Effects of Tree and Matrix Representations on Probability Problem Solving

• In Event: Poster Session 1
  In Poster Session: Research in Mathematics Teaching and Learning

Abstract

The present study examines how different diagram types affect solvers’ choice of solution for combinatorics probability problems. College and graduate students solved combinations and independent events problems with one of four types of diagram or no diagram. These problems could be solved by either an “outcome-search” solution utilizing the classical definition of probability, or a “sequential-sampling” solution invoking the multiplication rule. Results revealed a strong diagrammatic effect on how probability principles and problem structures were interpreted for the problems and solutions were chosen. The results suggest that people process and solve combinatorics problems by aligning visuospatial features of a diagram with the underlying mathematical structures. The findings offer instructional insights on design of visual aids in introductory probability education.

Authors

• Chenmu Xing, Wesleyan University

• James E. Corter, Teachers College, Columbia University

• Doris Zahner, Council for Aid to Education