Honolulu, Hawaii
June 24, 2007
June 24, 2007
June 27, 2007
2153-5965
Mathematics
15
12.1557.1 - 12.1557.15
10.18260/1-2--1645
https://peer.asee.org/1645
375
Sharlene Katz is Professor in the Department of Electrical and Computer Engineering at California State University, Northridge (CSUN) where she has been for over 25 years. She graduated from the University of California, Los Angeles with B.S. (1975), M.S. (1976), and Ph.D. (1986) degrees in Electrical Engineering. Recently, her areas of research interest have been in engineering education techniques and neural networks. Dr. Katz is a licensed professional engineer in the state of California.
Bella Klass-Tsirulnikov is a senior academic lecturer at Sami Shamoon College of Engineering, Beer Sheva, Israel (former Negev Academic College of Engineering). She accomplished mathematics studies at Lomonosov Moscow State University (1969), received Ph.D. degree in mathematics at Tel Aviv University (1980), and completed PostDoc studies at Technion - Israel Institute of Technology (1982). From 1995 she also holds a Professional Teaching Certificate for grades 7 – 12 of the Israeli Ministry of Education. Dr. Klass-Tsirulnikov participates actively in the research on functional analysis, specializing in topological vector spaces, as well as in the research on mathematics education at different levels.
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
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
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