The results of our investigations into the elementary types of mathematical thinking are still tentative, but seem nevertheless to be fertile in suggestions for further work. At the present time it is more important for us to continue experimenting with the items we have gathered than to publish these items and thus put a stop to studies now in progress. However, we have an abundant store of certain types of items and a few of these will be reported here as illustrative of the method of studying error and item reliability. Certain details of the technique of evaluating specific questions or items will be explained here as this material readily lends itself to exposition.
Forms A and B of the scholastic aptitude test given in 1926 and 1927 contained a twenty problem arithmetic test (two) and a twenty-five problem test of the number completion type (six), both stock tests in various batteries of tests now used to measure 'intelligence.' Chapter II contains an exposition of the results of applying the tetrad difference technique to our various test collections, and the Annual Reports of 192711 and 192822 give fuller exposition of the 2-6 group factor.
In undertaking the construction of a mathematical test independently of the verbal test given in June 1928 and 1929, there were available the data from subtests two and six previously mentioned, sub-test ten Form B7, and from a series of investigations conducted by the writer with the assistance of Donald S. Snedden and Warren G. Findley at Cooper Union in New York City.
In 1921 the Institute of Educational Research at Teachers College, Columbia University, under the direction of Professor E. L. Thorndike, prepared a series of new-type examinations at the request of the College Entrance Examination Board for the information of teachers and to facilitate experiments and observations in secondary schools with a view to determining the value of such tests. In 1925, an algebra examination reprinted from Forms IB and IIB of this series with the permission of Professor Thorndike and the College Entrance Examination Board was given by the Department of Mathematics at Cooper Union to all applicants for the Night School of Engineering.
The reprinted examination given at Cooper Union included questions 1 to 32 and 36 to 40 inclusive of Form IB without change, omitting questions 33, 34, and 35 (graphs). Questions 1 to 7, inclusive, 12, 13, 15, and 16 of Form IIB were also used. The following credits were given: