News: How people learn Or dont
Childhood memories
Two books I've read recently have encouraged me to investigate my memories from childhood. In Tracy Zager's "Becoming the Math Teacher You Wish You'd Had", she urged me to think about my maths autobiography to see what influenced my current feelings about maths. In Stuart Brown's "Play", he urged me to think about my play history to see what influenced my current feelings and tendencies about play. In the spirit of those two, here are some of my earliest memories about maths and play.
Money and me
In the online resources for Becoming the Math Teacher You Wish You'd Had, Tracy Zager provides information about the benefits of writing a "math autobiography". I really have tried to do this, but I am having a lot of trouble organising my thoughs and memories. However, I reckon I can track some of my memories about one particular application of maths: money.
An opening gambit for the Numbers game
It was O'Week a couple of weeks ago, when new students arrive on campus to find out how uni works and the services they have access to. Our tradition for the last several years is to play Numbers and Letters on a big whiteboard out in public as a way to engage with students. This year I discovered a way to help people engage: write something on the board that is not a solution.
Finding an inverse function
There is a procedure that people use and teach students to use for finding the inverse of a function. My problem with it is that it doesn't make any sense, in two ways.
The Zumbo (hypothesis) Test
Here in ×îÐÂÌÇÐÄVlog, we are at the tail end of a reality cooking competition called "". In the show, a group of hopefuls compete in challenges where they produce desserts, hosted by patissier Adriano Zumbo. There are two types of challenges. In the "Sweet Sensations" challenge, they have to create a dessert from scratch that matches a criterion such as "gravity-defying", "showcasing one colour" or "based on an Arnott's biscuit". The two lowest-scoring desserts from the Sweet Sensations challenge have to complete the second challenge, called the "Zumbo Test". In this test, Zumbo reveals a dessert he has designed and the two contestants try to recreate it. Whoever does the worst job is eliminated.
Problem strings and using the chain rule with functions defined as integrals
In Maths 1A here at the ×îÐÂÌÇÐÄVlog of Adelaide, they learn that says that, given a function of x defined as the integral of an original function from a constant to x, when you differentiate it you get the original function back again. In short, differentiation undoes integration. And then they get questions on their assignments and they don't know what to do. They always say something like "I would know what to do if that was an x, but it's not just an x, so I don't know what to do".
[Read more about Problem strings and using the chain rule with functions defined as integrals]
Quadrilateral family tree
I have always loved the naming of quadrilaterals, right from when I first heard about it in high school. I'm not entirely sure why, but some of it has to do with the nested nature of the definitions – I like that a square is a kind of rectangle and a rectangle is a kind of parallelogram.
One reason I'll still use pi
Every so often, someone brings up the thing with tau (Ï„) versus pi (Ï€) as the fundamental circle constant. In general I find the discussion wearisome because it usually focuses on telling people they are stupid or wrong for choosing to use one constant or the other. There are more productive uses of your time, I think.
Brackets
I had a meeting with an international student in the MLC on Friday who has having a whole lot of language issues in her maths class.
A Day of Maths
Last Monday, I was invited into my daughter's Year 7 classroom to do a full day of maths with the students. It was the Best Day Ever. I had so much fun giving the students things to think about, and watching and helping the students think and talk about them.
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