Helen was not convinced that the two times table contains the same number of numbers as the seven times table. [A conversation she initiated herself going to bed, out of nowhere.] She understood the idea of using a bijection to show two collections have the same cardinality without counting them - I modelled it (conceptually, not physically) with smarties, buttons and a lot of string - and she could see how 2n <-> 7n works, but (not surprisingly) it just seemed wrong to her. Just wait till she finds out the rationals are countable! more
I'm firmly convinced that graph theory is a perfect subject to teach to young (primary school) children. It allows an introduction to core aspects of mathematics - abstraction, generalisation, formalism, proof - in a context where there's a concrete visual representation and without requiring significant prerequisite knowledge. It offers the possibility of building to more difficult material (matchings, Ramsey numbers) and methods and tools (variables, induction, reductio), but also a range of topics which can be introduced independently at a low level of complexity (graph colouring, paths, simple functions). more
If your school tells you to cram times-tables or fractions into your child, but they don't want to do that or don't enjoy doing that, don't make them multiply. If they don't enjoy the maths they are doing at school, don't try to force them to do it at home, that's only going to make them dislike it even more. Instead, play games with them, do things with numbers and shapes yourself, show them mathematics unrelated to anything they do in school, and give them fun maths books to read and videos to watch. I realise this is harder for most parents than my previous "don't make your child read" injunction, because fewer parents enjoy mathematics themselves than enjoy reading, but if you are maths-averse yourself think of this as an opportunity to learn something new alongside your children. more
Kenneth Katzner's Languages of the World is being updated and since I'd reviewed the previous edition I'd been asked for comments on that and had my copy lying around. Browsing through it with Helen, she decided that Georgian was the most attractive script, so we transliterated and translated the first word (ღმერთსა / ghmertsa = to God) in the sample text, with the aid of Google Translate and Wikipedia. We're not about to learn Georgian, but I think she understands the difference between transliteration and translation now.
Helen has flat out refused to log on to the Rock Stars Times Tables site her school has provided all students access to, because — going by the demonstration and explanation of it they were given in assembly — she thinks it is about high scores and competition. more
I never did end up running any kind of pre-school maths circle, and once the children started school there hasn't really been spare time in the week for such a thing. But some of my thoughts about teaching mathematics from two and a half years ago have progressed.
One of my principles is to try to avoid things that will be covered in school. more
Way back in my first year of university one of my computer science tutors, I think it was Chris Bullivant, gave me the somewhat puzzling advice never to mix Lebesgue integration and black magic. (This was before he evicted me and Catherine Playoust from his tutorial because our discussion of Knuth's Fundamental Algorithms was distracting him from teaching the rest of the class what a for loop was.) I'm wondering now if this remark was inspired by Kennan T. Smith's A Primer of Modern Analysis, which as well as explaining Lebesgue integration carries the (unexplained) subtitle Directions for Knowing All Dark Things, Rhind Papyrus, 1800 B.C.. more
My plans for formal early years teaching all came to nothing. more
I can remember my father Hansen taking me to the Sydney university Coop bookshop (then in the Transient building) and buying me a proper Hewlett-Packard scientific calculator. That was over thirty years ago — I'm not sure exactly when, but it must have been before I started uni — but the calculator still works perfectly (and I think I've only had to change the battery once). more
I've seen some surveys where mathematics ranks as the favourite subject of a plurality of primary school children, ahead even of art, and I'm starting to see how that could be. more
I was planning a rant about the dangers of formal assessment of mathematics in primary schools, the insanity of streaming maths classes based on knowledge of times tables at age nine, and suchlike. But there are more than enough depressing stories about the UK education system at the moment, so I've tried to make this a more positive piece, about some of the things I think children should learn about mathematics in primary school, along with a random collection of ideas for actual teaching. more
Our little girl (she was "a big little girl" for a while, but now insists she is "a big girl") has turned three and moved up to pre-school. The room change was a bit stressful for the first week, but she seems to have settled ok now, I think largely because her best friends have all moved with her. more
An illustration of how deeply the concept of fractals has entered into popular culture is that it makes an appearance in the song "Let it go" from the film Frozen, in the line "My soul is spiraling in frozen fractals all around". So Helen was trying to sing the word at two! more
I occasionally play at teaching Helen the cardinal numbers one to five, not in any organised fashion but every so often when she seems alert and curious and there are no more obviously interesting things for her to play with more
On Friday I made my first visit to the Mathematical Institute's shiny new Andrew Wiles building (on the old Radcliffe Infirmary site). The occasion was a talk by Thomas Stocker, co-chair of the IPCC AR5 Working Group 1, presenting an overview of their recently published report (that's the Intergovernmental Panel on Climate Change's The Physical Science Basis). more