Representations and the psychology of mathematics education

Goldin, Gerald A.; Janvier, Claude

doi:10.1016/s0732-3123(99)80057-1

Cited by 42 publications

(14 citation statements)

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“…Again, a lot has been written about the use of representations in solving mathematical problems (Goldin, 1998;Goldin & Janvier, 1998;Kaput, 1998;Vergnaud, 1998). While this study focused on standard representations (written/verbal, equations, graphs or drawings, and tables), we also recognized that a student's own and others' non-standard representations play a role in their development and provided evidence of deep and connected SCK.…”

Section: Using Multiple Standard Representationsmentioning

confidence: 99%

Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

Bair

Rich

2011

Mathematical Thinking and Learning

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Section: Using Multiple Standard Representationsmentioning

confidence: 99%

Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

Bair

Rich

2011

Mathematical Thinking and Learning

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“…His book [7] is still interesting to read. More recently, the Working Group on Representations [8] synthesized four different interpretations of the term 'representations'. For a bibliography about representation systems, in particular for mathematical education, see [9, pp.…”

Section: Mental Imagery For Mathematics and Computer Sciencementioning

confidence: 99%

Using mental imagery processes for teaching and research in mathematics and computer science

Arnoux

Finkel

2010

International Journal of Mathematical Education in Science and

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“…Several research studies have addressed the issue of representations and suggest a theoretical context for them (cf. Goldin and Janvier 1998;Goldin and Kaput 1996;Kaput 1987;von Glasersfeld 1987), while others focus on the translation from one representation of a concept to another (Duval 2002;Slavit 1997). Recently, researchers have focused their attention to the debate concerning semiotics, signs, symbolizing, representations and the concomitant processes of meaning production (Hitt 2002).…”

Section: Designing the Activitiesmentioning

confidence: 99%

Employing genetic ‘moments’ in the history of mathematics in classroom activities

Farmaki

Paschos

2007

Educ Stud Math

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The integration of history into educational practice can lead to the development of activities through the use of genetic 'moments' in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas -developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric transformations and reconfigurations -to develop mathematical models that can be employed for the solution of problems relating to linear motion. The representation of distance covered as the area of the figure between the graph of velocity and the time axis employed in these activities, leads on naturally to the study of problems on motion by means of functions, as well as allowing for the use of tools (concepts and propositions) from Euclidean geometry of relevance to such problems. By employing simple geometric transformations, equivalent real life problems are obtained which lead, in turn, to a simple classification of all linear motion-related problems. When applied to a wider range of motion problems, this approach prepares the way for the introduction of basic Calculus concepts (such as integral, derivative and their interrelation); in fact, we would argue that it could be beneficial to teach the basic concepts and results of Calculus from an early grade by employing natural extensions of the teaching methods considered in this paper.

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Representations and the psychology of mathematics education

Cited by 42 publications

References 1 publication

Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

Using mental imagery processes for teaching and research in mathematics and computer science

Employing genetic ‘moments’ in the history of mathematics in classroom activities

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