Use of models in the teaching of linear algebra

Possani, Edgar; Trigueros, María; Preciado, J.G.; Lozano, María del Carmen Núñez

doi:10.1016/j.laa.2009.05.004

Cited by 46 publications

(36 citation statements)

References 5 publications

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“…Our data show that this is not necessarily the case; the students in our study were able to use Computational thinking in a variety of sophisticated, productive, and reflective ways, including generating Computational justifications for claims and making strategic choices to limit the complexity of their calculations. Our work thus joins the body of literature presenting an optimistic picture of student reasoning in linear algebra (e.g., Possani et al 2010;Wawro 2014;Wawro et al 2012), and provides evidence for the utility of Computational reasoning. We also hope to have provided evidence for the analytic usefulness of including reasoning processes within the construct of Computational thinking.…”

Section: Discussionsupporting

confidence: 63%

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Students’ Use of Computational Thinking in Linear Algebra

Bagley

Rabin

2015

Int. J. Res. Undergrad. Math. Ed.

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In this work, we examine students' ways of thinking when presented with a novel linear algebra problem. Our intent was to explore how students employ and coordinate three modes of thinking, which we call computational, abstract, and geometric, following similar frameworks proposed by Hillel (2000) and Sierpinska (2000). However, the undergraduate honors linear algebra students in our study used the computational mode of thinking in a surprising variety of productive and reflective ways. This paper examines the solution strategies that the students employed to solve the problem, emphasizing their use of the computational mode of thinking.

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Section: Discussionsupporting

confidence: 63%

“…They showed that students continue to draw on these concrete images later as they work on more abstract tasks. Possani et al (2010) similarly used a realistic traffic modeling task to generate concept images for systems of linear equations and their solution methods.…”

Section: Literature Reviewmentioning

confidence: 99%

Students’ Use of Computational Thinking in Linear Algebra

Bagley

Rabin

2015

Int. J. Res. Undergrad. Math. Ed.

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“…Working with modelling and APOS frameworks Possani et al (2010) leveraged students' intuitive ways of thinking through a genetic composition of linear independence and systems of equations. Student use of different modes of representation in making sense of the formal notion of subspace was analysed by Wawro, Sweeney and Rabin (2011a), and their results suggest that in generating explanations for the definition, students rely on their intuitive understandings of subspace, which can be problematic but can also help develop a more comprehensive understanding of subspace.…”

Section: Linear Algebramentioning

confidence: 99%

Key Mathematical Concepts in the Transition from Secondary School to University

Thomas

Druck

Huillet

et al. 2015

The Proceedings of the 12th International Congress on Mathematical Education

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This report1 from the ICME12 Survey Team 4 examines issues in the transition from secondary school to university mathematics with a particular focus on mathematical concepts and aspects of mathematical thinking. It comprises a survey of the recent research related to: calculus and analysis; the algebra of generalised arithmetic and abstract algebra; linear algebra; reasoning, argumentation and proof; and modelling, applications and applied mathematics. This revealed a multi-faceted web of cognitive, curricular and pedagogical issues both within and across the mathematical topics above. In addition we conducted an international survey of those engaged in teaching in university mathematics departments. Specifically, we aimed to elicit perspectives on: what topics are taught, and how, in the early parts of university-level mathematical studies; whether the transition should be smooth; student preparedness for university mathematics studies; and, what university departments do to assist those with limited preparedness. We present a summary of the survey results from 79 respondents from 21 countries.

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“…Larson, Rasmussen, Zandieh, Smith, and Nelipovich (2007), Sierpinska (2000), Possani, Trigueros, Preciado, and Lozano (2010), among others, have found that both teachers and students consider this subject difficult. They have carried out research to study the obstacles that students face when learning concepts of Linear Algebra, how students learn its different concepts, and how they can be helped in the learning process.…”

Section: Introductionmentioning

confidence: 98%