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. |
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| 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] |
| Copyright of International Journal of Science & Mathematics Education is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 80375575 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: SECONDARY SCHOOL STUDENTS' UNDERSTANDING OF MATHEMATICAL INDUCTION: STRUCTURAL CHARACTERISTICS AND THE PROCESS OF PROOF CONSTRUCTION. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Palla%2C+Marina%22">Palla, Marina</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Potari%2C+Despina%22">Potari, Despina</searchLink><relatesTo>1</relatesTo><i> dpotari@math.uoa.gr</i><br /><searchLink fieldCode="AR" term="%22Spyrou%2C+Panagiotis%22">Spyrou, Panagiotis</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Science+%26+Mathematics+Education%22">International Journal of Science & Mathematics Education</searchLink>. Oct2012, Vol. 10 Issue 5, p1023-1045. 23p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Secondary+schools%22">Secondary schools</searchLink><br />*<searchLink fieldCode="DE" term="%22Comprehension%22">Comprehension</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+induction%22">Mathematical induction</searchLink><br /><searchLink fieldCode="DE" term="%22Proof+theory%22">Proof theory</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+analysis%22">Geometric analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Debate%22">Debate</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Science & Mathematics Education is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10763-011-9311-2 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 1023 Subjects: – SubjectFull: Secondary schools Type: general – SubjectFull: Comprehension Type: general – SubjectFull: Mathematical induction Type: general – SubjectFull: Proof theory Type: general – SubjectFull: Geometric analysis Type: general – SubjectFull: Debate Type: general Titles: – TitleFull: SECONDARY SCHOOL STUDENTS' UNDERSTANDING OF MATHEMATICAL INDUCTION: STRUCTURAL CHARACTERISTICS AND THE PROCESS OF PROOF CONSTRUCTION. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Palla, Marina – PersonEntity: Name: NameFull: Potari, Despina – PersonEntity: Name: NameFull: Spyrou, Panagiotis IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2012 Type: published Y: 2012 Identifiers: – Type: issn-print Value: 15710068 Numbering: – Type: volume Value: 10 – Type: issue Value: 5 Titles: – TitleFull: International Journal of Science & Mathematics Education Type: main |
| ResultId | 1 |
