Using the process of writing to reveal changes in middle school students' algebraic reasoning in response to open-ended writing prompts
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2014-05
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University of Hawaii at Manoa
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This qualitative study aims to reveal and describe those changes in middle school students' emergent algebraic reasoning by analyzing their written responses to open-ended mathematically themed prompts, constructed using the process of writing. In this study, I served as both the teacher and the researcher in my own classroom. All grade eight students in my Algebra I classes responded to seven open-ended mathematically themed prompts throughout the school year. Of those forty-four students, eleven were purposely chosen to participate in this study based on criteria such as academic achievement and proficiency with the English language. Furthermore, the students were deliberately chosen at the end of the school year to minimize any intentional or unintentional bias throughout the school year. Students wrote three drafts for each of the seven open-ended prompts and received teacher-to-student written feedback upon submitting their second draft. Each of the eleven students participated in a one-on-one interview at the end of the school year for the purpose of gaining an insider's perspective on their experience, validating the emergent themes from the written data, identifying possible contradictions within the written data and/or the students' shared experiences and providing internal validity during the analysis phase of the study. A content analysis focused on gleaning meaning suggested by students' written use of the symbolic and descriptive language of mathematics was conducted; both individual drafts and each set of collective drafts were analyzed. Individual drafts focused on the features that were not seen in the previous drafts and collective sets focused on students' conceptual maturation for each mathematics theme. This analysis revealed: a) students recaptured known information using a show-and-tell approach in their freewrite; b) students experimented in the construction and expression of their own mathematical understandings in their second draft; and c) students reconsidered, after receiving feedback, their preexisting ideas in their third draft. A three stage model, knowledge acquisition, mulling over working knowledge, and conceptual evolution, grounded in the data, describes the progression of students' conceptual understanding.
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Algebra--Study and teaching (Middle school)
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Theses for the degree of Doctor of Philosophy (University of Hawaii at Manoa). Education.
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