A study of training and transfer effects of comparison subtraction and one to one correspondence




Marshall, General G.

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The study had two basic purposes: (1) to determine if specific training procedures improve the ability of young children to, (a) model and solve comparison subtraction problems and (b) to solve one-to-one correspondence problems: and (2) to determine if specific training procedures improve ability in transfer to other subtraction types or one-to-one correspondence. An instructional sequence was constructed for comparison subtraction which involved counting, modeling with manipulatives, and experiences with semi-concrete materials. A second instructional sequence was constructed for one-to-one correspondence which was similar to the sequence for comparison subtraction except for the exclusion of counting. Four tests(one achievement and three transfer) for each of the two training methods were used for post-testing. The posttests were on one-to-one correspondence and the three types of subtraction problems. Three experimental groups were used in the study. One group was trained in modeling and solving comparison subtraction problems; a second group was trained in modeling and solving one-to-one correspondence problems, and the third group engaged in geometrical activities which were dissimilar to the first two groups. The training period extended nine calendar days during which six 30 minute sessions were held on six different days. The period was further divided into three sessions per school week. The sample was composed of multiethnic middle-middle-class students who were enrolled in grade one and whose ages ranged from 81 to 100 months. A pretest on quantitative comparisons was used to equate the groups and for the purpose of uniform group assignment. Several studies had found the test used in the present study to have high positive correlation with whole number problem solving abilities of first-grade students. Four major hypotheses were tested: one on training, two on transfer, and one on total subtraction performance. None of the hypotheses was rejected; however, a subhypothesis on comparison subtraction accuracy was rejected. The researcher concluded that the specific training procedures produced significant differences in abilities to solve comparison subtraction problems. The major reason for the failure to reject the null hypotheses was the high overall performance of the control group.