The Benefits and Limits of Social Interaction: The Case of Mathematical Proof

Balacheff, Nicolas

doi:10.1007/978-94-017-2195-0_9

Cited by 58 publications

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“…However, as a number of scholars have suggested at various times (e.g., Balacheff 1991;Bell 1976;DeVilliers 1990;Hanna 1990;Hersh 1993;Lakatos 1976), proof has other critical functions in mathematics in addition to verification. In particular, DeVilliers (1990) proposed that mathematical proof has six interrelated roles: verification, explanation, communication, discovery, systematization, and intellectual challenge.…”

Section: Theoretical Background Perspective On the Function Of Proof mentioning

confidence: 99%

Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof

Stylianou

Blanton

Rotou

2015

Int. J. Res. Undergrad. Math. Ed.

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This article presents the results from a study of 535 early undergraduate students at six universities that was designed to describe their views of the meaning of proof and how these views relate to their attitudes and beliefs towards proof and their classroom experiences with learning proof. Results show that early undergraduate students have difficulty with mathematical proof. In particular, the study showed that students' proof choices were strongly influenced by surface characteristics of the tasks. However, a large number of students appear to appreciate and acknowledge the rigor and central role of deductive proof in mathematics despite the difficulties they may face in producing proofs. Further, the study showed a strong positive relationship between students' beliefs about the role of proof and themselves as learners of proof, but weak relationship between proof ability and self-reported experiences with learning proof. Keywords Mathematical proof . Deduction . AttitudesArguments that the Bessence of mathematics lies in proofs^ (Ross 1998, p. 2) and that Bproof is not a thing separable from mathematics…. [but] is an essential component of doing, communicating, and recording mathematics^ (Schoenfeld 1994, p. 76) reinforce the centrality of proof in mathematical thinking. Moreover, not only does the act of proof Bdistinguish mathematical behavior from scientific behavior in other disciplinesÎ nt. J. Res. Undergrad. Math. Ed. (2015) (Dreyfus 1990, p. 126), it also serves as a tool for learning mathematics (Hanna 1990(Hanna , 1995Hersh 1993 MAA 2000), has emphasized this goal and has recommended that proof should be a part of students' mathematical experiences-especially of those students in mathematics-related programs. The report states that Bstudents should understand and appreciate the core of mathematical culture: the value and validity of careful reasoning, precise definition and close argument^(p. 6). Yet, research in mathematics education indicates that most students, in particular at the secondary school level, face substantial difficulties with proof (see Harel and Sowder 2007;Stylianou et al. 2009 for reviews). There also is evidence that college students face similar difficulties with proof as their high school counterparts. Most notably, Harel and Sowder (1998) showed that college students focus their attention on the format of the proof rather than the content. However, we know little about the conceptions of students as they are beginning to immerse themselves in college mathematics. Perhaps more importantly, we have not yet explored the relationship between students' understanding of proof and their beliefs towards proof. Indeed, we now know that mathematics performance in general, and the reading and writing of proofs in mathematics in particular, is a complex one that depends on a wide expanse of beliefs, knowledge, and cognitive skills and that is uniquely shaped by the realm in which learning occurs (Heinze et al. 2005). It is not at all clear, however, which of these beli...

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Section: Theoretical Background Perspective On the Function Of Proof mentioning

confidence: 99%

Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof

Stylianou

Blanton

Rotou

2015

Int. J. Res. Undergrad. Math. Ed.

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“…Other researchers stress the role of discourse in the mathematics classroom in reasoning and proof (Balacheff, 1991;Hanna, 1991;Maher, 1995Maher, , 2008. Balacheff (1991) differentiates between argumentation and mathematical proof by describing argumentation as a mathematical conversation intended to convince another student of the validity of an argument, and proof as an explanation that is accepted by a the larger community.…”

Section: The Role Of Community In Reasoning and Proofmentioning

confidence: 99%

“…Balacheff (1991) differentiates between argumentation and mathematical proof by describing argumentation as a mathematical conversation intended to convince another student of the validity of an argument, and proof as an explanation that is accepted by a the larger community. In contrast, he defines mathematical proof as meeting "the requirement for the use of some knowledge taken from a common body of knowledge on which people (mathematicians) agree" (p. 189).…”

