Limits of Functions as They Developed Through Time and as Students Learn Them Today

This paper discusses an approach to mathematics education based on the concept of ethical responsibility. It argues that an ethical approach to mathematics teaching lays the theoretical foundations for social justice concerns in the discipline. The paper develops a particular understanding of ethical responsibility based on the writings of Emanuel Levinas and discusses its implication for decision making on the curriculum and pedagogy in mathematics education. The paper argues that such an approach is consistent with a critical mathematics approach; however, it highlights the need to balance the concern about equity with that of quality. The paper concludes that this ethical stance, rather than being a normative criteria which dictates a particular line of action in different situations, it establishes a means to reflect on action and policy towards the achievement of more equitable access to high quality mathematics education.

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“…Juter, 2006). This includes formalized symbolic language, axiomatic thinking, standard efficient algorithms and proofs.…”

Section: Supporting the Students' Response-ability Through The Curricmentioning

confidence: 99%

Socially Response-able Mathematics Education: Implications of an Ethical Approach

Atweh

Brady

2009

EURASIA J MATH SCI T

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“…Sirotic and Zazkis (2007) claimed that underdeveloped intuitions often are due to flaws in formal knowledge and an absence of algorithmic experience. Such a result was also drawn from a study on students learning limits of functions (Juter, 2006) where many students' intuitive perceptions were incoherent with the formal concept image leaving the students with two different representations, one for theory and one for problem solving. Links between intuitions, formal knowledge and algorithms are necessary for anyone to understand the topic at hand.…”

Section: Individual Knowledge Representationsmentioning

confidence: 87%

Learning analysis: students’ starting point

Juter¹

2009

Nordic Research in Mathematics Education

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“…In empirical studies aiming at comparing students' learning of mathematical concepts with the historical development of the same concept, the conclusion is often made that students' conceptual understanding corresponds to a specific time period in the historical development of the concept. Another conclusion that is often made is that students learn a specific concept in tandem with the historical development of that concept (see, for instance, Juter (2006) and Moreno and Waldegg (1991)). In this section we elucidate, in turn, three essential problems that may arise in these studies with reference to evolutionary arguments: the problem of not considering different conceptual frameworks, the problem of tacitly assuming a platonic perspective, and the problem of not considering differencies in cognitive levels.…”

Section: Problems Arising From Posing Parallelism Claimsmentioning

confidence: 99%

“…Let us consider one of Juter's (2006) conclusions in the study referred to above, where she claims that "the students with problems explaining the limit definition appeared to be mainly at the stage of Newton and Leibniz with a sense of what they do but lacking the means to strictly formulate and explain the concept of limits" (Juter, 2006, p. 427). 7 It seems unfair to compare a student of today (just about to learn the fundamental concepts of calculus) with Newton, Leibniz, or Euler.…”

Section: The Problem Of Not Considering Differencies In Cognitive Levelsmentioning

confidence: 99%

On the relations between historical epistemology and students’ conceptual developments in mathematics

Bråting

Pejlare

2015

Educ Stud Math

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There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students' conceptual developments in mathematics. We problematize this attempt to link the two fields on the basis of Grattan-Guinness' distinction between "history" and "heritage". We argue that when parallelism claims are made, history and heritage are often mixed up, which is problematic since historical mathematical definitions must be interpreted in its proper historical context and conceptual framework. Furthermore, we argue that cultural and local ideas vary at different time periods, influencing conceptual developments in different directions regardless of whether historical or individual developments are considered, and thus it may be problematic to uncritically assume a platonic perspective. Also, we have to take into consideration that an average student of today and great mathematicians of the past are at different cognitive levels.

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Limits of Functions as They Developed Through Time and as Students Learn Them Today

Cited by 17 publications

References 11 publications

Socially Response-able Mathematics Education: Implications of an Ethical Approach

Socially Response-able Mathematics Education: Implications of an Ethical Approach

Learning analysis: students’ starting point

On the relations between historical epistemology and students’ conceptual developments in mathematics

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