Research into the Teaching and Learning of Linear Algebra

@inproceedings{Dorier2001ResearchIT,
  title={Research into the Teaching and Learning of Linear Algebra},
  author={J. Dorier and A. Sierpińska},
  year={2001}
}
It is commonly claimed in the discussions about the teaching and learning of linear algebra that linear algebra courses are badly designed and badly taught, and that no matter how it is taught, linear algebra remains a cognitively and conceptually difficult subject. This leads to (a) curricular reform actions, (b) analyzing the sources of students' difficulties and their nature, as well as (c) research based and controlled teaching experiments. This chapter is organized along these three axes… Expand

Topics from this paper

Characterising the teaching of university mathematics: a case of linear algebra
TLDR
It is looked at how teaching is constructed within the particular setting, with a critical eye on the learners, on learning outcomes and on the tensions experienced by the lecturer in satisfying student needs and mathematical values. Expand
The Teaching and Learning of Tertiary Algebra
This chapter reports on some current educational issues related to the teaching and learning of tertiary algebra—in particular, abstract algebra, discrete mathematics, linear algebra, and numberExpand
The learning and teaching of linear algebra: Observations and generalizations
Abstract This paper is about a teaching experiment (TE) with inservice secondary teachers (hereafter “participants”) in the theory of systems of linear equations. The TE was oriented withinExpand
A framework for mathematical thinking: the case of linear algebra
Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study,Expand
Computer Algebra Systems in the Learning and Teaching of Linear Algebra: Some Examples
What I have tried to point out in this paper with the examples of linear algebra work is that, as a mathematician, one does not need to be completely committed to using CAS nor drastically changeExpand
Local Instruction Theories at the University Level: An Example in a Linear Algebra Course
TLDR
The results of three cycles of a teaching experiment to design, try out, and improve a local instruction theory (LIT) on the teaching of the concepts of spanning set and span in Linear Algebra with first-year engineering students are presented. Expand
Emphasizing language and visualization in teaching linear algebra
TLDR
This paper considers the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra, and how he employed visualization and an emphasis on language to encourage conceptual thinking. Expand
Definitions are important: the case of linear algebra
In this paper we describe an experiment in a linear algebra course. The aim of the experiment was to promote the students' understanding of the studied concepts focusing on their definitions. ItExpand
Linear Algebra Snapshots through APOS and Embodied, Symbolic and Formal Worlds of Mathematical Thinking
TLDR
The research reported here is as part of the first named author's recent PhD thesis where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the learning and teaching of some linear algebra concepts. Expand
Teaching Linear Algebra
TLDR
The aim of the discussion group is to initiate a multinational research project on how to foster conceptual understanding of Linear Algebra concepts. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 17 REFERENCES
On a research programme concerning the teaching and learning of linear algebra in the first-year of a French science university
The paper discusses the current approach to the teaching of linear algebra in the first year at a French science university and the main difficulties that students have with this material. A briefExpand
On the Teaching of Linear Algebra
Foreword to the English Edition. Preface. Introduction. Part I: Epistemological Analysis of the Genesis of the Theory of Vector Spaces. 1. Introduction. 2. Analytical and Geometrical Origins. 3.Expand
Formats of Interaction and Model Readers.
Among the interactionist "sensitizing concepts" in mathematics education evoked in the works of Bauersfeld and Voigt [see Cobb and Bauersfeld, 1995], one in particular has attracted my attention inExpand
Meta level in the teaching of unifying and generalizing concepts in mathematics
Certain concepts in mathematics were not invented only to solve new problems; their aim was mainly to find general methods to solve different problems with the same tools. Such concepts, as those ofExpand
The role of formalism in the teaching of the theory of vector spaces
Abstract In the French tradition of Bourbaki, the theory of vector spaces is usually presented in a very formal setting, which causes severe difficulties to many students. The aim of this paper is toExpand
Mathematics: "In Context,""Pure," or "with Applications"?.
Education is nothing more than polishing of each single link in the great chain that binds humanity together and gives it unity The f;:lilings of education and human conduct spring as a rule from ourExpand
A general outline of the genesis of vector space theory
The following article presents a general outline of the genesis of the elementary concepts of vector space theory. It presents the main works that contributed to the development of these basicExpand
L'indépendance stochastique
The paper analyzes the historical development of stochastical independence from an epistemological point of view with the intention of obtaining an educational perspective for this concept. In theExpand
The axiomatization of linear algebra: 1875-1940
Modern linear algebra is based on vector spaces, or more generally, on modules. The abstract notion of vector space was first isolated by Peano (1888) in geometry. It was not influential then, norExpand
Basis and Dimension — From Grassmann to van der Waerden
Basis and dimension are two elementary notions in the theory of vector spaces. The origin of the term ‘basis’ comes from the possibility of expressing any element of a given set as a linearExpand
...
1
2
...