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The effect of a year's teacher-training course on the Vancouver Normal School students' understanding of arithmetic Kilgour, Alma Jean

Abstract

The meaning theory of teaching arithmetic requires that those who do the teaching understand the mathematical bases of arithmetic. This study was concerned with determining the extent to which one teacher-training institution was successful in raising the level of understanding of arithmetic on the part of its students during its usual year's programme. The 280 testees were students of the Vancouver Normal School. The data were obtained through the administration of Glennon's Test of Basic Mathematical Understandings at the beginning and at the end of the school year. The analysis of the data led to the following conclusions: 1. The teacher-training programme was effective in bringing about small but significant gains in the students' achievement of the basic mathematical understandings contained in Glennon's Test. The testees knew an average of 61.5 per cent of the understandings at the beginning of the study and an average of 66 per cent of them at the end of the study. 2. The understandings related to the decimal system of notation and to the integers and processes were well known to the students on both tests whereas those understandings related to decimals and processes, fractions and processes, and the rationale of computation were considerably less well known on both tests. 3. Significant gains were made in the areas of the decimal system of notation, integers and processes, fractions and processes, and the rationale of computation. The gains were fairly equal for the four areas of arithmetic. The section on decimals and processes showed no significant gains. The order of difficulty for the five areas of arithmetic included in Glennon's Test remained essentially the same for the test and retest. 4. Superior gains in achievement of the basic mathematical understandings were made by the students who were in the lowest quarter of the cases in the initial test as compared with those attained by the students who were in the highest quarter of the cases in the initial test. 5. The test items tended to be 3.5-choice rather than 5-choice items for this group of testees. As determined by the number of actual choices per item the level of understanding for this group was higher at the end of the year than it was at the beginning of the year. 6. 83 per cent of the rejection of the misleads which took place was made in favour of the correct answers to the items whereas 17 per cent of the rejection was made in favour of the incorrect alternatives. The latter finding indicates that the change (perhaps gain) which takes place in relation to certain items is incompletely assessed by the usual statistical procedures. 7. The mean of the gross changes involved in the shift of responses to and from the correct answers in the test-retest situation averaged six times the mean of the differences between the net changes in the responses. It is evident that minor changes are considered in present methods of estimating reliability, whereas the major changes are obscured and so ignored. In spite of the apparent inconsistency of the responses of the group to the test items in this study, reliability was .94, indicating that further research is necessary in the area of test reliability.

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