The Dangers of Math Magic

In the first paragraph of his paper, Erlwanger states that his purpose is to show the IPI system to be is unsuccessful because of the way in which it presents Mathematics to the learner. The main point is that the answer to the questions “What is the subject of Mathematics?” and perhaps more importantly “What is not Mathematics?” (according to Erlwanger himself) is in disjoint with the subject being taught to students such as Benny. The paper is, in a sense, simply Erlwanger’s own version of our own first blogs, albeit a little longer. For example, Erlwagner finds that Benny believes in a kind a Math “Magic” – if he applies the correct rules, rules which some guy devoted his life to creating, he will be able to produce the correct answer. The task is simply to find the rule that works for that particular problem, and as such, Benny has no trust in the consistency of Math. He has no idea whether his answer is right until the mysterious answer key hanging over his head deems to respond with a “Yes” or “No”. In contrast, Erlwagner sees Math as a rational subject, one in which separate concepts, such as fractions and decimals, can be related and answers can be verified according to common mathematical sense.

I think that Erwanger’s definition of Mathematics is still extremely applicable to learners today. In my own experiences in the schools, I find that teachers hand out Math worksheets and explicitly state “Don’t show any of your messy working on the paper”. How can a child conclude anything from this other than that a correct answer is all that is required from them? This encourages the kind of rule application favoured by Benny: Use any method that seems to work, regardless of whether or not it makes any kind of Mathematical sense! Teachers need to try and gain an understanding of how a child produces answers, and why he thinks the way he does.