An exploratory study into the development of cognitive and metacognitive processes in mathematics problem-solving via computer
Doehee Ahn, University of Alberta , Canada
University of Alberta . Awarded
In order to enhance students' mathematics problem-solving skills, many researchers have asserted that strategies should be taught more explicitly and specifically; however, there is still a relative lack of research on the combination of general and specific strategies to enhance cognitive and metacognitive processes in mathematics problem-solving skills.
This study, utilizing a general strategy, SPIDER, and two types of computer-based instruction (CBI) programs developed by the researcher, examined the effects of explicit strategies instruction on 105 sixth-grade students' mathematics problem-solving skills and on their attitudes toward mathematics problem-solving.
Students drawn from five public elementary schools were divided into three groups (experimental, CBI control, and traditional control) and further sub-divided on the basis of their mathematics problem-solving achievement levels (high and low).
The students were given the Mathematics Problem-Solving Process Questionnaire (MPSPQ) to measure their perceptions of mathematics problem-solving processes. They were also given the Mathematics Problem-Solving Test (MPST) which was developed for this research as well as the mathematics problem-solving sub-test of the Canadian Test of Basic Skills (CTBS-MPS) to measure their mathematics problem-solving performance. In order to measure their estimation of performance on the MPST, self-prediction of performance (SPP), self-evaluation of performance (SEP), accuracy of self-prediction of performance (ASPP), and accuracy of self-evaluation of performance (ASEP) were measured. An attitude survey was administered to investigate their attitudes toward mathematics, mathematics problem-solving, computer use, and the CBI program which they received.
The findings indicated that students in the experimental group (n = 39) who were exposed to explicit strategies instruction via computer showed a significantly greater improvement on the CTBS than those in the CBI control (n = 29) or traditional control (n = 27) groups. However, there were no significant differences observed on the MPST, SPP, SEP, ASPP, ASEP, and MPSPQ across the three groups. With respect to the attitude measure, it was observed that students who were exposed to the CBI program either with or without explicit strategies instruction developed more positive attitudes toward mathematics problem-solving. Interestingly, some students in the experimental group showed increased self-confidence in mathematics problem-solving and self-esteem, whereas such comments were not observed from students in the CBI control group.
Ahn, D. An exploratory study into the development of cognitive and metacognitive processes in mathematics problem-solving via computer. Ph.D. thesis, University of Alberta.
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