On a research programme concerning the teaching and learning of linear algebra in the first-year of a French science university

Dorier, Jean-Luc; Robert, Aline; Robinet, Jacqueline; Rogalski, Marc

doi:10.1080/002073900287354

Cited by 40 publications

(24 citation statements)

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“…Research indicates that formalism and the lack of set theory knowledge are among the reasons for students' struggles with and mistakes on hnear algebra concepts [1][2][3]. Dorier and Sierpinska [3] also add the nature and historical background of linear algebra among the reasons.…”

Section: Introductionmentioning

confidence: 95%

Lack of set theory relevant prerequisite knowledge

Dogan-Dunlap

2006

International Journal of Mathematical Education in Science and

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Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a group of linear algebra students' mistakes on a set of linear algebra questions. The paper also details an in-time intervention (a pedagogical approach) to enhance students' understanding of hnear algebra concepts through advancing their set theory knowledge. Mathematics teachers can consider similar approaches to address their students' mistakes.

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Section: Introductionmentioning

confidence: 95%

Lack of set theory relevant prerequisite knowledge

Dogan-Dunlap

2006

International Journal of Mathematical Education in Science and

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“…many students have the feeling of landing on a new planet and are not able to find their way in this new world. [2] Throughout the 1990s, a significant amount of research was carried out on the teaching and learning of linear algebra. Theories about exactly why students cannot see through the fog were espoused, and recommendations for changes to the way the subject is taught were made.…”

Section: Introductionmentioning

confidence: 99%

Linear algebra revisited: an attempt to understand students' conceptual difficulties

Britton

Henderson

2009

International Journal of Mathematical Education in Science and

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This article looks at some of the conceptual difficulties that students have in a linear algebra course. An overview of previous research in this area is given, and the various theories that have been espoused regarding the reasons that students find linear algebra so difficult are discussed. Student responses to two questions testing the ability to prove that a set is a subspace of a vector space are examined in some detail. Some conjectures are made as to why students found the task so difficult.

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“…Students' difficulties with the formal aspect of the theory of vector spaces are not just a general problem with formalism but mostly a difficulty of understanding the specific use of formalism within the theory of vector spaces and the interpretation of the formal concepts in relation with more intuitive contexts like geometry or systems of linear equations, in which they historically emerged. Various diagnostic studies conducted by Dorier, Robert, Robinet andRogalski between 1987 and1994 pointed to a single massive obstacle appearing for all successive generations of students and for nearly all modes of teaching, namely, what these authors termed the obstacle of formalism (Dorier 1997 and Part II, Chapter 1).…”

Section: Analyses Of the Language Of Linear Algebramentioning

confidence: 99%