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'" * / p dote t<Hr T"- HeIo^> EDUCATIONAL MEASUREMENTS THE MACMILLAN COMPANY NEW YORK • BOSTON - CHICAGO • DALLAS ATLANTA • SAN FRANCISCO MACMILLAN & CO., Limited LONDON • BOMBAY • CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, Ltd. TORONTO yyl^^fi^k;-'^-^ EDUCATIONAL MEASUREMENTS BY DANIEL STARCH, Ph.D. UNIVERSITY OF WISCONSIN AUTHOR OF "EXPERIMENTS IN EDUCATIONAL PSYCHOLOGY' THE MACMILLAN COMPANY 1916 All rights reserved Copyright, 1916, By the MACMILLAN COMPANY. Set up and electrotyped. Published July, 1916, Reprinted December, 1916. JforfajooD }3rt80 J. S. Cuahing Co. — Berwick & Smith Co. Norwood, Mass., U.S.A. 3o5\ ACKNOWLEDGMENT The author wishes to express his appreciation of the permission to reproduce the scales and tests developed by various investigators. Particular acknowledgijients are due to Professor E. L. Thorndike, Dr. L. P. Ayres, Professor S. A. Courtis, Professor F. J, Kelley, Dr. B. R. Buckingham, Dr. F. W. Ballou, Professor M. B. Hillegas, and Dr. H. O. Rugg. Acknowledgments are also due to the writer's colleagues, Chancellor E. C. Elliott, with whose collabora- tion the investigation of marks was carried out, and to Professor V. A. C. Henmon, who has made suggestions in the course of the development of the writer's tests. CONTENTS CHAPTER PAGE I. Introduction i II. Marks as Measures of School Work 3 III. A Sample Survey of the Marking System in a High School i6 IV. The Measurement of Ability in Reading .... 20 V. The Measurement of Ability in Writing .... 60 VI. The Measurement of Ability in Spelling .... 89 VII. The Measurement of Ability in Grammar . .101 VIII. The Measurement of Ability in Arithmetic . .114 IX. The Measurement of Ability in Composition . -132 X. The Measurement of Ability in Drawing . .163 XI. The Measurement of Ability in Latin 171 XII. The Measurement of Ability in German . -177 XIII. The Measurement of Ability in French . .183 XIV. The Measurement of Ability in Physics . .188 XV. The Use of Standard Tests in School Experiments . 193 BIBLIOGRAPHY I99 EDUCATIONAL MEASUREMENTS CHAPTER I INTRODUCTION It is undoubtedly premature to write a book on educational measurements, because most of the measurements are in the experi- mental stage. There are, however, several reasons which more than offset this situation. In the first place, the need of definite, objec- tive measures of educational products is so great and the usefulness of the present available standard tests has been so generally demon- strated that a means of making the tests and scales more widely accessible is entirely justifiable. Second, the very fact that many of the tests are in the experimental stage is a reason for making them more generally available, so that they may be rectified, improved and extended through broader cooperation of educators over the entire coimtry. Third, it is hoped that more general application of educational measurements mil create a deeper scientific interest in educational matters. The current movement for measuring school products is one of the three or four most important fields of investigation in the scien- tific study of educational problems. Very material progress has been made during the last half a dozen years in the endeavor to devise accurate methods for measuring the actual achievements of pupils in school studies, so that we now have fairly accurate tests and scales for measuring attainment in most of the elementary schools studies and in several high school subjects. It is unnecessary to point out the scientific and practical value of such investigations for all who are connected ^vith the schools — administrators, supervisors, teachers, pupils and students of edu- cational problems. These tests will furnish tools for evaluating quantitatively the results of methods and factors in teaching and 2 EDUCATIONAL MEASUREMENTS learning, and for examining various aspects of efficiency of instruc- tion and administration of school systems. It is unnecessary to make a defense of educational measurements in the presence of intelligent persons who have a genuine scientific interest in the education of mankind. There are those who say that the real results of education are too subtle and too evasive to be measurable by any sort of quantitative tests. The only reply to offer is that we are making such measurements all the time by the millions of school marks assigned every year and by all the com- parative judgments of human qualities as better or worse, as greater or less, as more useful or less useful, which we are so free to make not only in educational affairs but in all phases of human activity. The sole purpose of standardized measurements is to refine these judgments, to make them more accurate and objective, to express them in terms of known units of a. definable character, so that we may be able to say, for example, that