Examining and promoting mathematical connections with concept mapping
Bartels, Bobbye J.
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Permalink
https://hdl.handle.net/2142/19078
Description
Title
Examining and promoting mathematical connections with concept mapping
Author(s)
Bartels, Bobbye J.
Issue Date
1995
Doctoral Committee Chair(s)
Glidden, P.L.
Department of Study
Education, Teacher Training
Discipline
Education
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Education, Mathematics
Education, Educational Psychology
Education, Teacher Training
Language
eng
Abstract
This exploratory study examined the way students make mathematical connections and the efficacy of using concept mapping as a tool for promoting connections explicitly during instruction. Nineteen students in an elementary mathematics methods course constructed group concept maps for five topics covered in the course. In this study, concept maps were used as a research tool and as an instructional tool.
Interpretive analysis of the concept maps constructed by cooperative groups ($n=5$) and the protocols of student discussion showed that four themes affected the connections students made: compatibility with prior knowledge, explicitness and frequency of the connection, consistency in terminology and presentation, and recency of the connection. These themes were found interwoven through the students' prior knowledge, the course textbook, class discussion, and concept mapping. Complexity in mathematics terminology interfered with students' connection-making, especially when coupled with their prior knowledge about a concept. Additionally, when students observed physical models of geometric solids they made better connections, as long as the models were discussed adequately.
Written explanations of mathematics concepts in the form of writing assignments and unit lesson plans were assigned to measure the number and kind of connections the preservice teachers might use during instruction. The number of connections on group concept maps correlated positively with the number of concept-to-concept connections in the writing assignments and unit lesson plans. Students used more concept-to-concept connections than any other kind, but they used more concept-to-manipulative and concept-to-real world connections with lower grade-level topics than with higher grade-level topics. An additional effect of concept mapping was observed as students' understanding of what it means to make connections grew during the semester to include a greater variety of connections.
The study contributed to the growing literature about how students make connections when constructing mathematical knowledge. Additionally, it concludes that concept mapping has value as an instructional tool for promoting explicit mathematical connections and for improving preservice elementary teachers' understanding of mathematical connections.
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