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Selinski, Natalie E.; Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle – Journal for Research in Mathematics Education, 2014

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation…

Descriptors: Mathematics Instruction, Algebra, Mathematical Concepts, Concept Formation

Chang, J.-M. – International Journal of Mathematical Education in Science and Technology, 2011

Linear algebra has become one of the most useful fields of mathematics since last decade, yet students still have trouble seeing the connection between some of the abstract concepts and real-world applications. In this article, we propose the use of thought-provoking questions in lesson designs to allow two-way communications between instructors…

Descriptors: Inquiry, Mathematics Instruction, College Mathematics, Teaching Methods

Diaz, Ana; Garcia, Alfonsa; de la Villa, Agustin – International Journal for Technology in Mathematics Education, 2011

This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…

Descriptors: Electronic Learning, Technical Writing, Open Universities, Information Management

Wawro, Megan; Sweeney, George F.; Rabin, Jeffrey M. – Educational Studies in Mathematics, 2011

This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from…

Descriptors: Algebra, Undergraduate Students, Interviews, Concept Formation

Nehme, Zeina – Mathematics Teaching, 2011

Contextual mathematics is an area of mathematics teaching and learning through which researchers and educators believe that mathematics is better taught, and learned, if connected to real-life situations and problems. It is also very helpful if it makes sense in the students' world. Thus, the author decided to start a project by creating a blog,…

Descriptors: Web Sites, Electronic Publishing, Matrices, Mathematics Instruction

Nyman, Melvin A.; Lapp, Douglas A.; St. John, Dennis; Berry, John S. – International Journal for Technology in Mathematics Education, 2010

This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

Descriptors: Mathematical Concepts, Algebra, Teaching Methods, Educational Technology

Montiel, Mariana; Bhatti, Uzma – Online Journal of Distance Learning Administration, 2010

This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…

Descriptors: On Campus Students, Graduate Students, Mathematics Instruction, College Mathematics

Stewart, Sepideh; Thomas, Michael O. J. – International Journal of Mathematical Education in Science and Technology, 2010

One of the earlier, more challenging concepts in linear algebra at university is that of basis. Students are often taught procedurally how to find a basis for a subspace using matrix manipulation, but may struggle with understanding the construct of basis, making further progress harder. We believe one reason for this is because students have…

Descriptors: Mathematics Instruction, Algebra, Mathematical Concepts, College Mathematics

Lapp, Douglas A.; Nyman, Melvin A.; Berry, John S. – International Journal of Mathematical Education in Science and Technology, 2010

This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding.…

Descriptors: Constructivism (Learning), Concept Mapping, Matrices, Mathematical Concepts

Corbalan, Gemma; Paas, Fred; Cuypers, Hans – Computers & Education, 2010

Two studies investigated the effects on students' perceptions (Study 1) and learning and motivation (Study 2) of different levels of feedback in mathematical problems. In these problems, an error made in one step of the problem-solving procedure will carry over to the following steps and consequently to the final solution. Providing immediate…

Descriptors: Feedback (Response), Student Attitudes, Motivation, Problem Solving

Wawro, Megan Jean – ProQuest LLC, 2011

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

Descriptors: Video Technology, Mathematics Education, Group Discussion, Persuasive Discourse

Shi, Yixun – International Journal of Mathematical Education in Science and Technology, 2009

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, "Using a sequence of number pairs as an example in teaching mathematics". Math. Comput. Educ., 39 (2005), pp. 198-205; Y. Shi, "Case study projects for college mathematics courses based on a particular…

Descriptors: College Mathematics, Student Interests, Algebra, Mathematics Instruction

Stewart, Sepideh; Thomas, Michael O. J. – International Journal of Mathematical Education in Science and Technology, 2007

Students often find their first university linear algebra experience very challenging. While coping with procedural aspects of the subject, solving linear systems and manipulating matrices, they may struggle with crucial conceptual ideas underpinning them, making it very difficult to progress in more advanced courses. This research has sought to…

Descriptors: Advanced Courses, Mathematics Instruction, College Mathematics, Mathematical Logic

Parker, Catherine Frieda – ProQuest LLC, 2010

A possible contributing factor to students' difficulty in learning advanced mathematics is the conflict between students' "natural" learning styles and the formal structure of mathematics, which is based on definitions, theorems, and proofs. Students' natural learning styles may be a function of their intuition and language skills. The purpose of…

Descriptors: Definitions, Intuition, Writing Skills, Language Skills

Scott, Damon – PRIMUS, 2007

For over a decade it has been a common observation that a "fog" passes over the course in linear algebra once abstract vector spaces are presented. See [2, 3]. We show how this fog may be cleared by having the students translate "abstract" vector-space problems to isomorphic "concrete" settings, solve the "concrete" problem either by hand or with…

Descriptors: Algebra, Undergraduate Study, Mathematics Instruction, College Science