Analyzing the written discourse in calculus textbooks over 42 years: the case of primary objects, concrete discursive objects, and a realization tree of the derivative at a point

Haghjoo, Saeid; Radmehr, Farzad; Ebrahim, Reyhani

doi:10.1007/s10649-022-10168-y

Cited by 6 publications

(2 citation statements)

References 58 publications

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“…The other 5 articles in Table 5 illustrate the vivid moment in the research on reading, writing, speaking and listening to mathematical language in school or university mathematics. We include examples that report studies on: words, grammar and linguistic patterns of additive word problems and how prospective elementary teachers analyse the mathematical language of these problems (Kwok et al, 2022); written mathematical languages and the related diagrammatic features in Iranian calculus textbooks (Haghjoo et al, 2022(Haghjoo et al, online/2023; linguistic challenges faced by student teachers of mathematics when reading the calculus sections of a mathematics textbook (Berger, 2019); cognitive and semantic challenges faced by novice and experienced undergraduate students in their reading of mathematical proofs and noticing of the mathematical-linguistic features (Dawkins & Zazkis, 2021); identification or development, in collaboration with teachers, of mathematical terminology and grammar for counting systems, measuring and comparing location and shapes in Indigenous mathematical languages (Edmonds-Wathen et al, 2019).…”

Section: Topic 5: Mathematical Language and Discoursementioning

confidence: 99%

Mathematics education research on language and on communication including some distinctions: Where are we now?

Planas

Pimm

2023

ZDM Mathematics Education

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In this article, we present a narrative review of mathematics education research on language and on communication over 2019–2022, but also look ahead by addressing challenges posed by the lack of distinction between language and communication. The persistence and significance of the problem of the distinction between language and communication are thus outlined in a historical moment of celebration of growth of research in the domain. Informed by the analysis of a selection of research journal articles and by our trajectories, we discuss influential topics in the recent discourse: multilingual mathematics classrooms; mathematics teacher education on language in mathematics teaching; multimodal mathematical communication; interaction and mathematics learning; mathematical language and discourse. We connect this with new emerging or old revisited concepts: instructional designing, gesturing, argumenting and languaging. We finish by further reflecting on multimodal mathematical communication and gesturing, and on the potential of expanding the notion of mathematics register towards a notion of mathematics communication register.

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Section: Topic 5: Mathematical Language and Discoursementioning

confidence: 99%

Mathematics education research on language and on communication including some distinctions: Where are we now?

Planas

Pimm

2023

ZDM Mathematics Education

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“…The role of textbooks as an opportunity to learn has received considerable attention in the research literature on the teaching and learning of K-12 mathematics. Among other things, this research has investigated students' opportunity to learn about mathematical topics such as linear functions and trigonometry (Wijaya et al, 2015), addition and subtraction of fractions (Alajmi, 2012;Charalambous et al, 2010), calculus (Haghjoo et al, 2023), probability (Jones & Tarr, 2007), statistics (Pickle, 2012), reasoning and proof (Stylianides, 2009;Thompson et al, 2012), proportional reasoning (Dole & Shield, 2008), and deductive reasoning (Stacey & Vincent, 2009).…”

Section: Introductionmentioning

confidence: 99%

Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study

Mkhatshwa

2023

EURASIA J Math Sci Tech Ed

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This study investigated opportunities to learn about optimization problems provided by undergraduate calculus textbooks. To accomplish this, we analyzed examples and practice problems from two calculus textbooks widely used in the teaching of calculus in the United States. Findings of this study indicate that a majority of the problems in both textbooks lack realistic and essential contexts, have matching or missing information, and require a low cognitive demand to solve. Setting up objective functions is either not necessary or it is straightforward for most problems in the two textbooks. In addition, both textbooks provide ample opportunities to interpret critical numbers and extrema in context. Overall, findings of this study suggest the existence of a relationship between known students’ difficulties with solving optimization problems and the opportunities to learn about optimization problems provided by calculus textbooks. Implications for several stakeholders, including calculus textbook authors and calculus instructors are discussed.

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Fostering pre-service teachers’ attention to mathematical objects: The realization tree mediator as a teaching representation

Weingarden,

Heyd-Metzuyanim

2024

J Math Teacher Educ

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Analyzing the written discourse in calculus textbooks over 42 years: the case of primary objects, concrete discursive objects, and a realization tree of the derivative at a point

Cited by 6 publications

References 58 publications

Mathematics education research on language and on communication including some distinctions: Where are we now?

Mathematics education research on language and on communication including some distinctions: Where are we now?

Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study

Fostering pre-service teachers’ attention to mathematical objects: The realization tree mediator as a teaching representation

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