Doing and talking about mathematics: A study of preservice elementary teachers
Civil, Marta
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https://hdl.handle.net/2142/20773
Description
Title
Doing and talking about mathematics: A study of preservice elementary teachers
Author(s)
Civil, Marta
Issue Date
1990
Doctoral Committee Chair(s)
Braunfeld, Peter G.
Department of Study
Education
Discipline
Education
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Education, Mathematics
Education, Teacher Training
Language
eng
Abstract
This dissertation analyzes the understanding and beliefs about mathematics of eight preservice elementary teachers as they did, talked, and wrote about mathematics during an eight week mathematics course. The method of instruction followed an open approach in which the student-subjects worked in small groups in a mathematics laboratory setting. The data for this study consist of tape-recordings of the subjects' peer-dialogues, written homework and essays, the subjects' diaries, tape-recorded task-based interviews, and observations of the subjects at work.
"Analyses of samples of the subjects' work on a variety of mathematics tasks, especially of their discussions, occupy much of this dissertation. These analyses illustrate the subjects' confusion and their efforts to make sense out of mathematics. Overall, most subjects enjoyed the group discussions and gave evidence of involvement in the mathematics tasks. Yet, their rather shaky understanding of many of the ideas discussed hampered much of their work. Furthermore, the subjects' beliefs about what doing mathematics entails, and about learning mathematics, often conflicted with the exploratory nature of many of the tasks. Often, the subjects focused on the product, on getting an answer, rather than on the process or on understanding the problem conditions. They wanted to do, or rather, wanted to be taught, mathematics the ""school way,"" which for them often meant using a formula or an algebraic approach, even when they did not understand these. They appeared to believe firmly in the superiority of the school ways; yet, using more informal techniques, some of them achieved real insights into the problems."
The subjects also expressed their beliefs and feelings about becoming teachers. They exhibited a genuine concern about their future teaching careers. For some subjects, this concern about teaching seemed to take precedence over their learning of mathematics. Their expressed ideas about teaching were conflictive: on one hand, they wanted to respect the children's ideas and thinking; on the other hand, they seemed more secure with the notion that, as teachers, they should tell the children how to do every piece of mathematics.
Mathematics courses for prospective elementary teachers should develop an understanding of mathematics, while challenging these students' often firmly held beliefs about learning and teaching mathematics, and addressing their needs as teachers to be. The findings in this study suggest that the following may be most useful in addressing these three issues: presenting prospective teachers with tasks likely to create cognitive conflict, providing opportunities for peer discussions on challenging mathematical questions, and presenting samples of children's work illustrating creative and unusual mathematics.
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