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Year

Title

Links

2008

MathML and JAVA Implementation in Linear Algebra

2003

Teaching Linear Algebra at University

1998

How to Take Advantage of Technology in the Classroom and Avoid Its Pitfalls

1998

Pedagogy and Content Issues Subgroup Report for the Park City Mathematics Institute Undergraduate Faculty Program

1998

Notes on a Lecture at Haifa

1997

Resources for Teaching Linear Algebra

1994

Proceedings of the Fifth SIAM Conference on Applied Linear Algebra

1994

Using MATLAB to Encourage Formation of Conjectures by Students

1993

The Linear Algebra Curriculum Study Group Recommendations for the First Course in Linear Algebra

1993

The College Mathematics Journal, Vol. 24, No. 1, Jan., 1993

1993

ILAS Education Committee Graduate Level Syllabi

1992

Gems of Exposition in Elementary Linear Algebra

MathML and JAVA Implementation in Linear Algebra  

Electronic Journal of Mathematics and Technology, Feb, 2009 by Duk-Sun Kim, Sang-Gu Lee

We have developed various JAVA matrix calculators for our linear algebra class, and have studied effective ways to display mathematical expressions on the web. With these efforts we were able to develop Random Problem Generator (RPG) with MathML using our JAVA matrix calculators. These new tools have adopted in our linear algebra blended learning classes in addition to our self-directed learning innovations. In this paper, we have introduced how we use our new Random Problem Generator (RPG) and how it has the behavior of students in their learning process.

[PDF File Download]

URL 

https://php.radford.edu/~ejmt/deliverAbstract.
php?paperID=eJMT_v3n1p1

http://findarticles.com/p/articles/mi_7032/is_1_3/ai_n32071811/

Teaching Linear Algebra at University  

Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in mathematics education in several countries. Our goal is to give a synthetic overview of the main results of these works focusing on the most recent developments. The main issues we will address concern:

• the epistemological specificity of linear algebra and the interaction with research in history of mathematics

• the cognitive flexibility at stake in learning linear algebra

• three principles for the teaching of linear algebra as postulated by G. Harel

• the relation between geometry and linear algebra

• an original teaching design experimented by M. Rogalski

2000 Mathematics Subject Classification: 97, 01, 15.

Keywords and Phrases: University teaching, Linear algebra, Curriculum,

Vector space, Representation, Geometry, Cognitive flexibility, Epistemology.

[PDF File Download]

URL 

http://arxiv.org/abs/math/0305018v1

The Linear Algebra Curriculum Study Group Recommendations for the First Course in Linear Algebra  
 

Author(s): David Carlson, Charles R. Johnson, David C.
                 Lay, A. Duane Porter

Source: The College Mathematics Journal, Vol. 24, No. 1
              (Jan., 1993), pp. 41-46

Published by: Mathematical Association of America (MAA)

Stable URL: http://www.jstor.org/stable/2686430

[PDF File Download]

URL

[Link To JSTOR]

http://www.jstor.org/stable/2686430

The College Mathematics Journal, Vol. 24, No. 1, Jan., 1993
 

The College Mathematics Journal which contains special issues on linear algbera.

Copyrights C 1993, Mathematical Association of America

Now that the calculus reform movement is well under way, the mathematics community has turned its gaze upon linear algebra. The debate about the linear algebra curriculum goes deeper than questions about the use of technology or about how to achieve leanness and liveliness. The debate is over the very nature of this subject which sits in the center of mathematical activity. Two distinct approaches to linear algebra are provided by the theorem that says that the ring of linear transformations on an n-dimensional space is isomorphic to the n by n matrices. Grumbling that "Mathematical education is still suffering from the enthusiasms which the discovery of this isomorphism has aroused," E. Artin stated the case for linear transformations in 1957 (see page 46). Our authors, some of the leading teachers and practitioners in the field, argue for a decidedly concrete, matrix-oriented approach to the first course.

