An Example of the Simplification of a Mathematical Procedure to Facilitate Computer Interactions that Maximize e-Learning: Quasi-Matrix Factoring of Quadratic Equations Having Real and Rational Roots

By Lloyd Hutchings and Susannah McCuaig.

Published by The Learner Collection

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Article: Print $US10.00
Article: Electronic $US5.00

Interactions between students of mathematics and instructional computers, particularly those which deal with the acquisition of new procedures, can be made far more efficient than they usually are by “modernizing or streamlining” the mathematical procedures involved. Despite waves of general restructuring in the elementary through tertiary mathematics curricula, the actual procedures which are currently the core of these curricula are (or vary only slightly from) those classical techniques which evolved when the electronic learning options which currently exist were not even dreamt of. This new potential efficiency can allow the programing of relevant mathematical procedures to move in single cognitive increments, permitting specific corrective feedback for every component of a procedure. The particular procedure examined in this paper is the factoring of quadratic equations (those having real and rational roots) without using the quadratic formula. This technique represents a highly efficient alternative to the quadratic formula, for all equations having real and rational roots, and it is so much more efficient than other alternative non-formula options (such as the “complete the square” procedure and the “intuitive” or “inspection” procedure) that it could eventually completely replace them. This new procedure employs an array which is a modified algebraic matrix or a “quasi-matrix”. This array greatly abbreviates and simplifies required factoring operations and makes every component of the procedure easily assessable to the programming of interaction exchange.

Keywords: Interactive Mathematical Programming, Appropriate Cognitive Increments, Effective e-Learning

The International Journal of Learning, Volume 15, Issue 2, pp.163-168. Article: Print (Spiral Bound). Article: Electronic (PDF File; 525.100KB).

Dr. Lloyd Hutchings

Professor, School of Education, Francis Marion University, Florence, South Carolina, USA

I graduated from Harvard College with a Bachelor of Arts and from Syracuse University with a Doctor of Philosophy. I completed a Postdoctoral Fellowship at the University of Southern California School of Medicine. For over 30 years I’ve been a professor at Francis Marion University. I’m especially interested in the learning of mathematics and in the making of mathematics more assessable to a broad range of students. I have developed a number of simplifying algorithms for the basic arithmetic operations, for some higher mathematical procedures, and for the balancing of chemical equations.

Dr. Susannah McCuaig

Professor, School of Education, Francis Marion University, Florence, South Carolina, USA

I received a Bachelor of Arts from The Colorado College, and a Master of Education and a Doctor of Education from Boston University. I have taught in Europe and have consulted at the international level. At Francis Marion University, I have coordinated our Early Childhood Education program and our Elementary Education Program and our Overseas Practice Teaching program. I have become especially interested in content readability and e-learning.


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