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Yerushalmy, Michal

doi:10.1023/a:1009769330476

Cited by 15 publications

(2 citation statements)

References 5 publications

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“…In comparison to regular approaches, our intervention paid more attention to the recognition of function families and graph features, to part-graph exploration, and to the reasoning with and about formulas. In innovative approaches, graphing tools have been used to learn to reason about functions using the structure of the formula, for instance, the composition and translation of graphs (Schwartz & Yerushalmy, 1992;Yerushalmy, 1997;Yerushalmy & Gafni, 1992), about the role of parameters (Drijvers, 2003;Heid et al, 2013), and about special function families (Heid et al, 2013). Pierce and Stacey (2007) suggested highlighting the formula's structure and key features when considering graphs in classroom discussions.…”

Section: Discussionmentioning

confidence: 99%

“…An essential aspect in our approach was the explicit focus on qualitative reasoning. The importance of this kind of reasoning and its omission in mathematics curricula has been stressed by Leinhardt et al (1990), Goldenberg, Lewis, and O'Keefe (1992), Yerushalmy (1997), andDuval (2006), who have indicated that qualitative reasoning could support the construction of meaning and understanding through its global focus. To our knowledge, this idea has never been applied in concrete and systematic teaching approaches.…”

Section: Discussionmentioning

confidence: 99%

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Promoting insight into algebraic formulas through graphing by hand

Kop

Janssen

Drijvers

et al. 2020

Mathematical Thinking and Learning

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Student insight into algebraic formulas, including the ability to identify the structure of a formula and its components and to reason with and about formulas, is an issue in mathematics education. In this study, we investigated how 16-and 17-year-old pre-university students' insight into algebraic formulas can be promoted through graphing formulas by hand. In an intervention of five 90-min lessons, 21 grade 11 students were taught to graph formulas by hand. The intervention's design was based on experts' strategies in graphing formulas, that is, using a combination of recognition and qualitative reasoning, and on principles of teaching complex skills. To assess the effect of this intervention, pre-, post-, and retention tests were administered, as well as a post-intervention questionnaire. Six students were asked to think aloud during the pre-and posttests. The results show that all students improved their abilities to graph formulas by hand. The think-aloud data suggest that the students improved both on recognition and reasoning, and give a detailed picture of how students used recognition and qualitative reasoning in combination. We conclude that graphing formulas by hand, based on the interplay of recognition and qualitative reasoning, might be a means to promote students' insight into algebraic formulas.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Promoting insight into algebraic formulas through graphing by hand

Kop

Janssen

Drijvers

et al. 2020

Mathematical Thinking and Learning

View full text Add to dashboard Cite

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An Instrumental Approach to Mathematics Learning in Symbolic Calculator Environments

Trouche¹

Mathematics Education Library

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International audienceA rapid technological evolution (Chapter 1), linked to profound changes within the professional field of mathematics (Chapter 3), brings into question the place of techniques in mathematics teaching (Chapter 5). These changes have created serious difficulties for teachers; obliged to question their professional practices, they make different choices regarding integration of new technologies and techniques (Chapter 4), choices that are linked to their mathematical conceptions and to their teaching styles.In this chapter, we place ourselves on the side of the students. We have already seen (Chapter 1) that they seem to adopt the new computing tools faster than the institution. In this chapter, we study more precisely their learning processes related to their use of symbolic calculators.First of all, we pinpoint the didactic phenomena taking place in the experiments; subsequently, we suggest a new theoretical approach aimed at giving a better description, for each student, of the transformation of a technical tool into an instrument for mathematical work

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