The Rapid Acceleration of Basic Mathematical Skills in Disadvantaged Children: Implementing and Assessing an Alternative Multiplication Algorithm.
- Abstract:Sixty six disadvantaged fourth grade students were identified on the basis of participation in federal (US) free, and reduced cost lunch programs. The ethnic balance of this population paralleled that of the school as a whole: 50% Afro-American, 49% Euro-American and 1% other. Teachers and students were assigned to treatment groups randomly. Review instruction in addition and developmental instruction in multiplication were presented conventionally to the control group and with low-stress algorithms to the experimental group. After criteria determined intervals of instruction, accuracy and attitudes were assessed. For addition, the experimental group showed, at retention measure, a 142% greater gain in accuracy than did the control group while using only 44% of the control groups’ instructional time. Negative/neutral responses disappeared from the experimental group, but remained marginally in the control group. For multiplication, the experimental group showed, at retention measure, a 232% greater gain in accuracy than did the control group (P‹ .005) while using only 26% of the control groups’ instructional time. Negative/neutral responses disappeared from the experimental group, but 26% remained in the control group (P‹ .05) Understanding these accuracy-time relationships was facilitated by using a variation of an industrial cost-effectiveness statistic. In the relevant formula, industrial cost was replaced by curriculum time and industrial unit production was replaced by measures of accuracy. This meant that accuracy of the experimental group (mean correct response) was divided by the accuracy of the control group, that quotient then being divided by the quotient obtained by dividing the instructional time of the experimental group (total hours) by the instructional time of the control group. This relationship expressed the relative teaching-learning efficiency of the experimental group versus the control group: for addition this indicated ∼325%; for multiplication ∼906%.
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