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Making sense of the effective population size formula
I was going to have a punchy title for this post, with a big moral to apply to the future, but I've decided I'm just going to describe to you what happened yesterday as I tried to learn some Genetics. You see what you can learn from my experience.
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Counting the story
Combinatorics is one of my favourite topics in discrete maths – that topic which is all about counting the number of ways there are to choose, arrange, allocate or combine things. I like the idea that I could theoretically find out the answer by writing down all the possibilities systematically and literally counting them, but that I can also come up with a quick calculation that produces the same answer by just applying some creative thought. It's this creativity in particular that appeals to me, so much so that I don't call it combinatorics, but "creative counting".
But I don't like cricket
When I was in primary school, one of my teachers once tried to teach us averages using cricket, and it is one of my strongest memories of being thoroughly confused in maths class.
The reorder of operations
The community of maths users the world over agrees that when evaluating an expression or calculation, some operations should be done before others. Mostly it's to prevent us having to be needlessly specific about what order to do calculations in, mathematicians being very concerned with efficient communication.
Out-of-body teaching experience
I have had a couple of new staff start in the MLC this semester. As part of the selection process they have to do a trial session in the Drop-In Centre, with me observing how they teach in order to give them feedback.
Pure play
The other day I did a workshop with students from Advanced Mathematical Economics III, which is more or less a pure maths course for economics students. It covers such things as mathematical logic, analysis and topology – all a bit intimidating for students who started out the degree with almost no mathematical background!
Obscuring the GST by making it simple
I was helping out at Roseworthy Campus yesterday as the Vet Medicine students were learning about budgeting for a Vet Clinic as a business. One aspect of this was calculating the amount of the cost of goods and services that was GST (stands for "Goods and Services Tax" – in other countries it's known as VAT or Sales Tax). The Excel sheet they were working in already had the formula worked in and it was this: GST = (Total Price)/11.
There is only one kind of function that distributes over plus
There is a very common thing that students do that causes pain, distress, confusion and depression in any maths educator who witnesses it. Both the error itself and the educator's response to it are very clearly described by this excellent picture from the blog "Math with Bad Drawings":
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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.)
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