-The Editors 

URL

[Link To JSTOR]

 http://www.jstor.org/browse/07468342/di020755

Gems of Exposition in Elementary Linear Algebra

David Carlson; Charles R. Johnson; David Lay; A. Duane Porter

The College Mathematics Journal, Vol. 23, No. 4. (Sep., 1992), pp. 299-303.

Do you have a favorite topic of elementary linear algebra that you teach in an especially nice way to your students? Or, an unusual proof or problem that is particularly good for communicating a fundamental idea? The Linear Algebra Curriculum Study Group would be pleased to have your contribution to a National Science Foundation sponsored project to collect and broadly disseminate such "gems of exposition in elementary linear algebra." We share several sample "gems" in the next section.

The purpose of the gems collection is to provide classroom teachers of linear algebra with a variety of potentially useful items. Eventually these items may find their way into textbooks. Of course, the ultimate goal is to help the approximately 140,000 students who take linear algebra annually to learn and retain fundamental ideas

URL

http://www.jstor.org/view/07468342/di020753/02p0104w/0

Edited by David Carlson, Charles R. Johnson, David Lay,Duane Porter, Ann Watkins, and William Watkins

Reviewed by Rebecca Berg

The articles in this collection discuss both the content of linear algebra courses and approaches to teaching such courses. The authors address elementary topics, such as row reduction, and more advanced topics, such as sparse matrices, iterative methods and pseudo-inverses. There are agreements:

• "Only under torture would I tell a student about Kramer's rule..."(Almon);
• "As an example of how familiarity with determinants can rot your brain...." (Axler).
   

URL

http://www.maa.org/reviews/linearalg.html

ILAS Education Committee Graduate Level Syllabi

Three course outlines for graduate level, year - long courses in Theoretical Linear Algebra, Numerical Linear Algebra, and Applied Linear Algebra.

URL

http://matrix.skku.ac.kr/ilas/er/tne1.pdf

Proceedings of the Fifth SIAM Conference on Applied Linear Algebra

These proceedings were from the conference held at Snowbird, Utah in June, 1994. They contain a number of short papers on educational topics presented in the minisymposium and the contributed papers session dedicated to linear algebra education. Edited by John G. Lewis, the Proceedings were published by SIAM in 1994. (ISBN 0-89871-336-6)

URL

Using MATLAB to Encourage Formation of Conjectures by Students

Jeff Stuart

Abstract : A short paper that examines some ways in which MATLAB can be used as an experimental matrix laboratory rather than merely a sophisticated matrix calculator.

Whereas MATLAB is often used in courses as a matrix calculator, we examine how it can be used as a matrix laboratory. In particular, by utilizing a variety of random matrix generators to produce large sets of structured, random matrices, and by employing simple test functions that call these generators, we show how students can be led to formulate conjectures about basic matrix functions and about some classical theorems in matrix theory.

URL

http://matrix.skku.ac.kr/ilas/er/tne2.pdf

How to Take Advantage of Technology in the Classroom and Avoid Its Pitfalls

Park City Mathematics Institute Undergraduate Faculty Program
Summer, 1998

Abstract: A report based on the discussion held by faculty participating in the PCMI program devoted to teaching undergraduate linear algebra.

URL

http://pcmi.ias.edu/

Pedagogy and Content Issues Subgroup Report for the Park City Mathematics Institute Undergraduate Faculty Program

Jane Day

California State University at San Jose

Summer, 1998

Abstract: An extensive report summarizing the discussions held by undergraduate faculty, mathematics education researchers and high school teachers participating in the PCMI program devoted to teaching undergraduate linear algebra. Attached to the report is a list of topics that undergraduates should understand upon completion of a linear algebra course, and a list of questions that could be used to probe that understanding.

URL

http://pcmi.ias.edu/

Notes on a Lecture at Haifa

Frank Uhlig

Auburn University

January, 1998

Abstract: Abstract: These notes on linear algebra education are based on notes prepared for a talk delivered at the Technion Israel Institute of Technology.

URL

http://matrix.skku.ac.kr/ilas/er/uhlig.haifa.ps