Date of Award

1980

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Education

Abstract

This study investigated two treatments in teaching subtraction of two-digit numbers with regrouping, and the effects of these treatments on ninety-four third-grade students. The first treatment named base-blocks (BB), consisted of the manipulation of ones and tens blocks to develop an understanding of the decomposition algorithm. The second treatment, named expanded notation (EN), consisted of the explanation of the decomposition algorithm using expanded numbers and the associative property of addition. Measures were obtained for computational skill and retention of that skill. Two teachers each taught both treatments to four comparable groups. There was a three-week preparation phase for the teachers during which they learned both methods. The learning phase for the students covered a period of one week. The retention phase covered the next six weeks. Four of the seven null hypotheses tested were accepted and three rejected. The four null hypotheses accepted are (1) The mean score of the students taught by teacher A is not significantly different from the mean score of the students taught by teacher B. (2) The mean score of the BB students is not significantly different from the mean score of the EN students. (3) There is no significant interaction between the treatment and the teacher. (4) There is no significant interaction between the teacher and the test. The three null hypotheses rejected are (1) The mean score of the students is not significantly different on the pre-test, the post-test, and the retention test. (2) There is no significant interaction between the treatment and the test. (3) There is no significant interaction among the treatment, the test, and the teacher. These results indicate that the students increased their computational skill significantly from the pre-test to the post-test, and to the retention test. Neither the teacher component nor the treatment component affected the results when considered separately. The treatment-test interaction is significant. The difference in mean score, on the retention test, is in favor of the BB treatment. The difference, therefore, in the amount of measured increase in computational skill during the retention period is due to the treatment. The teacher-treatment-test interaction is also significant. This indicates that the teacher affects the computational skill acquired by the learners during the treatment period if the computational skill is tested immediately following the learning phase. The treatment affects computational skill on the retention test. Both BB treatment groups showed significant gains on the retention test. There were three major types of errors that were in evidence on all the tests. These types of errors--consisting of subtracting the smaller number from the larger in a column, incorrect subtraction facts, and regrouping mistakes--were in evidence in both treatment groups. There was a difference in error patterns when the tests were considered. Subtracting the smaller number from the larger in a column accounted for sixty percent of the errors on the pre-test, but only twenty percent on the post-test and twenty percent on the retention test. The use of incorrect subtraction facts was consistent across all the tests. Regrouping errors accounted for only ten percent of the errors on the pre-test, but forty percent on the post-test and forty percent on the retention test. The small number of regrouping errors on the pre-test can probably be accounted for by conjecture that the students did not have any knowledge of regrouping. Other types of errors were consistent across all the tests.

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