The College - Chemistry Test in the Armed Forces ~nstitute THEODORE ASKOUNES ASHFORD Examinations Staff for the United States Armed Forces Institute and University of Chicago, Chicago, Illinois
INTRODUCTION
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ANY semce men and women are receiving trainin field of chemistry w ~ f i ein the Armed Forces, They may obtain their training of specialized which include inin the in chemistrv: in their subseciuent exneriences ...-..-.----correin connection with their duties: spondence courses through the unit& states- Armed Forces Institnte; by voluntary class instruction; or by independent study (1,2, 3, 4, 5, 6, 7). After leaving the services, a large number of veterans will want to resume their education in a college of their selection. Rather than give blanket credit for military experience as was done by many institutions in the last war, the United States Armed Forces Institute has adopted the point of view that the veterans' educational attainment can best be measured by comprehensive examinations. The examinations are prepared by the Examinations Staff for the Armed Forces Institute under the direction of Dr. Ralph W. Tyler, University Examiner and Chairman of the Department of Education of the University of Chicago. It is the plan of the Armed Forces Institute to measure whatever achievement may have been obtained by the veteran, that may be significant for his placement in the proper academic level (8, 9). I t should be emphasized, however, that in so doing the Armed Forces Institute does not assume the function of granting academic credit. It merely assumes responsibility to appraise as accurately and comprehensively as is practicable, the achievement of the veteran in any given field, and report it to the college. It then remains the prerogative as well as the responsibility of the veteran's chosen college to determine the extent to which .he has achieved the desired outcomes of the courses offered in the school, and then to place him a t the proper level. Proper placement might involve excusing the veteran from required courses (or parts of courses) in which he has demonstrated competence, or granting formal credit. ~
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THE FUNCTION O F THE TEST
Merely reporting the activities of the student in which he might have okained competence in chemistry is not likely to be meaningful to colleges. It becomes necessary, therefore, to write an examination which will make ~tpossible to report achievement in terms of the outcomes in the regu1ar given in The question may be raised whether it is not advisable to use one of the available standardized tests instead of writing a new test. The decision to write a new test was based largely upon the policy of the Armed Forces Institute to have a "secret" form not available to colleges. The policy was adopted in view of the fact that for many students performance on the test is the major, if not the sole criterion for obtaining credit, and hence the test should be kept out of circulation. On the other hand, it is desirable that the colleges be acquainted with what the test contains and what it attempts to measure. As a result of these considerations it was decided to construct two forms of the test, a military form to be kept secret by the Armed Forces Institute and a parallel civilian form to be available to colleges. One of the problems in constructing this examination is to define a typical or representative chemistry course upon which to base the test. There is no single "standard" course given in all the colleges. Courses in elementary chemistry vary widely from school to school, and even within the same school, for different programs. They vary in length from one semester to one year; in credit from two to ten semester hours; in difficulty, due to differences in scholastic ability; and finally in emphasis, some emphasizing general education, others practical technical training such as that found in engineering or agricultural programs, still others emphasizing the theoretical aspects of chemistry. Nevertheless, i t is confidently believed that there is a core material which is common to the majority if not to all the courses. By the proper selection of questions having a wide range of difficulty and testing a wide variety of situations, a fair measure of achievement in any &oursemay be obtained. Bv administer in^ the test to the various types of classes in various institutions, norms appropriate to each type of course may be derived. Moreover, any institution, by using the civilian form of the test on its own students, can establish local norms appropriate to the type or types of courses taught in that institution. 0
The subject test i n college chemistry i s designed to measure achimement in a n introductory college chemistry course. That such an examination is desirable is apparent from the fact that the training in chemistry in the Armed Forces is so varied that it does not correspond to the courses normally given in colleges.
PROCEDURE IN THE CONSTRUCTION OF THE TEST
The procedure followed in the construction of the test is the one commonly recommended by test experts and involves the following steps: 1. Formulation of the objectives which the student is expected t o attain in college chemistry. 2. Writing a large number of exercises designed t o measure these objectives. 3. Preparation of try-out forms of examination. 4. Administration of the try-out f o m s to groups of students in representative colleges. 5. Analysis of the results of the try-out. 6. Preparation of two final parallel forms on the basis of the results of the try-out. 7. Administration of the h a 1 forms in representative colleges, for the purpose of obtaining norms and tables of equivalence between the two forms.
