Generic examples: Seeing the general in the particular

Mason, John; Pimm, David

doi:10.1007/bf00312078

Cited by 200 publications

(121 citation statements)

References 4 publications

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“…In the context of elementary grades, some authors highlight the students' use of different representations to express a general relationship. For example, Mason and Pimm (1984) describe the use of everyday language as a fundamental resource to express generalization and its use can have influence in the use of algebraic symbolism to express the generalization. Radford (2010) recognizes the importance of gestures as a way to express generalization.…”

Section: Generalizationmentioning

confidence: 99%

Generalization in fifth graders within a functional approach

Pinto

Cañadas

2018

pna

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Section: Generalizationmentioning

confidence: 99%

Generalization in fifth graders within a functional approach

Pinto

Cañadas

2018

pna

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“…Justification types ranged from nonproof arguments including appeals to authority and empirical justifications to two forms of valid mathematical proofs, generic example proofs and deductive arguments. As described by Mason and Pimm (1984), a generic example refers to a specific example that is presented in such a way as to communicate generality across cases.…”

Section: Videocase Discussion Centered On Sckmentioning

confidence: 99%

Investigating Mathematical Knowledge for Teaching Proof in Professional Development

Lesseig

2016

IJRES

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Research documenting teachers' fragile understanding of proof and how it is advanced suggests that enhancing the role of proof in school mathematics will demand substantial teacher learning. To date, there is little research detailing what mathematical knowledge might support the teaching of proof or how professional development (PD) might afford such learning. This paper advances a framework for Mathematical Knowledge for Teaching Proof (MKT for Proof) that specifies proof knowledge across subject matter and pedagogical domains. To explore the utility of the framework, this paper examines data from four different PD settings in which teachers and leaders worked on the same proof-related task. Analysis of discussions across these four settings revealed similarities and differences in knowledge of proof made available in each setting. These findings provide a means to detail the MKT for Proof framework and demonstrate its usefulness as a tool for designing, analyzing and evaluating proof experiences in PD.

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“…This is a generic proof, that is "a proof carried out on a generic example" (LERON;ZASLAVSKY, 2013, p. 24). From the didactic point of view, the idea of generic example has been interpreted by Mason and Pimm (1984) as seeing the generic in the particular:…”

Section: The Idea Of Generic In Mathematicsmentioning

confidence: 99%

The Mathematical Work with the Derivative of a Function: Teachers’ Practices with the Idea of “Generic”

Panero

Arzarello²,

Sabena³

2016

Bolema

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This paper investigates the introduction of the derivative notion and, specifically, the introduction of the derivative function, as a significant moment in the development of mathematical work on functions. In particular, we analyse the process of genericization that two Italian teachers conducted with their grade 13 students, in order to make them shift from the derivative at a specific point x 0 to the derivative as a global function in the x variable. Specifically, we analyse the role of the teacher in the semiotic genesis of this process and investigate the role of semiotic resources therein. As a result, we highlight the importance of conducting carefully this shift from the pointwise x 0 sign to the global x sign, in order to gain an actual shift in the perceived properties of the derivative function, which depends on the x sign as a variable. In conclusion, we connect our findings to the model of the Mathematical Working Space of functions, with particular regard to the "visualisation" process and the semiotic axis.Keywords: Derivative Function. Generic. Perspectives on Functions. Calculus. ResumenEn este artículo se estudia la introducción de la noción de derivada, especialmente de la función derivada, como un momento significativo en el desarrollo del trabajo matemático relativo a las funciones. Particularmente, se analiza el procesos de genericización que dos profesores italianos conducen con sus estudiantes de último año de liceo, con el objetivo de de hacerlos pasar de la derivada en un punto específico x 0 a la derivada como una función global de la variable x. Específicamente, se analiza el rol del profesor en le génesis semiótica del proceso y se investiga el rol de los recursos semióticos implicados. Como resultado, se resalta la importancia de conducir cuidadosamente el paso desde el símbolo puntual x 0 al símbolo global x, para ganar un cambio real en las propiedades percibidas de la función derivada, que depende del símbolo x como variable. En conclusión, conectamos los resultados al modelo del espacio de trabajo matemático de funciones, con un particular énfasis en el proceso de "visualización" y el eje semiótico.Palabras claves: Función Derivada. Generico. Perspectivas en funciones. Cálculo.

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Generic examples: Seeing the general in the particular

Cited by 200 publications

References 4 publications

Generalization in fifth graders within a functional approach

Generalization in fifth graders within a functional approach

Investigating Mathematical Knowledge for Teaching Proof in Professional Development

The Mathematical Work with the Derivative of a Function: Teachers’ Practices with the Idea of “Generic”

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