Looking For and Using Structural Reasoning

Hawthorne, Casey; Druken, Bridget K.

doi:10.5951/mathteacher.112.4.0294

Cited by 8 publications

(3 citation statements)

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“…Finally, students from experiment 2 developed structural awareness [89] when combining cubes in distinct possibilities to obtain cuboids of a minimum surface area for a given volume. This structural type of reasoning [90] was also highlighted by the students in experiment 4 upon constructing planar and spatial fractals. As the complexity of the fractals increased, as in the case of the Menger sponge, students developed structural awareness in order to determine not only the number of copies needed to construct the next iteration, but also the positions in which they had to be placed within the three-dimensional space.…”

Section: Influence On Mathematics Activitymentioning

confidence: 55%

The Influence of NeoTrie VR’s Immersive Virtual Reality on the Teaching and Learning of Geometry

2021

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The use of dynamic, three-dimensional software with virtual reality offers new possibilities for the teaching and learning of geometry. We explore the effects of introducing the immersive virtual reality software NeoTrie VR in real classes. Within a Design Research framework, we present qualitative observational data to report how the collaboration among a software development company, university researchers, and schools produces improvements in the design and updating of the software; the geometrical content, representations, and mathematical activity that students have access to as well as the way teachers conceive and manage the teaching of geometry.

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Section: Influence On Mathematics Activitymentioning

confidence: 55%

The Influence of NeoTrie VR’s Immersive Virtual Reality on the Teaching and Learning of Geometry

2021

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“…A major goal of mathematics education is to nurture the view that conceives of mathematics as a field of intricately related structures rather than a series of computations to be carried out. Researchers have used "structural sense" (Hoch & Dreyfus, 2004), "structural thinking" (Mason, Stephens, & Watson, 2009;Mulligan & Mitchelmore, 2012), and "structural reasoning" (Harel & Soto, 2017;Hawthorne & Druken, 2019) to capture the habit of looking for and making use of mathematical structure.…”

Section: Literature Review and Theoretical Background Empirical And Smentioning

confidence: 99%

Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities

Yao¹,

Elia²

2021

INT ELECT J MATH ED

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Mathematical generalization can take on different forms and be built upon different types of reasoning. Having utilized data from a series of task-based interviews, this study examined connections between empirical and structural reasoning as preservice mathematics teachers solved problems designed to engage them in constructing and generalizing mathematical ideas aided by digital tools. The study revealed closer connections between naïve empiricism and result pattern generalization, between naïve empiricism and recognizing a structure in thought, between reasoning by generic example and process pattern generalization, and between reasoning by generic example and reasoning in terms of general structures. Results from this study imply that the ability to generalize based on perception and numerical pattern does not necessarily lead learners to generalize based on mathematical structure.

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“…Thus, the students were not able to "recognise an algebraic expression or sentence as a previously met structure" (Hoch & Dreyfus, 2005, p. 51). Put differently, the students failed to recognise similar mathematical properties in different forms (Hawthorne, & Druken, 2019). In contrast to applying set of procedures automatically as discoraged by Hawthorne and Drunken, by applying the rules of logarithms, the function 𝑦 = ln(cos 𝑥 tan 5𝑥) could have been written as its equivalent 𝑦 = ln(cos 𝑥) + ln(tan 5𝑥) before finding its derivative.…”

Section: Prospective Teachers' Mathematical Knowledge Of Equivalencementioning

confidence: 99%

We need to make up for the gap: University student teachers’ difficulties associated with basic algebraic manipulations

Mbhiza

MUTHELO

Chuene

2021

Journal for the Education of Gifted Young Scientists

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It is irrefutable that preparing successful mathematics teachers is a complex task, marked by a convergence of studies in content knowledge and instructional technologies. Considering the increasing number of students enrolling in South African teacher training institutions, it is essential to determine what mathematical knowledge gaps and understanding they bring from secondary school level for the purpose of configuring best strategies to prepare them to become effective teachers. This is the context for a study of first year undergraduate mathematics education students at the University of Limpopo. In this paper, we present our autoethnographical experiences of lecturing calculus courses for a teacher preparation programme. In this paper, we use autoethnography reflexivity to illustrate intersections between self and university society, the particular and the general, the personal and the politics of mathematical knowledge. The patterns that emerged from our interactions with students revealed that they experienced difficulties in understanding basic algebraic procedures and recognising structure to solve algebraic problems in the context of differentiation. This made us aware that we needed to configure effective strategies to make up for the identified elementary mathematics knowledge gaps, which we assumed students brought with from Grade 12. Our quest to make up for the algebraic knowledge gaps does not only serve the purpose of enabling our student teachers' mathematical knowledge, but to ensure that they develop good knowledge base needed to teach the subject during their training as well as once they qualify as teachers.

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Looking For and Using Structural Reasoning

Abstract: Examples of solving equations and inequalities, analyzing quadratic expressions, and reasoning with functions show three ways to engage students in this mathematical practice.

Cited by 8 publications

References 0 publications

The Influence of NeoTrie VR’s Immersive Virtual Reality on the Teaching and Learning of Geometry

The Influence of NeoTrie VR’s Immersive Virtual Reality on the Teaching and Learning of Geometry

Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities

We need to make up for the gap: University student teachers’ difficulties associated with basic algebraic manipulations

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