ERIC Number: EJ774732
Record Type: Journal
Publication Date: 2007-Jun
Reference Count: N/A
Preservice Teachers' Knowledge of Proof by Mathematical Induction
Stylianides, Gabriel J.; Stylianides, Andreas J.; Philippou, George N.
Journal of Mathematics Teacher Education, v10 n3 p145-166 Jun 2007
There is a growing effort to make "proof" central to all students' mathematical experiences across all grades. Success in this goal depends highly on teachers' knowledge of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating preservice elementary and secondary school mathematics teachers' knowledge of proof by mathematical induction. This research can inform the "knowledge about preservice teachers" that mathematics teacher educators need in order to effectively teach proof to preservice teachers. Our analysis is based on written responses of 95 participants to specially developed tasks and on semi-structured interviews with 11 of them. The findings show that preservice teachers from both groups have difficulties that center around: (1) the essence of the base step of the induction method; (2) the meaning associated with the inductive step in proving the implication P(k) [right arrow] P(k + 1) for an arbitrary k in the domain of discourse of P(n); and (3) the possibility of the truth set of a sentence in a statement proved by mathematical induction to include values outside its domain of discourse. The difficulties about the base and inductive steps are more salient among preservice elementary than secondary school teachers, but the difficulties about whether proofs by induction should be as encompassing as they could be are equally important for both groups. Implications for mathematics teacher education and future research are discussed in light of these findings.
Descriptors: Validity, Mathematical Logic, Preservice Teachers, Mathematics Education, Secondary School Teachers, Secondary School Mathematics, Preservice Teacher Education, Mathematics Teachers, Logical Thinking, Teacher Educators, Elementary School Teachers, Elementary School Mathematics
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Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Secondary Education
Audience: Teachers; Researchers
Authoring Institution: N/A