Moronic math methods
[20 Jan 2006]
Finally I have found a kindred math educator. I agree with many of the issues raised by Harold Brochmann in his Questions page (no longer available), especially:
- A lot of the mathematics processes that we force students to do are a waste of their time and ours.
- Who cares what the roots of a 6th degree polynomial are. If we ever really need to know in real life (highly unlikely), then we should use computers to do it (see my Polynomial Equations section in Interactive Mathematics) and in mathematics education we should spend more time understanding what the solution to an equation means and how it is used to solve real problems, rather than fidding around with remainder theorems…
- It is much better that students understand probability and statistics (interpretation of real stats, not mindless calculations where no-one knows what they are finding anyway)
- Students should understand personal finance – so that they don’t bankrupt themselves like the US has done to itself.
- Mathematics is a filter for further education – how unfair is that? It’s like saying “You can’t pirouette (in ballet) and stay on your toes for hours, so you cannot come into our college.” Say, what?
- Ask many mathematics teachers/lecturers what this stuff is used for, and they usually answer “It is needed for higher mathematics”. Yes, and…? This is math for math’s sake, and it is serious.
- Ask many graduates when was the last time they solved a quadratic equation or conducted a Laplace transform (even the engineering graduates) and they will often ask – “Errr, what’s that again?”
I especially like Brochmann’s question about mathematics textbooks:
Why is it that the “word problems” appear at the end of the chapters?
Yes, I think there is a crisis in mathematics education.
We should allow students to explore real data (there is mountains of it on the Web, and they can collect more themselves), and draw meaning from describing that data.
They should experience authentic problems that may or may not be solved using algebra. The learning is in figuring out what the problem means, how to solve it and what the solution means.
Finally for this rant, I am wondering more and more whether mathematics should be taught separately at all. Maybe it should be designed into courses and that it should arise as a consequence of solving problems in those courses (science, sociology, history and economics come to mind.)
Whatever, we need a new approach…