a pupil can read three words per second of a certain passage and to report so and so much of it, that he knows the English meaning of 2000 Latin words and can translate without error sentences of specified difficulty. If there are any products or by-products of education which are too subtle to be distinguished or judged as existing in greater or less amounts, or as having higher or lower quality, we may be suspicious of their actual existence. Any quality or ability of human nature that is detectable is also measurable. It remains only to discover more and more accurate means of measurement. What we need more than anything else in teaching and in the administration of public schools is scientific method and caution in handling the problems confronted. Educators must instill into themselves the scientific point of view in looking at their problems. The old-time pedagogy is passing away quantitative studies, objec- ; tive measurements, and carefully observed facts are taking its place. The next great forward step in education will come when competent educators will use the schools as laboratories for legitimate experi- mentation conducted according to scientific procedure. CHAPTER II MARKS AS MEASURES OF SCHOOL WORK Marks are the universal measures of school work. Numerous and momentous problems in the operation of a school depend upon them, such as promotion, retardation, elimination, honors, eligibility for contests and societies, graduation, admission to higher institu- tions, recommendations for future positions and the lik^T^Until a decade ago, no one questioned either the validity or the fairness of these measurements. It was tacitly assumed that marks were al- most absolutely correct, or very nearly so, a fact attested by the surprisingly common practice of marking to the fractional part of a point even on a loo percentage basis. If we consider marks from a scientific viewpoint as a measur- ing scale, three fundamental questions arise: (i) How fine a scale of units may be used satisfactorily? (2) How reliable are the ratings made on the particular scale adopted? (3) How shall the marks be distributed? That is, How frequently in the long run shall each unit on the scale be assigned? The second problem will be taken up first. In order to show precisely the accuracy, or rather the inaccuracy, of marks, the following investigation will be cited. The Reliability of Marks The Reliability of Marks in the Case of English. The recent studies of grades have emphatically directed our attention to the wide variation and the utter absence of standards in the assign- ment of values. Dearborn pointed out in his investigation the large inequalities in the standards of grading employed by different teachers. Of two instructors in the same departinent one gave to 43 per cent of his students the grade of " excellent " and to none the grade of " failure," whereas the other gave to none of his stu- dents the grade of " excellent " and to 14 per cent the grade of " failure." : 4 EDUCATIONAL MEASUREMENTS Finkelstein made a comparison of the marks assigned to the students in a course which was in charge of one instructor during the first semester and in charge of another instructor during the second semester, the students remaining the same throughout the year. The distribution of the marks was as follows Exempt from ex- amina- 0-59 60-69 70-79 80-89 90-160 tion ist instructor 9.5 25.5 32.3 26.6 6.1 12.5 2d instructor 3.5 24.9 34.1 43.7 3.8 37.7 Such wide differences are no doubt due in part to a difference in the students and in the nature of the work, but largely to a differ- ence in the standards of marking. In order to determine precisely the personal equation in evalu- ating the work of pupils, it is necessary to eliminate all variable elements, such as difference in amount and kind of work covered by the class, emphasis upon different topics, differences in teaching ability and differences in the pupils themselves. An investigation was made to determine the range of variation and the reliability of the marks assigned by different teachers to the same papers. Two examination-answer papers, written by two pupils at the end of the first year's work in English, in high school, were reprinted by plates, so that the handwriting, the errors and changes made by the pupils, the neatness, etc., were reproduced exactly as in the original papers. These two papers were marked carefully by one hundred and forty-two teachers of first-year English according to the practices and standards of their respective schools. The grades assigned by the one hundred and forty-two teachers are represented by accompanying distribution charts. The range of marks is indicated along the base line of each chart and the num- ber of times each grade was given is indicated by the number of dots above that grade.

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