Intuitive Functional Concepts: A Baseline Study on Intuitions

Dreyfus, Tommy; Eisenberg, Theodore

doi:10.2307/749011

Cited by 48 publications

(24 citation statements)

References 11 publications

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“…He found Tall's (1992) discussion of cognitive roots to be a useful idea for introducing functions but also wanted to focus on the structural aspects of functions. Dreyfus & Eisenberg (1982) describe the objectification of the function concept as the "transition to the conception of a function as a single mathematical entity" (p. 120). Others have used similar language in their discussions of students' processes of symbolizing mathematical ideas (Sfard, 1995;Cobb, Boufi, McClain, & Whitenack, 1997).…”

Section: Personally Relevant Function Problemsmentioning

confidence: 99%

“…Functions, in particular, have been analyzed from the students' perspective (Dreyfus & Eisenberg, 1982;Even, 1993;Tall, 1992). Tall (1992) approached the idea of informal knowledge by defining a cognitive root as an approach or problem that builds on students' informal knowledge and also provides a foundation for mathematical development (p. 497).…”

Section: Relevant Taskmentioning

confidence: 99%

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Examining Mathematics Classroom Interactions: Elevating Student Roles in Teaching and Learning

Kent¹

2017

INT J EDUC METHODOL

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Abstract:This article introduces a model entitled, "Responsive Teaching through Problem Posing" or RTPP, that addresses a type of reform oriented mathematics teaching based on posing relevant problems, positioning students as experts of mathematics, and facilitating discourse. RTPP incorporates decades of research on students' thinking in mathematics and more recent research on responsive teaching practices. Two classroom case studies are presented. A high school unit on functions is explored utilizing individual research on the part of the teacher to enact RTPP lessons. A middle school teacher enacts a RTPP lesson on proportions and utilizes this model to bridge students' incorrect additive reasoning strategies with correct multiplicative reasoning strategies. The results showed that both teachers were able to elevate students' roles in classroom discussions through implementation of RTPP. Individual research conducted by the high school teacher informed his RTPP approach while participation in professional development sessions with a classroom embedded component influenced the middle school teacher's enactment of RTPP lessons. Both teachers used specific teacher moves within RTPP to relinquish their role as mathematics experts in order to elevate their students' roles in classroom discussions. The RTPP cycle is offered as a potential model for studying mathematics teaching and learning across a variety of secondary mathematics classrooms.

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Section: Personally Relevant Function Problemsmentioning

confidence: 99%

Section: Relevant Taskmentioning

confidence: 99%

Examining Mathematics Classroom Interactions: Elevating Student Roles in Teaching and Learning

Kent¹

2017

INT J EDUC METHODOL

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“…Function is an essential concept in mathematics and it affects the whole mathematics curriculum (Laughbaum, 2003;Knuth, 2000;Beckmann, Thompson & Senk, 1999;Cooney, 1999;Dossey, 1999;Hitt, 1998;Dreyfus & Eisenberg, 1982). NCTM (1989) standards also stress "one of the central themes of mathematics is the study of patterns and functions."…”

Section: Understanding Of Function Conceptmentioning

confidence: 99%

“…It would have been much more appropriate to draw the diagram of the given expression. Dreyfus and Eisenberg (1982) say that multiple representations of functions as tables, arrow diagrams, graphs, formulas or verbal descriptions make it`s understanding difficult. Thompson (1994) stresses that the idea of multiple representations was built without careful thinking and it must be based upon the concept of multiple.…”

Section: A: It Is Not Because X = ±1 and Has Double Values (She Thenmentioning

confidence: 99%

Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts

Dede

Soybaş

2011

EURASIA J MATH SCI T

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The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers' understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were collected by a questionnaire and semi-structured interviews and analyzed using existential-phenomenology. The results show that the experiences of preservice math teachers related to these concepts can be summarized under six different titles, namely, confusion of the definition of function with one-to-one and onto properties, relating it with daily life (exampling), failure to take the functioning conditions into account, the relation between the values which make the function zero and roots of the equation, multiple representations of functions and taking the defining set of functions and equations into account .

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“…The strong algebraic approach in Shanghai particularly affected how the textbook introduced the concept first and the local property of gradient. A potential drawbacks to this algebraic approach is its abstraction because it is suggested that only children between 11 and 14 years old can understand the algebraic concept at the formal operations stage (Dreyfus & Eisenberg, 1982), though Grade 8 students in Shanghai are normally approxmately 14 years old. Lue (2013) concluded that the algebraic expression is the most challenging representation to be handled, even by Grade 10 students in Taiwan, after having examined the translations between representations within six kinds of elementary functions including linear function.…”

Section: Discussionmentioning

confidence: 99%

Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai

Yu-qian

Barmby

Bolden

2015

Int J of Sci and Math Educ

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Intuitive Functional Concepts: A Baseline Study on Intuitions

Cited by 48 publications

References 11 publications

Examining Mathematics Classroom Interactions: Elevating Student Roles in Teaching and Learning

Examining Mathematics Classroom Interactions: Elevating Student Roles in Teaching and Learning

Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts

Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai

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