~h~~~stepswill be discussed in some detail in order to make clear the nature of the test. FORMULATION O F OBJECTNES
The members of the Examinations Staff met with a number of experienced teachers of chemistry to determine what the student is expected to achieve in a "typical" course in college chemistry. The problem is essentially to deline as clearly as possible the "typical" among the better chemistry courses. A number of widely used textbooks were examined and the literature was consulted, particularly the articles written in recent years, dealmg directly with objectives of chemistry instruction (10, 11, 12, 13, 14, 15, 16). As was expected, the stated and implied objectives diiered somewhat both in nature and in the way in which they were stated. A digest of all sources, however, indicated a substantial agreement. Two types of objectives were iecognized; one expressed in terms of the subject matter of chemistry and the other expressed in terms of the abilities of the students which the courses were designed to develop. As a further aid in constructing the examinations these two types of objectives were considered as two different variables and were placed on a two-dimensional chart. Table 1 is an abbreviated form of the analysis of the objectives, which, after deliberation, was considered as representing a "typical" course. The catent objectives are along the horizontal axis and define the subject matter treated in elementary chemistry. They are a comprehensive list of the ideas of chemistry. For convenience these ideas have been grouped into five major areas, roughly corresponding to the chronological order in which they are presented in most courses. It is recognized, of course, that this grouping of content is in some respects arbitrary and that other mouaines are aossible. However, this grouping is sufficiently mean&ul to most teachers of chemistry to serve as a basis for the construction of the test. The behaerior objectives are expressed in terms of what the student is expected to be able to do with the material of chemistry. They may be considered as "ability" objectives or "levels of attainment" though a
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hierarchy is not necessarily implied by the latter phrase. WRITING EXERCISES
The next step in the construction of the examination for each subject Write a large number of matter area and a t each level of attainment. A few sample items, similar to those included in the test will illustrate this step and will give a clearer idea of the scope and nature of the test. The legend before each item indicates the classification of sample items with respect to both "behavior" and "content" objectives; thus the firstitem classified as 1-5. tests information (I) in area 5. I, ~
~ ~ ~ ~ ~ (a) Knowledge of important f a d s . 1-5. Which of the following wiU produce a combustible gas on reaction with cold water? A. Hydrogen chloride. B. Sodium oxide. C. Ethane. D. Calcium. E. Calcium carbonate. Knowledge of definitions of important terms. .1. Wbich of the followingbest defines the term "isotopes?' A. Elements having the same atomic weight but different atomic numbers. B. Elements having the same atomicnumber but different atomic weights. C. Elements in the same group of the periodic system but in different series fe. p.. Na and K). D. Elements with the same atomic weight hut different chemical properties. E . Elements existing in two crystalline forms, as graphite and diamond. Acquaintance with important concepts. '-1. Two hypothetical metals M and N have the same valence. What can he said about the two elements? A. If the hydroxide of M is a strong base, then the hydroxide of N must he a strong base. B. If the formula of the chloride of M is MCln, then the formula of the chloride of N is NCL. C. If M dissolves in HCI, then N must also dissolve in
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D. The per cent of chlorine in MC1, is the same as the per cent of chlorine in NCb. E. None of the above inferences about N may he drawn from what is known about M. ( d ) Vwbal understanding of princifilles and theories. 1 4 . Which of the following equals the number of electrons found in the orbits of a neutral atom? A. The number of neutrons. B. The atomic weight. C. The number of protons subtracted from the atomic weight. D. The number of electrons in the nucleus. E. The atomic number. ( 8 ) General knowledge of the physical and chemical properties of substances.
1-5. What isobtained when steam is passed over red-hot mb?
A. Hydrogen and carbon dioxide. 1%. Hydrogen and carlmn monoxalc C. Carbon monurirle and hydrogen pcrsnidr. D. Hydrogen and carbon. E. Carbon dioxide and carbon monoxide. 1-6. Which of the followine of reaction between - is a oroduct . copper and concentrated nitric acid? A. CuN03. B. NO.,
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111. Quantitative Application o j Principles.
D. N,. E. CuO. 11. Application of Principles. (a) Fundional understanding of principks and theories of chemistry and their inierrelationships. 11-2. Both NaNOa and KN08 are strong electrdytes. Which of the following best represents a solution containine both NaNOs and KNOB?
