Students’ proof schemes: Results from exploratory studies

Harel, Guershon; Sowder, Larry

doi:10.1090/cbmath/007/07

Cited by 421 publications

(464 citation statements)

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“…Besides it is concluded that students do not need to prove the statement since they believe that its accuracy seems very clear (Harel & Sowder, 1998), their awareness about whether their own demonstrations are proofs is changeable (Chazan, 1993b), they attempt to prove through verbal expressions, they believe that they can prove a statement with a few examples (Weber, 2001) and desire towards proving is low since proving is hard for them.…”

Section: Discussion Conclusion and Suggestionsmentioning

confidence: 99%

“…In general, the interview data related to proving shows that prospective teachers do not know how to use their current knowledge (Weber, 2001), therefore, have difficulties in understanding and producing proofs (Güven, Çelik & Karataş, 2005;Harel & Sowder, 1998;Jones, 2000;Martin & Harel, 1989;Moore, 1994), they are not able to decide from where to start proving (Sarı, Altun, Aşkar, & 2007;Weber, 2001) and have difficulties in remembering knowledge later because of memorization (Condradie & Firth, 2000;Galindo, 1998). which they may utilize when they become teachers can be provided (Herbst, 2002;Mariotti, 2000).…”

Section: Discussion Conclusion and Suggestionsmentioning

confidence: 99%

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İlköğretim Matematik Öğretmen Adaylarının Üçgenlerin Öğretiminde Geometrik İspatları Kullanabilme Becerileri

Güner¹,

Topan²

2016

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

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-In this study, it was aimed to reveal prospective elementary mathematics teachers' abilities of using geometric proofs in triangle teaching. The data of this study which was based on the techniques of qualitative research was obtained from students attending third class of elementary mathemat ics teacher education program at a public university in the north of Turkey, in 2013-2014 academic year. As data colletion tool, five openended questions which were prepared by the researchers taking the opinions of experts were used and the obtained data was analyzed through content analysis. The results show that proving abilit ies of prospective teachers are low. Three volunteer prospective teachers were made a semi-structured interviews with the intent of examining their proofs in detail. The obtained interv iew data have exposed that prospectice teachers usually attempt to produce geometric proofs using elementary, concrete and practical solution ways in terms of their own perpectives.

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Section: Discussion Conclusion and Suggestionsmentioning

confidence: 99%

Section: Discussion Conclusion and Suggestionsmentioning

confidence: 99%

İlköğretim Matematik Öğretmen Adaylarının Üçgenlerin Öğretiminde Geometrik İspatları Kullanabilme Becerileri

Güner¹,

Topan²

2016

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

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show abstract

“…(Yevdokimov, 2010. ) Over the longer term, the convincing power of the emerging rules for the child is often rooted not only in the observation that the rules 'work' in all available situations, but in the external role of authorities such as a parent, a teacher or a textbook (Harel & Sowder, 1998).…”

Section: What Is Proof For Growing Individuals?mentioning

confidence: 99%

Cognitive Development of Proof

Tall

Yevdokimov

Koichu

et al. 2012

New ICMI Study Series

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“…In mathematics education, there is ongoing concern with how students and teachers alike appreciate various forms of mathematical argument, especially proof (Harel & Sowder, 1998). Schoenfeld (1989), for example, suggests that instead of understanding proof as a form of explanation, many students conceive of it as a means for arriving at the truth of the empirically obvious.…”

Section: The Structure Of the Argumentmentioning

confidence: 99%

Visualizing the emergent structure of children's mathematical argument

Strom

2001

Cognitive Science

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Mathematics educators suggest that students of all ages need to participate in productive forms of mathematical argument (NCTM, 2000). Accordingly, we developed two complementary frameworks for analyzing the emergence of mathematical argumentation in one second-grade classroom. Children attempted to resolve contesting claims about the "space covered" by three different-looking rectangles of equal area measure. Our first analysis renders the topology of the semantic structure of the classroom conversation as a directed graph. The graph affords clear "at a glance" visualization of how various senses of mathematics-as imagined, as performed, and as historically rooted-were interrelated. The graph represents the emergence and intercoordination between conceptual and procedural knowledge in the ebb and flow of classroom conversation. The graph has not just descriptive, but also predictive power: Interconnectedness among the nodes of the graph representing the first 40 min of conversation predicted the structure of recall in the final ten minutes by children who had played little overt role in the conversation up to that point. The second, complementary framework draws upon Goffman's expanded repertoire of roles in speech to demonstrate how the teacher orchestrated this classroom conversation to establish coherent argument. In this second analysis, we establish how the teacher mediated between the everyday talk of her students and the discourse of mathematics. Her revoicing of student talk created interstices for identity and participation in the formation of the argument. Together, the two forms of analysis illuminate the emergence of mathematical argument at two levels: as collective structure and concurrently, as individual activity.

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Students’ proof schemes: Results from exploratory studies

Cited by 421 publications

References 0 publications

İlköğretim Matematik Öğretmen Adaylarının Üçgenlerin Öğretiminde Geometrik İspatları Kullanabilme Becerileri

İlköğretim Matematik Öğretmen Adaylarının Üçgenlerin Öğretiminde Geometrik İspatları Kullanabilme Becerileri

Cognitive Development of Proof

Visualizing the emergent structure of children's mathematical argument

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