Making Your Own Sense
Reflections on maths, learning, and the Maths Learning Centre.
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Education research reading: effective feedback
After warning months ago that there would be more posts about my research reading, but I didn't follow through. Finally here is a "Research Reading" post. This one is about how feedback helps students learn. I'll discuss several papers which list principles/challenges for providing effective feedback.
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The Sausage-Stacking Theorem
It's no secret that the powers of two are some of my favourite numbers. There are so many interesting things to say about them that often I don't know where to begin! (In case you're not au fait with the terminology, the powers of two are the numbers you can make by starting with 1 and multiplying by 2 over and over. The list starts out 1, 2, 4, 8, 16, 64, 128 etc.)
The square root of two
In first year maths, they briefly study the five families of number: the natural numbers N, the integers Z, the rational numbers Q, the real numbers R, and the complex numbers C. In particular, they focus on the distinction between the rational numbers and the real numbers. A classic proof they are given at this time is one that the number √2 is irrational. This blog post is about some alternative proofs.
Sleeping through Miss Marple
My wife and I like to watch mystery shows together like Poirot, Midsomer Murders and Miss Marple. Unfortunately I have a slight problem: when watching television in a comfortable position, I tend to drift in and out of sleep, no matter how interesting the show might be. This can be quite disasterous for mystery shows, especially ones with major unexpected plot twists.
Inspiration, not instructions
We have a big problem-solving poster on the MLC wall that gives students advice for solving problems. One of those pieces of advice is that to decide what to do for your current problem, you could look at other problems for inspiration. Yesterday I saw the dangerous results of what happens if you look at other problems for instructions rather than inspiration.
Jack Frost's centre
On the weekend I watched the film "Rise of the Guardians" by Dreamworks Pictures, and it is a very enjoyable film. In it, Jack Frost is enlisted by the Man in the Moon to join the Guardians of Childhood—who already have Santa Claus, the Easter Bunny, the Sandman and the Tooth Fairy in their ranks—and together they fight the evil Pitch Black, who is the Bogeyman.
Complex is not the same as complicated
The Complex Numbers are unfortunately named. Most people take the word complex to mean "difficult to understand", so the very name we give this family of numbers sets students up to think it's going to be a lot of hard work to understand them. This is sad, because they really are very very cool and not quite as difficult as people make them out to be.
The advent calendar function
In a previous post I discussed how we need ways to think about functions that are not curves on an x-y-plane. Well I have a seasonally-appropriate one for you: the Advent Calendar.
The Fear of Mollycoddling
Recently I was a guest at a planning meeting for a certain school and ended up in a session where we discussed how we can better support students in terms of their wellbeing. We were shown a news report highlighting the fact that the suicide rate in professionals of this particular discipline is four times higher than the general population. One of the major factors mentioned in the news report was that professionals in this discipline are very unlikely to seek support from anyone when they are struggling, having been trained too well to be self-sufficient while they were students.
A function is not a graph
When students learn about functions at school, we spend a lot of time forging the connection between functions and graphs. We plot individual points, and we find x-intercepts and y-intercepts. We use graphing software to investigate what the coefficients do to the graph, and discuss shifting along the x-axis and y-axis. We make reference to the graph to define derivatives and integrals. Some teachers help students to recognise from the formula of a function what general shape its graph ought to have, such as recognising that a quadratic function must have a parabola-shaped graph. (I wish this last point was much more strongly pushed, actually.)
