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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2069/194
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| Title: | The Mathematical Discourse of Undergraduate Mathematics Majors: The Relation to Learning Proof and Establishing a Learning Community |
| Authors: | Remillard, Katherine S. |
| Keywords: | Commognition
Learning as Participation
Mathematical Discourse
Mathematical Learning Community
Mathematical Proof |
| Issue Date: | 16-Sep-2009 |
| Abstract: | This study addressed the inherent and age-old quandary of learning mathematical
proof. The aim of the study was to explore the nature of the learning of mathematical
proof by undergraduate mathematics majors through the lens of discourse. Additionally,
the study investigated mathematics majors’ sense of a learning community in relation to
their participation in a seminar on learning mathematical proof utilizing small-group
discourse. A communicational approach to cognition—or commognition—provided the
theoretical and research perspective for the study.
The setting of the study was a zero-credit seminar focusing on mathematical proof
for freshman and sophomore mathematics majors. The primarily qualitative study had
nine participants. A multiple methods strategy of data collection was employed. First,
audio recordings of small-group discourse on mathematical proof were collected along
with participants’ related work. Participants additionally completed the Classroom
Community Scale survey. Finally, interviews were conducted. Focal and preoccupational
analyses were performed on the audio data to determine the object-level and meta-level
features of the mathematical discourse/learning. Descriptive statistics and typological
analysis were used respectively to summarize the survey and interview data.
A synthesis of these analyses revealed the complexity of learning mathematical
proof; that is, of becoming a more expert participant in the discourse of mathematicalproof. Small-group discourse appears to be a comfortable way for novice interlocutors to
approach a more expert discourse on proof. Moreover, there may exist in discourse
between novice interlocutors natural opportunities, called discursive entry points, in
which experts could intervene to steer the discourse towards increasing sophistication.
Additionally, the study revealed several complex and interrelated factors related to
learners’ thinking (communication) of mathematical proof. The factors include:
discursive contributions/role of interlocutors, discursive foci of interlocutors,
difficulty/familiarity of mathematical content, negotiating effective communication,
commognitive conflict, and power. Finally, interlocutors had a sense of community in the
seminar on mathematical proof utilizing small-group discourse. The discourse may also
have contributed to the connectedness that participants felt with their fellow math majors
both inside and beyond the seminar walls. Moreover, the participants viewed being able
to communicate about mathematical proof as the conduit to a universal math community. |
| URI: | http://hdl.handle.net/2069/194 |
| Appears in Collections: | Electronic Dissertation
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Files in This Item:
| File |
Description |
Size | Format |
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| Katherine Remillard Cover & Abstract.pdf | | 38Kb | Adobe PDF | View/Open |
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