Section: The Role Of Community In Reasoning and Proofmentioning

confidence: 99%

“…In this way, arguments can be shared and new, revised arguments can be coconstructed. Researchers also maintain that participating in discussions about mathematical ideas in a community of learners leads to mathematical reasoning (Balacheff, 1991;Cobb, Stephan, McClain, & Gravemeijer, 2001;Maher, Powell, Weber, & Lee, 2006). Cobb (2000) stresses the relationship between an individual student's ways of thinking and the overall classroom practices in building students' mathematical understanding.…”

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Learning to reason in an informal math after-school program

Mueller

Maher

2009

Math Ed Res J

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This research was conducted during an after-school partnership between a University and school district in an economically depressed, urban area. The school population consists of 99% African American and Latino students. During an the informal after-school math program, a group of 24 6th-grade students from a low socioeconomic community worked collaboratively on open-ended problems involving fractions. The students, in their problem solving discussions, coconstructed arguments and provided justifications for their solutions. In the process, they questioned, corrected, and built on each other's ideas. This paper describes the types of student reasoning that emerged in the process of justifying solutions to the problems posed. It illustrates how the students' arguments developed over time. The findings of this study indicate that, within an environment that invites exploration and collaboration, students can be engaged in defending their reasoning in both their small groups and within the larger community. In the process of justifying, they naturally build arguments that take the form of proof.

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“…A TI estuda a transposição dos saberes sábios para o meio digital, de acordo com as exigências específicas dos meios eletrônicos. Em outras palavras, é o processo em que o conhecimento, tendo origem em um saber sábio de referência e sendo dirigido para determinado saber aprendido pelo estudante, passa, necessariamente, por uma modelização informatizada (BALACHEFF, 1991). No nosso entendimento, a TI parte de um pressuposto fundamental da TD -a transposição de um conhecimento de uma determinada área do saber para outra -porém possui especificidades relacionadas aos meios digitais.…”

Section: Introductionunclassified

Práticas de ensino de língua portuguesa com as TDIC

Caiado

Morais

2013

ETD - Educ. temat. digit.

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RESUMO:O objetivo desta pesquisa foi investigar o processo pedagógico que envolvia as práticas das professoras de Língua Portuguesa (doravante LP), especificamente, como elas utilizavam as novas Tecnologias Digitais da Informação e Comunicação (doravante TDICs) no ensino-aprendizagem de LP, nos anos finais do Ensino Fundamental. Realizamos um estudo qualitativo no qual observamos as aulas de três professoras de LP pertencentes a redes de ensino diferentes: federal, estadual e privada. Estabelecemos categorias de análise, que emergiram da observação da práxis das professoras. Em seu marco teórico, a presente pesquisa se inscreve nos estudos sobre transposição didática, transposição informática, multiletramentos e letramento digital, assumindo como perspectiva teórica a linguagem em sua natureza social e dialógica, produzida como ação humana. Constatamos que as três professoras possuíam práticas diferenciadas no que concerne ao uso das TDICs. Os resultados sinalizaram para a falta ou carência na formação de algumas professoras para a utilização da tecnologia digital como meio de aprendizagem e revelaram a sua utilização como fator motivacional na maior parte das aulas de LP. Acreditamos que há necessidade de a instituição escolar modificar seus currículos de LP e assumir, em seu projeto político-pedagógico, as TDICs na qualidade de elementos estruturantes de novos processos educativos.Palavras-chave: Ensino-aprendizagem. Língua portuguesa. Prática pedagógica. Tecnologia digital. PRACTICE TEACHING OF PORTUGUESE LANGUAGE WITH TDICABSTRACT:The objective of this research was to investigate the educational process involving the practices of teachers of Portuguese Language (henceforth LP), specifically, how they used the new digital technologies of information and communication (henceforth TDIC) in teaching-learning of LP, in the final years of elementary school. We conducted a qualitative study in which we observed three classes of LP teachers belonging to different school systems: federal, state and private. Established categories of analysis , which emerged from the observation of the practice of teachers. In his theoretical framework, this research is included in the studies of didactic transposition, transposition computer , multiliteracies and digital literacy , assuming as a theoretical perspective the language in its social and dialogical nature, produced as human action. We note that the three teachers had different practices regarding the use of TDIC. The results signaled the absence or lack the training of some teachers to use digital technology as a means of learning and showed its use as a motivational factor in most classes of LP. We believe there is a need for educational institutions to modify their curriculums of LP and take in his political pedagogical project, TDIC as the structural elements of new educational processes.

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The Benefits and Limits of Social Interaction: The Case of Mathematical Proof

Cited by 58 publications

References 4 publications

Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof

Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof

Learning to reason in an informal math after-school program

Práticas de ensino de língua portuguesa com as TDIC

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