News: Thoughts about maths thinking
The Operation Tower
I don't like BODMAS/BEDMAS/PEMDAS/GEMS/GEMA and all of the variations on this theme. I much prefer to use something else, which I have this week decided to call "The Operation Tower".
Digit Disguises
This blog post is about a game I invented this week, and the game is AWESOME, if I do say myself.
Context fatigue
Context fatigue is a particular kind of mental exhaustion that happens after having to make sense of multiple different contexts that maths/statistics is embedded in. I feel it regularly, but I feel it most strongly when I have spent a day helping medical students critically analyse the statistics presented in published journal articles.
Struggling students are exploring too
I firmly believe that all students deserve to play with mathematical ideas, and that extension is not just for the fast or "gifted" students. I also believe that you don't necessarily need specially designed extension activities to do exploration – a simple "what if" question can easily launch a standard textbook exercise into an exploration.
Trying maths live on Twitter
Once upon a time, I decided I would be vulnerable on Twitter. As part of that, when someone posted a puzzle that I was interested in, I decided that I would not wait until I had a complete answer to a problem before I responded, but instead I would tweet out my partial thinking. If there were mistakes I would leave them there and respond with how I resolved them, rather than deleting them and removing the evidence that I had made a mistake. I wanted the whole process of solving problems to be out there in plain sight for everyone to see.
Tutorials for an intro Arts course: Story makes sense of number
Sometime in the past, I was approached by academics in the Faculty of Arts to discuss the numeracy skills of the students in their faculty. They wanted to discuss how they might include numeracy skills in some of their courses across all the degrees they teach. It was a lot bigger than the MLC could reasonably do, but I said I would certainly be able to do a small thing in a few courses, and certainly help their students in the MLC itself when they came to talk.
[Read more about Tutorials for an intro Arts course: Story makes sense of number]
The second part of the Four Fours
The four fours is a rather famous little puzzle that requires some creativity and also gets people thinking about how the operations interact with each other. One thing I find both frustrating and fascinating is what happens when people come up with numbers that are very hard to produce with the standard basic operations of addition, subtraction, multiplication and division. People seem to be focused on producing the results in any way they can, rather than asking whether it's possible to produce the results. You also start getting solutions using All The Things, even though it's totally possible to get the answer for some of them just using the most basic of operations.
The Seven Sticks and what mathematics is
This week I provided games and puzzles at a welcome lunch for new students in the Mathematical Sciences degree programs. I had big logic puzzles and maths toys and also a list of some of my eight most favourite puzzles on tables with paper tablecloths to write on.
Zooming in to see the slope
A lot of people introduce the derivative at a point as the slope of the tangent at that point, which to me is quite confusing. It seems to me that the reason we want the derivative is that it is a measure of the slope of our actual function at that point, not the slope of a completely different thing. To me, the thing is that the function itself is pretty much straight if we are close enough to it, so when we're looking really close, saying it has a slope at this point is a meaningful thing to say.
The Number Dress-Up Party
I created the Number Dress-Up Party puzzle way back in 2017 and every so often I stumble across it again when searching Twitter for other stuff. When I stumbled across it today, I decided it was time to write it up in a blog post.
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