Proof Frames of Preservice Elementary Teachers

Martin, W. Gary; Harel, Guershon

doi:10.2307/749097

Cited by 196 publications

(108 citation statements)

References 4 publications

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“…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. International comparisons of students (e.g., Healy & Hoyles, 2000) confirm this point, and apparently, many teachers hold similar views (Martin & Harel, 1989). These findings indicate a need to consider the epistemological foundations and corresponding forms of mathematical argument.…”

Section: The Structure Of the Argumentsupporting

confidence: 52%

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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Section: The Structure Of the Argumentsupporting

confidence: 52%

Visualizing the emergent structure of children's mathematical argument

Strom

2001

Cognitive Science

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“…In general, the written data related to proving shows that geometric proving skills of prospective teachers are weak (Healy & Hoyles, 2000;Kahan, 1999;Senk, 1985), they have difficulties in proving (Chazan 1993a;Harel & Sowder 2007;Hart, 1994;Healy & Hoyles, 2000;Martin & Harel 1989;Riley, 2004;Senk, 1985), they have misconceptions like that only an example which shows accury of the statement or a numeric demonstration is e nough for proving (Goulding, Rowland, & Barber, 2002;Knuth, 2002;Ma, 1999;Martin & Harel, 1989;Morris, 2002;Simon & Blume, 1996) and they are not able to transfer their current knowledge into the process of proving.…”

Section: Discussion Conclusion and Suggestionsmentioning

confidence: 99%

“…The results of the studies related to proving which are conducted with prospective elementary mathematics teachers, prospective secondary mathematics teachers, elementary and secondary mathematics teachers reveal that teachers consider empirical infere nces, that is, arguments based on examples and numerical calculations as proving (Goulding, Rowland, & Barber, 2002;Knuth, 2002;Ma, 1999;Martin & Harel, 1989;Morris, 2002;Simon & Blume, 1996). Almeida (2001) has also stated that pupils' views of proo f have been generally empirical, and they may have difficulties in justifying their results due to lack of their knowledge.…”

Section: Nef-efmedmentioning

confidence: 99%

“…To be succesful in geometry teaching, proof should be integrated into this lesson (Harel, 2008). Although there are sort of research including the difficulties in proving (Chazan, 1993a;Hart, 1994;Martin & Harel, 1989;Senk, 1985), the studies focusing on learning of geometric proofs are limited (Herbest, 2002;McCrone & Martin, 2004 ). From the scarcity of the studies related to proof in geometry and towards prospective elementary mathematics teachers, the aim of this study is to determine the abilities of prospective elementary mathematics teachers in geometric proving in the subject of triangle.…”

Section: Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimentioning

confidence: 99%

“…Hence, most of the student do not know the differences between empirical and deductive arguments (Chazan, 1993b). Therefore, arising of the difficulties in geometry and the other domains in terms of students is inevitable (Martin & Harel, 1989).…”

Section: Nef-efmedmentioning

confidence: 99%

See 2 more Smart Citations

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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Mathematical Learning

Lehrer

Lesh

2003

Handbook of Psychology

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Lehrer and Lesh review research in the psychology of mathematical learning and mathematics education through a genetic, developmental framework that reflects both cognitive and sociocultural perspectives on learning. The authors examine individual cognitive processes and sociocultural contexts that underscore mathematical thinking. Origins of mathematical learning are linked to the development of argument. The role of inscriptions, notations and symbolic patterns are reviewed as a distinct form of mathematical literacy. These ideas are applied to studies of geometry measurement that stress spatial visualization and to mathematical modeling. A final section presents implications for classroom learning and describes how to create a classroom culture that values mathematical explanation, thinking, and instructional design.

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Proof Frames of Preservice Elementary Teachers

Cited by 196 publications

References 4 publications

Visualizing the emergent structure of children's mathematical argument

Visualizing the emergent structure of children's mathematical argument

İlköğretim Matematik Öğretmen Adaylarının Üçgenlerin Öğretiminde Geometrik İspatları Kullanabilme Becerileri

Mathematical Learning

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