physiology {Jnmhi- Gl -„j«„ Average Per Cent ot V 1/ llbV L nation 5 er Sx 1r Ix 8 Ranh Dispersal AAA 5 3 1 1 1 1 2. 1.67 CAA 4 2 2 2 2 3 2.3 .42 BAA 3 4 3 3 3 2 3. .42 CCC 1 1 4 4 9.5 10.5 5. 8.91 BAB 10 8 7 8 4 5 7. 2.81 CBA 7 10 9.5 6 5 7 7.3 2.16 CAC 8.5 8 8 9 6 10.5 8.3 1.73 CBC 8.5 8 5.3 5 13 14 9. 7.04 CAB 11.5 5.5 9.5 13.3 7.5 8 9.5 7.32 AAB 14 15 11 7 7.5 4 9.8 9.13 CBB 2 5.5 5.5 13.5 13 19 9.8 25.02 BAC 13 15 17.5 10.5 13 6 12.3 10.31 BBA 17 11.5 13 10.5 15.5 10.5 13. 3.29 BBB 11.5 13 13 12 15.3 14 13.2 1.25 CCB 6 15 13 13.5 22.5 14 14. 25.20 ABA 17 19.5 15 17 9.5 16 16.7 9.18 BBC 21 11.5 17.5 22 11 19 17. 10.74 AAC 17 21 20.3 15 26.5 10.3 18.4 19.37 CCA 21 19.5 17.5 22 22.3 17 19.9 2.26 ABB 19 17.5 25.5 18.5 18 23 20.3 4.37 BCC 14.5 26.5 17.5 22 22.5 19 20.3 9.73 BCB 24 17.5 22.5 20 18 23 20.8 3.33 BCA 21 24 25.5 18.3 22.5 23 22.4 3.39 ABC 24 22 20.5 25.5 22.5 26.5 23.3 2.31 ACA 26.5 24.5 25.5 25.5 18 23 23.8 6.80 ACC 24 23 22.5 27 22.3 26.5 24.3 1.83 ACB 26.5 26.5 25.5 22 26.3 23 25. 1.79 The Concentration OF Answers IN Certain Combinations The twenty-seven combinations may be ranked in each grade according to the total number of answers received, disregard- ing the quota of the different sciences. They may also be ranked in each science according to the total number of answers 90 Science for the Grades received, disregarding the quota of the different grades. A glance at these totals as recorded in Table XVIII. shows the striking fact that certain combinations practically pre-empt the three highest and the three lowest ranks, indicating certain marjor tendencies in the general reactions of children toward different sciences in the different grades. Examination of the three highest ranks for each of the grades shows that only six different combinations occupy eigh- teen possible positions. These combinations, and the number of times each occurs, are as follows : AAA, 4 ; CAA, 3 ; GAG, 3 ; CBC, 3; CCC, 3; BAA, 2. It is apparent that the power of direct assimilation of subject-matter, represented by the middle letters of these combinations, is not characteristically pre- ceded by any appreciable amount of previous knowledge, the deficiency of which in these large groups of children is very striking. The power of application seems to appear suddenly as an acquirement of the larger groups of children in the seventh and eighth grades, this ability being lacking in the fifth and sixth grades. The combinations most rarely met with, occupying the three lowest ranks, are only four in number for eighteen posi- tions. Their distribution is as follows : ACA, 6 ; ACB, 5 ; BCA, 5 ; BOB, 2. These combinations are exclusively those in which failure in direct assimilations is accompanied by partial or complete success in the other two phases of the reaction — pre- vious knowledge and power of application. In other words, it is inconceivable that any appreciable number of children would possess the ability to reason further along a line of scientific explanation when the direct first premise was not understood. The results here tabulated thus confirm one of the best-known pedagogical principles — that reasoning cannot proceed from the unknown. It appears equally impossible that children should fail in direct assimilation, and at the same time possess a reasonable amount of previous knowledge of the topics which they were studying. The correctness of the tendencies shown in this part of the table needs no confirmative argument. In the sciences the fifteen positions in the three highest ranks are occupied by but six different combinations, distribut- ed as follows: AAA, 3; CAA, 3; GAG, 3; GCG, 3; GBG, 2; CAA,1. The general deficienecy in previous knowledge, indi- cated by the first letter of the combinations, is evident in all sciences. Ability in the power of application, indicated by the third letter of the combinations, is characteristic of these larger groups in certain sciences — Physiology, Physiography, Biology ; but the lack of this power is just as striking for Physics and The Ticenty-Beven Combinations 91 Chemistry. Ability in direct assimilation is decidedly promi- nent in the large groups of children in the same three sciences, and lacking in the same two as mentioned. It appears that the reaction of children to a science shows the first evidence of success in response to direct statements and questions, and that both previous knowledge and ability to apply are products of considerable experience. Facts apparent- ly understood from the plain statement of teacher or text are likely to remain isolated, in the mind of a child, and unaccom- panied by any previous knowledge or ability to reason in a dis- tressingly large number of cases. The combinations rarely met with— seven different combina- tions, occupying fifteen positions — are again those in which satisfactory previous knowledge and successful application would be accompanied by failure in direct assimilation. We would not expect a normal child to write such a paper, and the table shows that the children did not. This principle is true of any science, as it is of any grade. TABLE XVIII. DisTBiBtJiiON OP Answers, by Grades, in the Twentt-Sbven Combinations. All Sciences Included 5 Sr 6x 1r ■)Webb, H. A. : "A Preliminary Test in Chemistry," Journal of Educational' Psychology, Vol. X., No. 1, page 36 (January, 1919). The Underlying Type 10." similate facts — an abilitj- well illustrated by the well-known ease with which they master the language. Efforts to cause powers of reason and observation to function when by the laws of child psychology these powers are in a rudimentary stage of development will result in waste of energy on the part of both teacher and child. As the use of General Science spreads to the grades, it is hoped that both content and method -nill be built upon a firm foundation of educational principles determined by experi- ment. As in the great manufacturing industries of our country, the experimenting should be done in the laboratory, not in the factory. Tests on small, but adequate, groups of children should be relied upon more and more to determine the wisdom of our methods, with all the accuracy of the analytical chemist brought to bear on the problem. With the nation awake to the great waste of effort which some of our educational practices permit, and with an appreciation of the delicacy of the precious material which our teachers attempt to mold and fashion into the finished product as good citizens, each able to make a living and appreciate the necessary refinements of culture, a truly scientific spirit is demanded in education. The standard test, the survey, and other types of quantitative educational analy- sis, have of necessity been evolved. There never was a time when dogmatic statements based on mere opinion were less ap- propriate. It is hoped that this study has contributed in some degree to the sum of experimental knowledge in education. I wish to acknowledge my sincere indebtedness to Prof. •John J. Didcoct, Professor of Secondary Education, George Peabody College for Teachers, for helpful advice in planning this study and his kindly criticisms of the interpretations from the data obtained. I also have been encouraged by the atti- tude of Prof. Shelton -J. Phelps, Professor of School Admin- istration, George Peabody College for Teachers, who has ex- amined especially the statistical methods used. To other in- .structors in the institution, and especially to the gentlemen of the Seminar, I am grateful for suggestions, comments, criti- cisms, and encouragement.