ERIC Number: ED324226
Record Type: Non-Journal
Publication Date: 1990-Aug
Reference Count: N/A
Halves, Pieces, and Twoths: Constructing Representational Contexts in Teaching Fractions. Craft Paper 90-2.
Ball, Deborah Loewenberg
Learning to teach mathematics for understanding is not easy. First, practice itself is complex. Second, many teachers' traditional experiences with and orientations to mathematics and its pedagogy are additional hindrances. This paper examines teaching practices and reviews some of what is known about prospective and experienced elementary teachers. In analyzing practices, the document's focus is on one major aspect of teacher thinking in helping students learn about fractions: the construction of instructional representations. One teacher's practice is analyzed to highlight the complexity inherent in the construction of fruitful representational contexts with students. Prospective and experienced teachers' knowledge, dispositions, and patterns of thinking relative to representing mathematics for teaching are discussed. It is argued that attempts to help teachers develop their practice in the direction of teaching mathematics for understanding requires a deep respect for the complexity of such teaching and depends on taking teachers seriously as learners. A list of 62 references is provided. (CW)
Descriptors: Cognitive Development, Cognitive Structures, Elementary Education, Elementary School Mathematics, Epistemology, Fractions, Learning Strategies, Literature Reviews, Mathematics Education, Mathematics Teachers, Teacher Education, Teaching Methods, Thinking Skills
National Center for Research on Teacher Education, 116 Erickson Hall, College of Education, Michigan State University, East Lansing, MI 48824-1034 ($5.35).
Publication Type: Opinion Papers; Information Analyses
Education Level: N/A
Sponsor: Office of Educational Research and Improvement (ED), Washington, DC.
Authoring Institution: National Center for Research on Teacher Education, East Lansing, MI.