(a) Calculations involving gas laws. 111-1. A dry gas has a volume of 200 ml. a t 20°C. and 730 mm. of mercury. What is the volume of the gas a t standard conditions? 293 760 A. 2 0 0 X - X - . 273 730 273 730 B. 200 X X -. 293 760 273 760 C. 200 X - X 293 730 273 760 D. 200 X X-. 293 730 E. None of these.
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oxidation-reduction reaction: S- + CuS. A. Cu++ B. Cu++ 4NHa Cu(NH&++ C. Cu++ 20HCu(0HL. . .D. Cu s CuS. E. CuO HISO& CuSO( H1O. ( c ) A@plication of principles i n situations similar lo those mcountered i n e typical course. 11-3. The following system is in equilibrium a t a high temperature:
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+ + + + +
3H2
+
Na, Mg, Al, Zn, Fe, Ni, Pb, HZ, Cu, Ag,
Naf Mg++ Al+++ Zn++ Fe++ Nif+ Ph++ H+ cu++ Agf
On the basis of the electromotive series, which of t h e following pairs of suhstances may he expected to react? All solutions are of the same concentration. Capper and hydrochloric acid. Hvdroeen and metallic CoDDer. c&& and lead nitrate s&tion. Mercury and magnesium sulfate solution. Nickel and lead nitrate solution.
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A. B.
+ NZG 2NHa + heat
(All substances are gases.) What will he the result if the pressure on the system is increased? A. The amount of Ha and Nz will increase. B. The amount of NHs will increase. C. The amount of all three suhstances will increase. D. The reaction will go t o completion t o the right. E. No change will take place. ( d ) Application of principles in new situations taken from everyday life. 113. Although a heap of grain will burn very slowly, flour dust suspended in the air in a room may explode if ignited. Which of the following best explains this difference? A. Small particles give more energy than large particles on reacting. B. Small particles offer a great surface of contact with air. C. Greater circulation of air about the smaller particles distributes the heat more evenly. D. Small particles burn more completely than large particles. E. The heat of reaction of small particles is greater. (e) Interpretation of a set of data and drawing conclusionsfrom them. 11-2. Electromotive Series (Activity Series).
A. B. C. D. E.
(b) Calculation involving molecular and atomic weights. 111-1. Which of the following expressions gives the weight of a liter of chlorine, Cl., a t standard conditions? The atomic weight of chlorine is 35.5.
C. D.
E. (6)
35.5 22.4 71.0 22.4 35.5 X 22.4. 71 X 22.4. 71 X 22.4 760 X 273'
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Calculetion o j percentage composition.
111-1. .What is the per cent of oxygen in sodium carbonate, NasCOs? (Atomic weights, Na = 23; C = 12; 0 = 16.) 16 A. X 100. 51 16 B. - X 100. 106 48 C. - X 100. 106 48 D. - X 100. 130 E. None of these.
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(d) Stoichiometric calculations. . 111.1. Sodium nitrate on heating decomposes according t o the equation: iNaNOs
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2NaN01
+ Ot
(Atomic weiehts: Na = 23: N = 14: 0 = 16.) h a t weightof oxygen can be obtained on heating 8.5 grams of NaNOa? A. 1.6 grams. B. 1.6 X 22.4 grams C. 3.2 grams. 3.2 D. - grams. 22.4 E. None of these. (e) Skill i n balancing equations. 111-1. Balance the following equation for the reaction between copper and concentrated sulfuric acid. ( ) C u + ()H2SO4-()CuSO~+ 0S01-t OHSO When the equation is correctly balanced, what number appears before H2SOa? A. B. C. D.
1. 2. 3. 4.
