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SECONDARY SCHOOL STUDENTS' UNDERSTANDING OF MATHEMATICAL INDUCTION: STRUCTURAL CHARACTERISTICS AND THE PROCESS OF PROOF CONSTRUCTION.

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Title: SECONDARY SCHOOL STUDENTS' UNDERSTANDING OF MATHEMATICAL INDUCTION: STRUCTURAL CHARACTERISTICS AND THE PROCESS OF PROOF CONSTRUCTION.
Authors: Palla, Marina1, Potari, Despina1 dpotari@math.uoa.gr, Spyrou, Panagiotis1
Source: International Journal of Science & Mathematics Education. Oct2012, Vol. 10 Issue 5, p1023-1045. 23p.
Subject Terms: *Secondary schools, *Comprehension, Mathematical induction, Proof theory, Geometric analysis, Debate
Abstract: In this study, we investigate the meaning students attribute to the structure of mathematical induction (MI) and the process of proof construction using mathematical induction in the context of a geometric recursion problem. Two hundred and thirteen 17-year-old students of an upper secondary school in Greece participated in the study. Students' responses in 3 written tasks and the interviews with 18 of them are analyzed. Though MI is treated operationally in school, the students, when challenged, started to recognize the structural characteristics of MI. In the case of proof construction, we identified 2 types of transition from argumentation to proof, interwoven in the structure of the geometrical pattern. In the first type, MI was applied to the algebraic statement that derived from the direct translation of the geometrical situation. In the second type, MI was embedded functionally in the geometrical structure of the pattern. [ABSTRACT FROM AUTHOR]
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Database: Education Research Complete
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Abstract:In this study, we investigate the meaning students attribute to the structure of mathematical induction (MI) and the process of proof construction using mathematical induction in the context of a geometric recursion problem. Two hundred and thirteen 17-year-old students of an upper secondary school in Greece participated in the study. Students' responses in 3 written tasks and the interviews with 18 of them are analyzed. Though MI is treated operationally in school, the students, when challenged, started to recognize the structural characteristics of MI. In the case of proof construction, we identified 2 types of transition from argumentation to proof, interwoven in the structure of the geometrical pattern. In the first type, MI was applied to the algebraic statement that derived from the direct translation of the geometrical situation. In the second type, MI was embedded functionally in the geometrical structure of the pattern. [ABSTRACT FROM AUTHOR]
ISSN:15710068
DOI:10.1007/s10763-011-9311-2