A brief course in the teaching process

by George D. Strayer

The above details are compiled from the scores of individual systems as given in tables III and IV, the median cost being that given in table XXI. As measured by the time used in school, the thirteen systems with less than the median cost stand slightly the better; and as measured by the time including home study, the thirteen systems with more than the median time cost stand somewhat the better. The time used in school is doubtless the more exact measure, but, as shown in table XXI, some systems depend on home study to a considerable extent. Hence both measures are used. The lack of relation indicated in this general way is shown more accurately in the table, page 263, in terms of coefficients of correlation.

The order of systems in this table is determined by the first column, which gives the average serial standing as determined by the ratios of time to products. The right-hand column under each heading gives the ratio of time expenditure to abilities produced, and the left-hand column gives the serial order of that system as measured by the highness of the ratio, i.e. highness of cost per unit of product; e.g. in system IV the ratio of time to reasoning is 3.99 (see fourth column), the highest ratio in reasoning (determined by dividing the time cost, 1854 week minutes, by 464, the points made in reasoning). The ratio of time to fundamentals in this system is .52; giving an average ratio of 2.26. That is to say, the ratio of time to abilities in system IV is as 2.26 to 1, the highest among the twenty-six systems.

That there is no direct ratio between time expenditure and abilities is again shown by this table. For example, system XXII, which spends the least amount of time (see table XXI), ranks fourth from the lowest in abilities (see table XXII), ranks 25th, that is, next to the highest, in ratio of time cost to abilities produced; and, what is even more striking, system XXVI, which spends third from the least amount of time, ranks third from the highest in abilities and 26th or highest in the ratio of time cost to abilities produced.

That a large amount of time expended is no guarantee of a high standard of abilities may again be convincingly seen by comparing the ratios of the five systems spending the smallest amount of time with the five spending the largest. Of the five spending the least time, the average ratio is .80, which corresponds with the 23d or the 3d from the best in ratio; and of the five spending the greatest amount of time, the average ratio is 1.57, which corresponds with the 4th poorest in ratio.

The last three tables have each shown the decided lack of relationship between time cost and abilities produced, and hence for these systems it is evident that there is practically no relation between time expenditure and arithmetical abilities; and, in view of the representative nature of these twenty-six systems, it is probable that this lack of relationship is the rule the country over.

This is not to say that a certain amount of time is not essential to the production of arithmetical abilities; nor that, given the same other factors, operating equally well, the product will not increase somewhat with an increased time expenditure. What is claimed is that, as present practice goes, a large amount of time spent on arithmetic is no guarantee of a high degree of efficiency. If one were to choose at random among the schools with more than the median time given to arithmetic, the chances are about equal that he would get a school with an inferior product; and conversely, if one were to choose among the schools with less than the median time cost, the chances are about equal that he would get a school with a superior product in arithmetic.[39]

So far, then, as ability in arithmetic means ability to handle such foundation work as is measured by the tests in this study, this “essential” has not necessarily suffered by the introduction of other subjects and the consequent reduction of its time allotment.

One would need to read the whole study to appreciate fully the nature of the investigation. From the pages quoted, however, it must be apparent that: (1) schools and school systems vary greatly in the results which they secure in arithmetic; (2) the excellence of the work done is not directly proportional to the time expended. We will find it necessary to revise our opinions with regard to the organization of school subjects, the allotment of time, the methods of teaching, and the like, in proportion as we have careful investigation in these several fields.

For Collateral Reading