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Using Neural Networks to Motivate the Teaching of Matrix Algebra for K-12 and College Engineering Students

Abstract

Improving the retention of engineering students continues to be a topic of interest to engineering educators. Reference 1 indicates that seven sessions at the 2006 ASEE Annual Conference were devoted to this subject. In order to be successful in an engineering program, it is recognized that students must have a solid background in mathematics. Studies have shown that students will be more motivated to study and learn mathematics if abstract mathematical concepts are presented in the context of interesting examples and applications2 – 5. To become appealing and relevant, abstract mathematical concepts should be connected to engineering and real life issues, as suggested by the guidelines of ASEE Engineering K-12 Centre6.

In two previous papers7 - 8 the co-authors have presented methods for improving the teaching of important mathematical concepts to K-12 and college level engineering students. In reference 7, the co-authors provided a method of teaching the concept of infinity that combines a rigorous development of the concept of infinity in freshman level mathematics courses for engineering students and an intuitive approach to infinity with hands-on exercises for K-12 students. In reference 8, the co-authors developed materials on topics from number theory, essential to the field of data security and suitable for K-12 students, as well as for remedial or preparatory courses for engineering freshmen.

This paper represents the third part in this continuing project of developing methods for improving the teaching and learning of mathematical concepts for engineering students. It presents an interesting context in which to teach simple matrix algebra, developing practical applications that can be used for both K-12 and college level algebra courses. The main application demonstrated in this paper is the design of a character recognition system, using a simple neural network. It leads to a series of interesting exercises with practical applications. The authors contend that these applications will motivate students to practice matrix operations which otherwise may seem tedious and to further motivate them to focus on their mathematics courses.

I. Introduction

The teaching of matrix algebra takes place in a variety of courses. In K-12, students are typically introduced to matrix operations in their second year algebra courses and/or pre-calculus. In college, students come across matrix algebra in pre-calculus, linear algebra, differential equations and linear systems courses. In lower division college mathematics, the widely used application of matrix operations is typically the solution of simultaneous equations, based on the fundamental idea of viewing a system of linear equations as a product of a matrix and a vector (see for example, section 1.4 of reference 9).

It is not until the upper division engineering courses that students see interesting practical applications of linear algebra. The standard college textbooks on linear algebra provide application models of matrix algebra and linear systems used in economics, computer graphics

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Katz, S., & Klass-Tsirulnikov, B. (2007, June), Using Neural Networks To Motivate The Teaching Of Matrix Algebra For K 12 And College Engineering Students Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--1645