One Elementary Teacher's Struggle to Encourage Thinking in Her Mathematics Classroom: A Metaphorical Analysis (Qualitative, Case Study, Ethnographic)
Brandau, Linda Iris
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https://hdl.handle.net/2142/68971
Description
Title
One Elementary Teacher's Struggle to Encourage Thinking in Her Mathematics Classroom: A Metaphorical Analysis (Qualitative, Case Study, Ethnographic)
Author(s)
Brandau, Linda Iris
Issue Date
1985
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
Abstract
This one year intense study of mathematics teaching and learning focussed on one elementary teacher who taught at a private school for about 25 children, aged 5-10 years old. About 100 hours of fieldnotes, audiotapes, and videotapes were made of this teacher's mathematics classroom and other in-school activities, such as teacher meetings. About 150 hours of audiotapes were made of out-of-school discussions between the teacher and the researcher. These discussions focussed on classroom observations, planning future lessons, evaluating the children's progress, and the teacher's beliefs about mathematics and mathematics teaching.
Verbatim transcripts were made of portions of all the observations. The protocols were analyzed to explain this teachers' struggle to encourage thinking in mathematics. The struggle involved the teacher gaining insight into how her students seemed to learn by memorizing procedures to get right answers, without having much understanding of the process used. Although she gained this insight, she struggled with trying to alter the established patterns within her classroom.
To help explain her struggle, data were analyzed by using a "wilderness tours" metaphor, where school mathematics was compared to a mountain, teaching to being a guide, and learning to being a mountaineer. Just as mountaineering and guiding would be more difficult due to weather-related illusions, there were illusions within the classroom interaction that sustained the teacher's assumption that the children were making standard connections between mathematical ideas. The illusions all involved the childrens' right and/or expected answers to the teacher's or textbook's questions. Data showed that getting these right answers did not necessarily mean "understanding" was present.
The metaphorical analysis led to the conclusion that to have promoted the kind of thinking she wanted, the teacher would have needed to be more of an Outward Bound type of guide. That is, she needed to place the children in more situations for which risks could be taken and for which learning by problem solving and by trial and error would occur. It was proposed that the teacher was afraid that she would not have been able to handle the mistakes and/or emergencies that could have arisen in such risky situations. She felt inadequate about her own mathematical abilities. Another reason such fear was evoked was that the consequences of the children making mistakes or getting "lost" mathematically, were high. The teacher was held accountable for the children's learning and could be blamed for any "mis-learnings".
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