When Proficient Secondary Mathematics Learners Encounter Counterexamples: An Investigation of the Bases of Their Reasoning

• In Event: Roundtable Session 47
  In Roundtable Session: Secondary and Postsecondary Mathematics Conceptions and Understanding

Abstract

This study investigated how secondary students react when encountered counterexamples to a pattern or conjecture. An instrument consist of four mathematical problems was developed for an interview that investigated the bases of students’ reasoning in approaching these problems. Each problem in the instrument involves unexpected counterexamples to a pattern or a seemingly true statement. Four secondary school students participated in the interviews and their written work and interview transcripts were qualitatively analyzed. Findings of the study indicated that such problems could create a cognitive conflict between counterexamples and nonmathematical intuitions. Such a conflict might lead to students reflecting on their own explanation. However, students might also take several other cognitive paths in this situation.

Author

• Yating Liu, Old Dominion University