Building Mathematical Connections through Communications

1
Building Mathematical Connections through
Communications

• Elizabeth B. Uptegrove
• Felician College
• uptegrovee_at_felician.edu

• Carolyn A. Maher
• Rutgers University
• cmaher3_at_comcast.net

2
Introduction

• NCTM Standards
• Connections -- Students should understand how
  mathematical ideas interconnect
• Communications -- Students should organize and
  consolidate their mathematical thinking through
  communication

3
Analysis of Problem-Solving Session

• Students helped each other understand some
  features of Pascals Triangle
• Students identified connections between two
  isomorphic problems
• Students collaborated and communicated their ideas

4
Research Question

• How did communication among these students
  contribute to the groups success in making sense
  of combinatorics problems?

5
Background

• Four students from longitudinal study
• First grade through college
• After-school problem-solving session
• Sophomore year of high school

6
Data Sources

• Videotapes (2 cameras)
• Transcripts selected for
• Discussions related to Pascals Triangle
• Discussions related to combinatorics problems
• Transcripts coded for
• Student-to-student communications
• Students making connections

7
Theoretical Perspective

• Maher (1998)
• Students develop and consolidate mathematical
  understanding through communication
• Sharing and comparing representations gives
  students a chance to build deeper understanding
• Sfard (2001)
• Participating in discourse about ideas helps
  students to think mathematically

8
Results

• We examine three events in which critical ideas
  emerged
• Context
• Mathematical ideas that emerged
• Students strategies, heuristics, connections
• Reactions to others ideas