An investigation of preservice teachers?use of guess and check in solving a semi open-ended mathematics problem

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• 作者：Mary Margaret Capraro^a ; ^{mmcapraro@tamu.edu}  ; [Author Vitae] ; Song A. An^a  ; [Author Vitae] ; Tingting Ma^a  ; [Author Vitae] ; A. Fabiola Rangel-Chavez^a  ; [Author Vitae] ; Adam Harbaugh^b  ; [Author Vitae]
• 关键词：Problem solving ; Open ended ; Guess and check
• 刊名：Journal of Mathematical Behavior
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：31
• 期：1
• 页码：105-116
• 全文大小：361 K

文摘

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs?reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.