E. None of these. The Scientific Method. (a) The relation between theory and expwimenl-expwimental evidence for a theory, and its exfilplenation of phenomem i n terms of thcorv. IV-2. Statement: Sodium chloride is a strong electrolyte. 1. What is the best ex- A. Sodiumchlorideisvery soluble in water. perimental evidence for this statement? 8 . Sodium chloride solu(A, B. C, D, E) tion is a good canduc2. What is the best theotor of electricity. retical explanation of C. A sodium chloride soluthis statement? tion freezes helow O0C. (A, B, C, D. E ) D. Sodium chloride is formed by electron transfer. E. Sodium chloride molecule contains free electrons. (b) Assumption necessary for e given onclusion. IV-2. A student analyzes an unknown liquid to determine whether i t contains sulfate, SO4-. He adds a clear barium chloride solution and obtains a white precipitate. He finds that the precipitate is insoluble in hydrochloric acid. The student concludes that the unknown contains a sulfate. This conclusion, however, may or may not be valid. I t is based not only upon the experimental results but also upon some assumptions, i. e., things taken for granted. Classify each of the following statements 1 to 6 by marking. A. If it is an assumption which must be made to make the conclusion valid. B. If it is an assumption that has no bearing on the . validity of the conclusion. C. If it is not an assumption because it is a statement of IV.
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A. B. C. D. E.
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fate. 4. Barium sulfate is the only barium salt which is insoluble in water and hydrochloric acid. 5. Barium sulfate is insoluble in water. 6. Barium chloride is the only barium salt that produces a precipitate with a sulfate. Considering the entire experiment, with which of the following conrlu4oni would you a p e ? ' . The unknown dtlinircly ront:ain, a sulfate B. The unknown probably coratuint a *ulfatr. hut thc evidence is iu&ffici&t t o make i t certain C. The unknown probably does not contain a sulfate though the evidence is insufficient t o exclude it. D. The unknown p h i t e l y does not contain a sulfate. (c) Determining whether a statement i s true because it i s e statement qf obserwtion, true i n the sense that it is a consequence of an accepted theory, or is true simply by definition. IV-3. "Heat is given off in all exothermic reactions." How would you characterize this statement? A. The statement is based upon observation of a typical exothermic reaction. B. The statement is based upon observation of a large number of exothermic reactions. C. The statement is true because it is in accord with the 9 kinetic molecular theory. D. The statement is true because it is in accord with the law of conservation of energy. E. The statement is true by definition. ( d ) Fadors which should be contro2lcd i n a n experiment. IV-2. I t is desired to study the effat oJ temperature on the rate a t which sodium chloride dissolves in water. The A series of determinations are procedure is t o add an excess of salt to a limited
amount of water and after stirring for some time t o evaporate a small sample and weigh the residue. Which of the followinn should he k e ~constant t durinn. any one determination? The extent to which sodium chloride dissolves. The solubility of sodium chloride in water. The temperature of the water. The average size of the crystals of sodium chloride. The amount of solid left undissolved.
TRY-OUT FORMS O F THE TEST A large number of exercises, similar to those given above, were written in all the areas listed under content objectives. Representative items were then taken so as to sample each of the subject matter areas and each of the four levels of attainment, and a try-out form was prepared. This test was administered to about 300 students who had completed a course in chemistry in representative collepes. The results were analyzed to determine the appropriateness of the test. he scores of the students were tabulated, to obtain a measure of the over-all difficultv of the test. Each auestion was further analyzed, to determine its difficulty and its discriminating power. The latter is obtained by comparing the performance of the students who did well in the test as a whole, to the performance of those who did poorly in the test as a whole. THE
USE OF THE CONSULTANTS
At this point, the aid of the consultants was sought. The consultants were chosen from among experienced teachers of college chemistry, who have also had experience in examination construction. Four consultants and three members of the staff of the Armed Forces Institute met in a conference, and examined each question using their judgment as teachers, and considering the statistical results of the analysis. Each item thus considered, was either retained, improved, or rejected. In addition, the judgment of the group was sought on the question of the validity of the objectives and the suitability of the examination as a whole. On the basis of the conference a revised try-out form was nrenared and submitted to the consultants for their suggestions and approval. One of the questions asked was whether the consultant, as a teacher, would be willing to recommend credit for a veteran in his own institution, on the basis of satisfactory performance in this test. All consultauts answered in the affirmative. About 40 other teachers who examined the test also answered this question in the affirmative. The revised try-out form was then administered t o about 400 students in representative colleges and the results were again analyzed. 1
