Modules as Learning Tools in Linear Algebra

Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff; Loch, Sergio

doi:10.1080/10511970.2013.867293

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…For example, Cooley et al (2007) developed a linear algebra course combined with learning about APOS theory and found the focus on a theory for how mathematical knowledge is generated enriched understanding of linear algebra. Another group of researchers used a design research approach simultaneously creating instructional sequences and examining students' reasoning about key concepts such as eigenvectors and eigenvalues, linear independence, linear dependence, span, and linear transformation (Henderson et al 2010;Larson et al 2008;Sweeney 2011).…”

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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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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“…Several studies emphasized the use of DGE for the visualization, especially in Geometer's Sketchpad (Gol Tabaghi, 2014;Caglayan, 2015) and GeoGebra (Beltrán-Meneu, Murillo-Arcila, & Albarracin, 2016;Turgut, 2019). Cooley et al (2014) availed themselves of the affordances of GeoGebra to aid students' visualization of the ways in which points on polygons are transformed. Turgut (2019) presents a careful analysis of students' use of the dragging tool in GeoGebra to make sense of transformations matrix, using a lens of semiotic mediation.…”

Section: Literature Reviewmentioning

confidence: 99%

Interactive Tools for Linear Algebra: Geouniud

Lepellere

Zucconi

Asbahi

et al. 2020

SIE

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GeoUniud is a user-friendly platform built-in interactive tutors which allow students to investigate specific tasks by selecting their own input values and working through a problem in a step-by-step fashion together with immediate feedback at each step. Lessons and exercises are stored and organized with a careful use of randomized controlled contents as exercises, geometrical pictures and abstract reasoning. The lessons are augmented by a virtually infinite collection of examples, and by interactive representations of concepts. As example we show the design of two interactive tools about linear transformation and change of basis in order to develop students’ sense-making in a dynamic geometry environment (DGE) within the perspective of semiotic mediation.

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“…The PLC began with an online reading seminar on learning theories and moved to project meetings at each other's campuses at which we used the knowledge of the learning theories to develop carefully planned materials, which we called modules, that were appropriate for the different institutions and their students. The researchers have described the development and implementation of these materials elsewhere (Cooley, Vidakovic, Martin, Dexter, Suzuki, and Loch, 2014;Cooley & Vidakovic, 2013;Cooley, Vidakovic, Martin, Dexter, Suzuki, and Loch, 2013;Martin, Loch, Cooley, Dexter and Vidakovic, 2010). The focus in this report is on a more detailed analysis of written reflections that student participants provided in response to questions about their engagement, perceived learning, self-confidence, and notions of the broader nature of mathematics.…”

Section: Introductionmentioning

confidence: 99%