ERIC Number: ED396931
Record Type: RIE
Publication Date: 1996-Apr
Reference Count: N/A
Students' Difficulties with Proof by Mathematical Induction.
Baker, John Douglas
The cognitive difficulties encountered by 40 high school and 13 college students beginning to learn the proof technique of mathematical induction were investigated. Students provided data in the form of proof-writing and proof-analysis tasks followed by interviews to clarify their written responses. Both groups of students had significant difficulties with the proof technique, both procedurally and conceptually. The evidence suggests that mathematical content knowledge played a significant role in difficulties. Many students focused on the procedural aspects of mathematical induction far more often than on conceptual aspects. The evidence collected suggests that examples play a critical role for many students in verification, for insight, and as patterns for how proof should be conducted. There was some evidence of students trying to reason mathematically using everyday reasoning. Difficulties predicted by earlier studies with proof by mathematical induction, other forms of proof, and problem solving were confirmed. (Author)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Mathematical Induction
Note: Paper presented at the Annual Meeting of the American Educational Research Association (New York, NY, April 8-12, 1996).