THE FINAL FORM OF THE TEST
On the basis of the analysis of the second try-out form, two final forms, a military and a civilian, have been prepared. These forms are parallel, containing The paired items which are similar but not two forms will be administered in a number of representative colleges and in several types of C ~ S S ~for S
TABLE 1 Area I
I \ Behavior objeetiver
Concept of chemical change. element, compound; laws of chemicalcombination.kinetic molecular theory, gas laws, atomic theory; chemical symbolism. formula^, equations, and stoiddometric ca1culations
Solutions, ionizatiao 'ids, bases, salts, neualization, hydrolysis .tivity series, and
Oridation-reduetia eats of reaction, I
AIC~ 4
Arm 5
Atomic structure od chemical behavior, od the periodic syr!m
The chemistry of t h e ,ore commonelement3 od their compounds. he physical and them-
I. Ability t o recall importan, information Knowledge of importsnl facts Knowledre of definition ol important terms Acquaintance with impor. t a n t eoneeptr Verbal understanding ol theories and principles General knowledge of the physical properties and chemi. eal behavior of the more imoortant elements and their eompoundr 11. Ability t o apply princi01es i n makin.- sim01e oredietiona Funetionaluoderatandingoi t h e principles and theories of chemistry and their inter-
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situations similar to those en. countered in a typical course Application of principles in new 3ituationr taken from everyday life Interpretation of a set of data and drawing eooclusionl from them 111. Ability to apply principles quantitatively by earrying out calculation. Quantitative significance 01 chemical symbolism Balancing chemical equa. tions 1V. Ability t o use t h e seienti6" method. I t include. the following sweets of t h e scientific method: Distinction between observed phenomena and their theoretical explanation Explaining phenomena in terms of theor" Giving t h e erperimeota1 evidence for a theory Identifying t h e aesumption necessary for a niven eonclusion Identifying t h e factor tbaf must be controlled in sn ex. periment Identifying statement? which are true merely by definition
standardization purposes. From the standardization, it will be possible to establish norms and to prepare a table of equivalent scores for the two forms of the test. As previously mentioned the military form will be retained by the Armed Forces Institute to be given to service men prior to discharge from the armed forces. The other form, the civilian form, will be available to colleges and universities through the American Council on Education, 15 Amsterdam Ave., New' York 23, New York. Either form of the test contains 110 items and requires about two hours of testing time. The exercises
are multiple response items and can be answered on a separate answer sheet, which can be scored either by an electrical scoring machine or by hand. It is divided into four sections along the vertical axis of the objectives, namely Information, Application of Principles, Quantitative Application of Principles, and Scielitific Method. Each section can be scored separately so that an independent measure of each of the four "abilities" mentioned under "behavior objectives" may be obtained. Moreover, the test can be scored a second time so that separate scores for each of the five subject matter areas mentioned under "content ob-
jectives" may be obtained. In addition, of course, a total score may be obtained. INTERPRETATION AND USE OF THE O F VETERANS
TEST I N
PLACEMENT
As has been mentioned above, the decision of the placement of the veteran rests with the college which the veteran chooses. The Armed Forces Institute will report to the school for each veteran a total score and nine part-scores. Four part-scores will be independent measures of each of the "behavior objectives" and five part-scores will be independent measures of the five "content areas," listed above. In addition, the Armed Forces Institute will supply a set of norms for the total score and the part-scores, representing the over-all average of the liberal arts colleges in the country. At first, for purposes of economy the norms will be limited to liberal arts colleges giving a fd-year course. At a later time it might be possible to establish other sets of norms which would be more suitable for diierent types of institutions and different courses. Thus additional sets of norms for one-semester courses in liberal arts colleges, or for engineering schools may be established. With the aid of these norms, the admission officer or the instructor in a given school will be in a better position to appraisethe achievementof each veteran in terms of the educational objectives of the school. The use of the part-scores will be found particularly useful, for they can be considered separately and combined in such a way as to approximate the courses given in the school. For example, if in a given school "Application of Principles" is considered very important while "Information" is considered unimportant, then the former partscore can be given a proportionally greater weight and the