Many studies provide insights into students' conceptions of various linear algebra topics and difficulties they face with multiple modes of thinking needed for conceptualization. While it is important to understand students' initial conceptions, students' transfer of learning of these conceptions to subsequent courses can provide additional…

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

Decision matrices are valuable engineering tools. They allow engineers to objectively examine solution options. Decision matrices can be incorporated in K-12 classrooms to support authentic engineering instruction. In this article we provide examples of how decision matrices have been incorporated into 6th and 7th grade classrooms as part of an…

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

In this paper, we review the rules and game board for "Chutes and Ladders", define a Markov chain to model the game regardless of the spinner range, and describe how properties of Markov chains are used to determine that an optimal spinner range of 15 minimizes the expected number of turns for a player to complete the game. Because the Markov…

This article presents a few methods for generating Sudoku puzzles. These methods are developed based on the concepts of matrix, permutation, and modular functions, and therefore can be used to form application examples or student projects when teaching various mathematics courses. Mathematical properties of these methods are studied, connections…

Dodgson's method of computing determinants is attractive, but fails if an interior entry of an intermediate matrix is zero. This paper reviews Dodgson's method and introduces a generalization, the double-crossing method, that provides a workaround for many interesting cases.

When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…

When we use technology to teach mathematics, we hope to focus on the mathematics, restricting the computer software systems to providing support for our pedagogy. It is a matter of common experience, however, that students can become distracted or frustrated by the quirks of the particular software system being used. Here, experience using the…

The article is aimed at a partial problem of science process skills development--the evaluation of educational outcomes. In comparison to evaluation of obtained knowledge, the skills development is not so easy to be objectively evaluated. The article provides a proposal of an evaluation tool and describes the first results of its research…

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

The use of matrix multiplication in the theory of Markov chains is demonstrated without directly discussing any probability theory. The technique that is developed is applied to ratio and mixture problems that are in changing states. (JP)

A game is presented in which computation by a stepping-stone method is used to solve minimax problems. An additional application of this game is used for finding the Pearson correlation coefficient by non-parametric techniques. The game provides considerable computational practice as well as a motivational problem solving situation. (JP)