Date of Award
Doctor of Philosophy
Curriculum and Instruction
The purpose of this study was to investigate the effect of the use of an Alternative-Solution Worksheet (ASW) on American ninth-grade students' problem solving performance, and to determine the extent to which instruction in alternative solutions promotes "look back" strategies. "Look back" strategies are based on Polya's (1973) problem solving steps, and they are an examination of what was done or learned previously. The ASW was designed to encourage students to utilize "look back" strategies by generating alternative solutions to the problems. This mixed-methods study was conducted with two existing groups of ninth-grade Algebra I students. An experimental group of 18 students received instruction in utilizing the ASW for two 55-minute class periods a week for a period of four weeks. A comparison group of 14 students did not receive any instruction. Data for this study were collected by pre- and post-testing, ASWs, focus groups, and one student's "think aloud" process. For the quantitative analysis, a one-way ANCOVA was conducted to determine if there was a significant difference in the mean post-test scores between the experimental group and the comparison group. The students' pre-test score was the covariate. The findings indicated that the experimental group scored slightly better on the post-test, and R2=.345, a medium effect size. There were no significant correlations between the ASW scores and the pre- and post-test scores, but the ASW scores were significantly correlated with the students' EXPLORE9 math and reading percentiles. The qualitative findings indicated that "look back" occurred at all six levels of Bloom's Revised Taxonomy, but it is the "look back" that occurs at the upper three levels, in the context of higher order thinking skills, that results in better mathematical problem solving abilities. In addition, positive affective changes were evident despite little improvement in students' mathematical problem solving abilities. The results of this study indicated that higher order thinking skills need to be practiced regularly so students can use them effectively.
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