latter a smaller weight or even be ignored altogether. Similarly, if the student performs satisfactorily on some of the areas (listed under content of objectives) and poorly on others, he may be advised to attend the local course in the parts in which he is weak and be excused from the parts in which he has done satisfactorily. While the norms supplied by the Armed Forces Institute will be found helpful, ideally, each school should establish its own norms. By using the form of the test which is available to colleges, and administering it to its own students, the school would be nble to place the veteran among its regular students with a minimum of maladjustment or injustice either to the veteran or to the school. It should be stressed, at this point, that much more important than the assigning of letter grades is the effective guidance and placement of individuals. Suppose, for example, that the report of the Armed Forces Institute shows that a returning service man on taking the subject test in college chemistry, has demonstrated a considerable knowledge of the facts of chemistry, but showed less ability to apply this information in solving chemical problems and an insufficient understanding of the scientific method. Although the college may be inclined to grant credit on the basis of the test results, effective guidance and placement of the individual will
necessitate consideration of various possibilities. The man may be enrolled in an advanced course and the instructor may plan supplementary remedial instruction in the areas of the deficiencies mentioned. Or, if a sufficient number of entering students exhibit the same general level of competence or pattern of abilities, the given individual may be enrolled in a special section formed for such students. Again, it may be decided that the regular advanced college course is already adapted to the needs of such students and that no special provisions are necessary. In any event, it would be well for a personnel officer of the college, in cooperation with the instructor of the college chemistry course, t o observe the progress of the student in order to make what further adjustments may prove necessary. TESTS I N OTHER COLLEGE CHEMISTRY COURSES
By the cooperation of the Committee on Examinations and Tests of the Division of Chemical Education of the American Chemical Society a complete battery of tests will soon be available to the Armed Forces Institute for testing service men. The Committee has nndertaken to construct tests in qualitative analysis, quantitative analysis, organic chemistry, and physical chemistry. Each of these tests will be about two hours long, but may be given in two 55-minute periods. As in the case of the test described in this paper, there will be a military and civilian form for each field. The civilian forms will be the regular tests constructed by the Committee, and will be available to teachers through the Cooperative Test Service, 15 Amsterdam Ave., New York 23, New York. The author wishes td express his indebtedness to the following, who served as consultants and in other capacities: Dr. Frank P. Martin of Purdue University, Dr. James Parsons of the Chicago City Colleges, Dr. Laurence S. Foster of Brown University, Dr. P. W. Selwood of Northwestern University, Dr. William Hered of Indiana University and the United States Armed Forces Institute, Dr. Ben Bloom of the Board of Examinations of the University of Chicago, Dr. Max Engelhart of the United States Armed Forces Institute, and Dr. Herbert Thelen of the United States Armed Forces Institute. LITERATURE CITED
(1) American Council on Education, Bulletins no. 24 and 36. Higher Education and National Defense, ACE: Washington. D. C. (2) Wmww, "The college training program of the Armed Forces," The Annals of the Am. Acad. of Pol. end Sac. Sci., 231, 58-64 (Jan., 1944). (3) BROWN,"Off-duty educational service in the Armed Forces," ibid., 47-52. (41 ~,BENBOW."Uni~ersitvof the Armed Forces." 3. Educational Soc., XVI, 9 ( ~ a y 1943). ; (5) ESPY, "Guidance in the Armed Forces Institute," Our Army, XVI, 1%20 (Feb., 1944). ( 6 ) Army Institute Catelog, Special Service Division, Services of S u ~ ~ l vWar . Deoartment. Washineton. D. C. Write to 'Lpmed Force; ~nstitute. ~ a d i % n ,Wisconsin, . for copies. (7) Institute Coursesfor United States NauelPersonnel. Address: Navy Registrar, Army Institute. Madison, Wisconsin.
(8) TnER. "Sound credit for military experience," The Annals of the Am. Acad. of Pol, and Sac. Sci.. 231, 5G64 (Jan., 1944). (9) AMERICANCOUNCILON EDUCATION. Sound Educational Credit for Mililory Experience, ACE: Washington, D. C. (1943). p. 35. (10) Symposium: "What are our objectives in teaching chemistry?" J. CHRM.EDUC.,2 , 9 7 1 4 7 (1925). "Objectives of the courses in general chemistry," (11) BRINKLEY, ibid.. 7,1869-75 (1930).
(12) BEADBURY, "What shall we teach in chemistry?" Sch. Sci. Math., 35, 36&73 (April, 1935). (13) SMITH, "Accepted objectives in the teaching of general chemistry,'' J . CHEM.EDUC.,12, l a 3 (1935). (14) SELWOOD, "The course in general chemistry," ibid.. 16,46671 (1939). (15) H ~ m n I c K s ,"The varied objectives in service courses in general chemistry." ibid., 19, 2 6 5 6 (1942). (16) HENDRICKS AND SMITH."Measurable objectives of college chemistry," Sch. Sci. Math., 36, 747-52 (1936).
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