Date of Award:
Doctor of Education (EdD)
School of Teacher Education and Leadership
Department name when degree awarded
Ross R. Allen
The purpose of this study was to investigate the relationship between addition and subtraction as inverse operations, to determine how drill in addition facts will affect knowledge of subtraction facts; to infer, if possible, when addition is conceptualized as an operation with reversibility; and to determine at which grade levels a particular method of drill is effective.
The sample was drawn from Logan, Utah , small, city school district of 3700 students. The experimental groups consisted of 12 elementary and eight secondary existing classrooms of students. The control groups consisted of 10 elementary and five secondary existing classroom groups. A total of 1007 elementary and secondary students were involved in the study. The sample included treatment and control groups from first through the ninth grades.
The treatment consisted of administering drill on the addition facts, to classroom groups using the overhead projector.
All students were tested three times, at the beginning of the study, after one week and after two weeks; using two tests, an Addition Facts Test, which contained the 100 basic addition facts, and a Subtraction Facts Test which contained the 100 basic subtraction facts. Four scores were considered for each test; "time'', the "number left out", the "number missed", and the "total error". Gain scores showing loss or progress from the pretest to each of the two posttests were computed for each of these four scores. All groups corrected their own test papers immediately after taking the tests . The statistical analysis included the following:
Correlation coefficients were computed between addition and subtraction scores for each of the four scores mentioned.
Correlation coefficients were computed between the addition and subtraction scores for each gain score.
Two-way analyses of variance were computed for grade level effect and treatment effect for each of the 16 gain scores.
The results included:
The correlation coefficients for addition and subtraction "time" scores were positive and significant at every grade level. The correlation of the first grade, .30, was significantly lower than that of the second grade, .72. The correlations showed an increasing trend to .87 at the seventh grade, then a falling off in the eighth and ninth grades.
The correlation coefficients for addition and subtraction error scores were positive and significant for the "number left out" and "total missed" scores for grades one through seven.
For the two posttests, the correlation coefficients for the "time" gain scores from the first grade were negative. They were positive and significant for grades two, four, five, seven, and eight. The results for the correlation of error gain scores were mixed.
Of the 16 two-way analyses of variance for gain scores, five showed significant F ratios, two were concerned with addition and three with subtraction; four analyses showed significant grade level effect, three analyses showed significant treatment effect, and two showed significant interaction.
On nine scores there were large differences between fir s t and second grade grou ps . The results are consistent with what one would expect if first grade students had not formed the concept of addition as an operation with reversibility.
The results are consistent with what one would expect if: at the second grade level, addition were conceptualized as an operation with reversibility for a good portion of the students, yet the r e were a good number for whom this reversibility were limited or inoperative; the concept of addition as an operation continued to develop with a more pronounced reversibility during grades three and four.
It was concluded that:
First grade children do not possess the requisite understanding to profit from drill of the type used in this study.
Second grade students have a good start on understanding and can profit from practice experiences in addition and subtraction.
Maximum gains were made in third and fourth grade gr oups with the type of drill used in the study.
Davidson, Ted E., "The Effects of Drill on Addition-Subtraction Fact Learning With Implication of Piagetian Reversibility" (1975). All Graduate Theses and Dissertations. 4243.
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