Moronic math methods
By Murray Bourne, 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...
See the 2 Comments below.
19 Apr 2012 at 11:22 pm [Comment permalink]
The thing about mathematics education is that nobody really gets why they are learning this stuff. Yes, we know that WE can use trigonometry in real life, and WE also know and care that trigonometry is even used to design the games children like to play on computers; but why should they care? They just play the game.
I especially liked the "required for higher mathematics" part. And what is that higher mathematics required for? Nothing. Absolutely nothing, at least for them. We might use polar coordinates in plotting the lengths of Archimedean spirals, but many people interpret that as "unnecessary". Mathematics is just a horrifying topic taught at school!
What is my opinion? I do agree that the education is faulty, but it isn't faulty because mathematics is a separate lesson. It is mostly faulty because we teach unnecessary stuff to people even if they do not want to learn it. What use will surd manipulation be to a lawyer? Nothing. And that's the point. People should be able to pick the topics of mathematics they want to learn after a certain grade, say 6, when maths actually starts to get advanced that people will not need it. People who like it can go on and those who don't can stop. This, of course, brings up another thought: "Who in the world would want to take math?"
This is just the problem of our present education system. It should be altered properly so that children will actually enjoy going to school, instead of seeing school as a place where teachers are the masters and they torture you with unnecessary knowledge that you won't even need, and then ask questions to you about it and decide your future (to be honest, it is really what is happening right now). This should be changed.
20 Apr 2012 at 6:52 am [Comment permalink]
@Starfall: There is an element of broccoli eating in all this - there are some things that are "good for you" that may not be pleasant at the time. And we do need to expose everyone to many different aspects of education, so they can find their various niches. Problem is, as you say, in most countries it's compulsory, and rarely a lot of fun.
I totally agree with your last paragraph!