The purpose of this study was to explicate one preservice middle grades mathematics teacher's Knowledge of Content and Students (KCS) in the context of multiple solution strategies. This study's purpose is to underline the importance of preservice teachers' KCS and provide possible investigative methods for evaluating preservice teachers' KCS. Specifically, the research inquiry guiding this study focused on how a middle school preservice mathematics teacher displays KCS when engaging with tasks about pattern recognition and linear functions in the context of multiple solution strategies. The data consisted of three videotaped semistructured interviews with the preservice mathematics teacher as well as the written work she produced during the interviews. This study explicated one preservice mathematic teacher's performance regarding two important themes of KCS: generating multiple possible solution strategies of middle school students and explaining multiple student solution strategies. In terms of generating multiple solution strategies of middle school students, the study found that the preservice mathematics teacher provided the same solution strategies that she employed when she solved the problems by herself. Regarding explaining multiple student solution strategies, this study revealed that the preservice teacher did not explicate how typical middle school students reason. The preservice teacher had limitations when explaining the possible procedures that students might have used to solve problems when given the final student solutions. With regard to the teacher's abilities to recognise and understand students' typical understandings and misunderstandings, the study demonstrated that the preservice teacher was capable of explaining some solution strategies but not all of them.
This study aims to explore one preservice teacher's interpretation of student mathematical thinking using pattern recognition and linear function tasks. Specifically, the research question for this study was as follows: How does a preservice middle grade mathematics teacher interpret student mathematical thinking using tasks designed to test students' pattern recognition and linear function abilities? The preservice teacher, Amy, was a middle school preservice teacher from the Mathematics and Science Education Department of a major land-grant university in the southeastern Unites States. The data consists of Amy's responses during a face-to-face, semi-structured interview, written work she produced during the interview, and a careful analysis of a transcript of the interview. With regards to interpreting important mathematical ideas in students' work in the National Council of Teachers of Mathematics [NCTM] videos, this study found that the preservice teacher provided explanations of specific important mathematical ideas and their meaning. When the preservice teacher interpreted students' mistakes or misconceptions, she explained the misconceptions mathematically rather than providing specific examples from the video. In terms of interpreting the similarities between students' reasoning, the preservice teacher's description of the similarities between students' reasoning was broad. Depending on the task and how many times she watched the videos, either one or two times, the extent to which she provided evidence varied when she interpreted the differences between students' reasoning. This study revealed that the strength of the preservice teacher's interpretation strategies varied depending on the tasks. The preservice teacher did not provide detailed explanations of students' reasonings when watching NCTM videos even though she solved all the tasks in multiple ways and explained the key concepts while solving the problems.
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