First Blog

Proposition .  Students should learn to solve problems in multiple ways.  Can this be so or are we asking yet again our students learn even more than what is needed? The short answer is "yes." Let me explain.  First, the math teaching community has embraced, I think correctly, the idea of multiple representations.  This means looking at data and functions in multiple ways graphs, tables, formulas, and the like.  In fact, I've written on this. See http://disted6.math.tamu.edu/newsletter/newsletters_new.htm#current_issue for the three articles. Second and more generally, the more facets of the same thing a person is familiar with, the better is his knowledge of it. When it comes to problem solving, the same rule applies.  If a person can solve a problem in two or more different ways, this is an indicator of their understanding of the problem and techniques to solve it.  If they can solve it in only one way, this is an indicator that they have a single method in their mind. 

Problem Solving – the pathway to the impossible Life is problem solving.   From work to school to religion; in love in pleasure, in strife, we are always solving something.  Some problems are simple, some tricky, some poorly defined, some complex.  Many are impossible. We have not set about to discuss school math problems.  In a sense, these are the simplest of all because much of the toolkit needed for solving them have been presented in the course.  These problems are those with the greatest clarity, a unique solution, and for them there is always a final resolution.  You get it or you don’t.  We have an array of problem solving methods, from logic to emotion, from instinct to intuition, from random to programmed, and more.  These methods are applied individually or in combination, often generating intrinsic conflicts, resulting is partials solutions, no solution, personal solutions, new problems, new situation, and impossible situations.  Results can be satisfying or frustrating,