High school geometry students' justification for their views of empirical evidence and mathematical proof

Chazan, Daniel

doi:10.1007/bf01273371

Cited by 241 publications

(143 citation statements)

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“…She even used the word 'proof' -though not necessarily in a deductive mathematical sense. This situation is quite contrary to the findings in the literature, as students' validation of a mathematical statement often takes the form of testing it against a few examples even at the more advanced levels (Chazan, 1993b;Coe and Ruthven, 1994). In the case of dynamic geometry, students often think that they can justify a claim by empirically checking the diagram (Laborde, 2004) -that is, by dragging.…”

Section: Resultscontrasting

confidence: 45%

Tracing the change in discourse in a collaborative dynamic geometry environment: From visual to more mathematical

Öner

2016

Intern. J. Comput.-Support. Collab. Learn

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In this paper, we investigate what appears to be an intermediate developmental stage in geometrical thinking according to Sfard's commognitive framework. More specifically, we examine the change in three middle-school students' mathematical discourse as they worked on a geometry construction problem within a virtual collaborative dynamic-geometry environment. We trace how their word use, use of visual mediators, and routines changed character during an hour-long collaborative problem-solving session. Our findings indicate that students gradually moved from a visual towards a more formal discourse --one that is primarily characterized by a routine of constructing dependencies. We conclude that interacting with expert interlocutors may not be the only path towards advancing one's mathematical discourse; this process may also take place within a computer-supported collaborative-learning setting. Thus, collaborative dynamic geometry can be viewed as an effective material condition for learning geometry.

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Section: Resultscontrasting

confidence: 45%

Tracing the change in discourse in a collaborative dynamic geometry environment: From visual to more mathematical

Öner

2016

Intern. J. Comput.-Support. Collab. Learn

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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%

“…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%

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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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“…There are many reports about students who accept or offer perceptual or empirical evidence without going on to abstract some property and construct a general argument (Chazan, 1993;Harel & Sowder, 1998), but there is less discussion of how they might make this next step. Certainly the issue is considered important; Raman (2003) observes that mathematicians sometimes think about proofs in terms of "key ideas" that serve to link their formal and informal understanding, and Rowland (2001) suggests specific principles for using generic examples to help students understand and construct general proofs.…”

Section: Relationship To Other Research and Theoriesmentioning

confidence: 99%

Mathematicians’ perspectives on the teaching and learning of proof

Alcock¹

2010

Research in Collegiate Mathematics Education. VII

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Abstract. This paper reports on an exploratory study of mathematicians' views on the teaching and learning that occurs in a course designed to introduce students to mathematical reasoning and proof. Based on a sequence of interviews with five mathematicians experienced in teaching the course, I identify four modes of thinking that these professors indicate are used by successful provers. I term these instantiation, structural thinking, creative thinking and critical thinking. Through the mathematicians' comments, I explain these modes and highlight ways in which students sometimes fail to use them effectively. I then discuss teaching strategies described by the participants, relating these to the four modes of thinking. I argue that teaching aimed at improving structural thinking tends to dominate, and that courses that introduce proof, regardless of classroom organization, should address all four modes in a balanced and integrated way.

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High school geometry students' justification for their views of empirical evidence and mathematical proof

Cited by 241 publications

References 6 publications

Tracing the change in discourse in a collaborative dynamic geometry environment: From visual to more mathematical

Tracing the change in discourse in a collaborative dynamic geometry environment: From visual to more mathematical

İlköğretim Matematik Öğretmen Adaylarının Üçgenlerin Öğretiminde Geometrik İspatları Kullanabilme Becerileri

Mathematicians’ perspectives on the teaching and learning of proof

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