Attending to the Structure of Mathematical Statements: Secondary Students' Difficulties and Interpretations

• In Event: Roundtable Session 11
  In Roundtable Session: Student Reasoning and Understanding in K–12 Mathematics Classrooms

Abstract

TThis paper reports on a part of a large study which examined students’ understanding of the interplay between examples and proving or disproving of mathematical statements. Data were collected through task-based interviews with twelve, high-attaining high-school students as they evaluated truth-value of statements from algebra and geometry. The study identified three types of difficulties in interpreting the logical structure of statements, namely: a difficulty to recognize existential quantifier; a difficulty to recognize statements’ domain and property; and/or to recognize the hierarchy between them; and a difficulty to understand what it means to “to contradict” a statement. These difficulties interfered with students’ performance on proof-related tasks and suggest a need for greater attention to logical aspects of proving in high-school setting.

Author

• Orly Buchbinder, University of New Hampshire