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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.

Stream: Pedagogies and Teaching Practices

Paper: Example of the Simplification of a Mathematical Procedure to Facilitate Computer Interactions that Maximize e-Learning, An

I graduated from Harvard University 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 College 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. I would enjoy collaborating with any colleagues who have similar interests.

I received a Bachelor of Arts from The Colorado College, and the Master of Education and a Doctor of Education from Boston University. I have taught in Europe then consulted extensively at the international level. But have, in a sense, settled and Francis Marion University. For a while I directed the Elementary Education Program and the Early Childhood Program.I currently direct to the Oversees Student Teaching Program, which at this time is based in New Zealand. I'm especially interested in improving the learning, and especially in the e-learning techniques, for a broad range of students. Sometimes my interest related linguistics analyses lead me into mathematical applications.