Justification in the mathematics classroom: A study of prospective elementary teachers

Simon, Martin; Blume, Glendon W.

doi:10.1016/s0732-3123(96)90036-x

Cited by 144 publications

(86 citation statements)

References 13 publications

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“…For example, one might hope that students would explain their reasoning in science or history classes as well as in mathematics. In contrast, sociomathematical norms focus on regularities in classroom actions and interactions that are specific to mathematics (Hershkowitz & Schwartz, 1999;McClain & Cobb, 2001a;Sfard, 2000a;Simon & Blume, 1996;Voigt, 1995;Yackel & Cobb, 1996). Examples of sociomathematical norms include the criteria that are established in a particular classroom for what counts as a different mathematical solution, a sophisticated mathematical solution, and an efficient mathematical solution, as well as for what counts as an acceptable mathematical explanation.…”

Section: Data Sources and Methods Of Analysismentioning

confidence: 99%

Learning About Statistical Covariation

Cobb

McClain²,

Gravemeijer³

2003

Cognition and Instruction

135

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In this article, we report on a design experiment conducted in an 8th grade classroom that focused on students' analysis of bivariate data. Our immediate goal is to document both the actual learning trajectory of the classroom community and the diversity in the students' reasoning as they participated in the classroom mathematical practices that constituted this trajectory. On a broader level, we also focus on the learning of the research team by documenting the conjectures about the students' statistical learning and the means of supporting it that the research team generated, tested, and revised on-line while the experiment was in progress. In the final part of the article, we synthesize the results of this learning by proposing a revised learning trajectory that can inform design and instruction in other classrooms. In doing so, we make a contribution to the cumulative development of a domain-specific instructional theory for statistical data analysis.Our purpose in this article is to report on a 14-week classroom design experiment conducted with a group of eighth-grade students that focused on statistical covariation. In presenting the analysis, we focus on both the trajectory of the students' learning and our own learning about the means of supporting the students' learning. This latter issue, the learning of the research team, is central to the design experiment methodology, in that conjectures about the trajectory of students' learning are tested and modified on-line while experimenting in a Requests for reprints should be sent to Paul A. Cobb,

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Section: Data Sources and Methods Of Analysismentioning

confidence: 99%

Learning About Statistical Covariation

Cobb

McClain²,

Gravemeijer³

2003

Cognition and Instruction

135

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“…Chazan, 1993;Moore 1994). The difficulty in understanding the nature of proof has also been reported among prospective elementary school teachers (Simon, 1996) and experienced high school teachers (Knuth, 2002). Understanding the nature of proof, in addition to its theoretical interest, seems essential for thinking about how to teach students about proof, both at the university level and throughout the K-12 level, as is recommended by the new NCTM standards (NCTM, 2000).…”

Section: Public and Private Aspects Of Proofmentioning

confidence: 96%

Untitled

Raman¹

2003

Educational Studies in Mathematics

102

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“…Regarding the issue of persistence, the Education Committee of the European Mathematical Society (2011a) noted that the misconception is held by many students and in many countries (i.e., the problem is widespread) and that many students continue to hold the misconception even after explicit instruction about the nature of proof (i.e., the problem is also resistant to remediation). Other problems that meet our definition of key and persistent problems of students' learning in the area of proof include the misconception that a single counterexample is insufficient to refute a false mathematical generalization (e.g., Mason & Klymchuk, 2009;Simon & Blume, 1996) or the misconception that a conditional statement is equivalent to its converse (e.g., Hoyles & Küchemann, 2002;Yu, Chin, & Lin, 2004). In Stylianides and Stylianides (in press) we discuss three characteristics that we consider important for researchers to take into account as they design classroom-based interventions to address key and persistent problems of students' learning in the area of proof: (1) the interventions have an explanatory theoretical framework about how they Bwork^or Bcan work^in relation to their impact on students' learning; (2) they have a narrow and well-defined scope, which makes it possible for them to have a relatively short duration; and (3) they have an appropriate mechanism to trigger and support conceptual change.…”

Section: The Futurementioning

confidence: 99%

Research-based interventions in the area of proof: the past, the present, and the future

Stylianides

2017

Educ Stud Math

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The concept of proof has attracted considerable research attention over the pastdecades in part due to its indisputable importance to the discipline of mathematics and tostudents' learning of mathematics. Yet, the teaching and learning of proof is an instructionallyarduous territory, with proof being recognized as a hard-to-teach and hard-tolearn concept atall levels of education. Prior research has examined, documented, and cast light on theprocesses underpinning different problems of classroom practice in the area of proof, buthas paid less emphasis on acting upon such problems to generate possible solutions throughresearch-based interventions in mathematics classrooms. In this Editorial, we first situate thecontributions in this Special Issue in a brief chronological account of scholarly work on research-based interventions in the area of proof, and we conclude with a proposal for somehigh-leverage directions for future research.Keywords Proof . Interventions . Classroom-based research . Teaching . Learning . MathematicsIn this Editorial, we offer a brief chronological account of scholarly work on research-based interventions in the area of proof. We begin with a consideration of the past in order to situate the Special Issue, which reflects the present state of research in this area. We conclude with a projection into the future by looking ahead 15 or 20 years from now and thinking what we would like intervention-oriented research in the area of proof to accomplish by that time.

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Justification in the mathematics classroom: A study of prospective elementary teachers

Cited by 144 publications

References 13 publications

Learning About Statistical Covariation

Learning About Statistical Covariation

Untitled

Research-based interventions in the area of proof: the past, the present, and the future

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