Conceptual blending: Student reasoning when proving "conditional implies conditional" statements

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

Conceptual blending describes how humans condense information, combining it in novel ways. The blending process may create global insight or new detailed connections, but it may also result in a loss of information, causing confusion. In this paper, we describe the proof writing process of a group of four students in a university geometry course proving a statement of the form conditional implies conditional, i.e., (p→ q). ⇒. (r→ s). We use blending theory to provide insight into three diverse questions relevant for proof writing: (1) Where do key ideas for proofs come from?, (2) How do students structure their proofs and combine those structures with their more intuitive ideas?, and (3) How are students reasoning when they fail to keep track of the implication structure of the statements that they are using? We also use blending theory to describe the evolution of the students' proof writing process through four episodes each described by a primary blend.

Original languageEnglish (US)
Pages (from-to)209-229
Number of pages21
JournalJournal of Mathematical Behavior
Volume33
DOIs
StatePublished - Mar 1 2014

Keywords

  • Conceptual blending
  • Conditional statements
  • Geometry
  • Key idea
  • Proving
  • Undergraduate mathematics education

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics

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