News: Thoughts about maths thinking
Numbers don't change the situation
The coordinator of first year Chemistry had a chat to me the other day about how to support students in solving word problems. The issue is that students have trouble using the words to help them decide what sorts of calculations need to be done in order to solve the problem. This issue is not new – people have been solving word problems for thousands of years, and the maths education literature is littered with papers discussing the issue. No clear concensus has been reached, of course, because there are any number of factors that affect students' ability to solve problems.
Two kinds of division
If you had to explain what the expression "10 ÷ 5" (that is "10 divided by 5") meant, what would you say? To be clear, I'm not asking for the answer, I'm asking for a story that will give it meaning.
Elsa's Freedom
Disney's Frozen came out on DVD last week and my family and I watched it on Saturday. It's a very good movie with an excellent theme about the real nature of true love which is not usually seen in a "princess movie". There are also two different stories about freedom, which is pretty common in a princess story (consider Rapunzel in Tangled and Jasmine in Aladdin). It's this I want to talk about today.
The Right Hand Rules
Students in Maths 1M are learning the cross product at the moment. This is a way to multiply two vectors in 3D space – let's call them v1 and v2 – to produce a new vector, which is called v1Ìý× v2. The length of this new vector is related to the lengths of the two original vectors and the angle between them, and the direction is perpendicular to both of the original vectors. However there are two possible directions it could point and still be perpendicular to both. We need a consistent way to choose which of the two options to use, and this is provided by the so-called "right-hand rule".
Wrapping up integrals
I love wrapping presents. I'd like to say it's because of the warm glow I have inside from giving a gift to someone else – and that feeling is certainly there to an extent – but I'm sorry to say the main reason is because I like the process of wrapping presents itself.
Maths is not Science
Let me say it again a little more emphatically: Maths is NOT Science. The major difference I want to focus on here is the concept of truth. Things are true in Maths, but they are not in Science.
Why don't people bring me raw data?
We often get research students visiting us to get help with analysing their data, even though it is not actually our job to help them and we are not formally qualified to help either. But I still sit with them and listen to their woes and give what advice I can, because I know how little support for statistics there is at this university.
Australia's Got Dedication
In the MLC Drop-In Centre, it sometimes happens that students succeed quite well at their maths, and yet somehow they manage to actually feel bad about it. They say that they only succeeded because they worked hard, and not because they are "good at maths", implying that somehow natural talent is more worthy of praise. Well I'm here to say this is the most ridiculous thing I have ever heard.
Ancient boxplots
When we learn things, we tend to get the impression that the things we learn have been passed down to us from the ancients. We think that the ways of thinking and doing we are presented with are the only way to think and do, and they were decreed by some all-knowing prophet in prehistorical time.
You will never see this problem again
"Now you understand that you'll never see this problem again, don't you?" I said, after a particularly productive problem-solving session at the MLC whiteboard with a group of students.
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