PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Flip vs. fold: What is so important about the rigidity of a motion?
Page: 1140
This report will investigate the mathematical and pedagogical consequences of flipping versus folding in the identification of reflection symmetry. Preliminary results are presented from a teaching experiment aimed at exploring the development of one undergraduate student’s understanding of symmetry. The analysis indicated that throughout the teaching experiment, the student held two distinct versions of reflection symmetry. One version was what most would identify as reflection, while the other was an iterative process based on the participant’s ability to fold the figure. In this report, we share what this student identified as symmetries and how she justified her methods. In addition, we discuss why the definition of isometry necessitates a rigid motion and how the motion of folding is insufficient for identifying symmetries correctly. Lastly, we consider why understanding a rigid motion is advantageous for students who want to consider symmetries in more sophisticated mathematical contexts such as group theory.