Making Your Own Sense
Reflections on maths, learning, and the Maths Learning Centre.
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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.
"Basic"
What do you think of when you hear the word "basic"? For example, when you see a topic in a maths textbook entitled "Basic Algebra", what comes to mind?
Quadric Cameo
As I said recently, quadrics hold a special place in my heart and I get excited every time the topic comes around in Maths 1B. Quadrics have so many cool things you can say about them, and are such a great opportunity to talk about the deep connection between algebra and geometry. I personally could teach an entire 12 week course on nothing else. But paradoxically, this is also why I feel a sense of frustration every time the topic comes around in Maths 1B.
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.
My conic likes to hide in boxes
Conics (or conic sections if you like) are very close to my heart. My PhD thesis was about conics and their higher-dimensional relatives, and way back in high school they were one of the bits I particularly loved. So it's no surprise that I get excited each semester when the Maths 1B students study them.
Technological Excuses
Technology can do a lot to facilitate good learning: Some of the stuff we ask students to do doesn't really need to happen when they're all together in the classroom, and technology can make it possible for the students to do these things in other places (such as at home, in Hub Central, on the train, or lying in the sun on the banks of a river), and give us more time in the face-to-face sessions for interaction. Some of the ways we have of assessing students are very labour-intensive on the teacher's side, and using technology for these things can allow the teachers to put more energy into other bits of the students' learning experience. It's not feasible to give every one of your six hundred students one-on-one time to explain concepts in multiple different ways, but technology can give them the opportunity to access further resources to support their learning.
Does it matter that roosters don't lay eggs?
There is a particularly annoying puzzle that goes something like this:
[Read more about Does it matter that roosters don't lay eggs?]
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