Two musings (incomplete ideas) to share…
Real World Maths
Many maths teachers and commentators are convinced that linking the learning to the real world will make maths more interesting and relevant and, in turn, increase students’ motivation and engagement (too many to link to – I will add links once I’ve sifted through the gazillions saved from Twitter). Intriguingly, it’s a claim more commonly made in schools where there are problems with engagement or with results, and is seen as a possible solution. I haven’t heard it mentioned much by teachers in schools where maths results are very high, or from maths graduates (although I am now truly into the realm of anecdata).
I wonder what they would make of these Glorious Extracts from North Korean textbooks? (source: Nothing to Envy – Barbara Demick)
1. 8 boys and 9 girls are singing anthems in praise of Kim-il-Sung. How many are singing in total?
2. 3 soldiers from the Korean People’s Army killed 30 American soldiers. How many American soldiers were killed by each of them if they all killed an equal number of enemy soldiers?
3. A girl is acting as a messenger to our patriotic troops during the war against Japanese occupation. She carries messages in a basket containing 5 apples, but is stopped by a Japanese solider at a checkpoint. He steals two of her apples [obviously]. How many are left?
By the above logic, N Korean students would be amongst the most enthused and engaged in the world… (For the avoidance of doubt: I am being facetious).
Dan Meyer made a helpful diagram to think about how context and style of question can affect how intriguing or challenging a question is for students:
I think that Dan has honed in on something critical, although it’s hard to ignore some of my own biases. My students are most engaged and excited, and ready to grapple with cognitively challenging content, when it’s more towards the top-left quadrant (think UKMT-style questions, or cool patterns, or counter-intuitive results, or a sudden spark that reveals the underlying structure of a problem). However, that is the type of maths that excites me the most, so they could simply be responding to my moods and enthusiasm. I am one of those happy weirdos who does abstract problems to relax (KS4 algebra is a good route to soothe a headache), so I am perhaps not a good barometer of what students will find interesting or exciting.
I had the good fortune of finding out on Saturday that, despite an A level in English, I didn’t actually know what a fable was. More humbling, I thought I knew but turned out to be just making inferences from the contexts when I tended to hear or read the word and had no formal definition beyond ‘it involves animals and morals’ (oof).
If my memory serves me correctly, what makes fables distinctive as a structure is that they are a vehicle to examine an idea and the characters maintain constant traits in order to underline the key aspects of the idea(s). It’s for this reason that animals are often used (Aesop’s Fables, Animal Farm) as attaching a single idea to a character is a bit more difficult with humans. By contrast, a classic novel (i.e. a romain) tends to have characters undergo change in response to the world.
In terms of Bloom’s taxonomy, this is a piece of knowledge that allows me to evaluate/synthesise/self-congratulate because it is more abstract and higher up the triangle of goodness. I had a sudden realisation of the blindingly obvious: I was only enjoying this knowledge, able to check that I really understood it, and finding it useful and interesting, because I had lots of plots, characters, stories and themes already in my memory.
This suggests an argument in favour of Bloom’s as a tool for thinking about learning; the more abstract knowledge was enabling me to synthesise/re-examine books and poems I had read in the past and see them in a new and (even more) interesting light. Bloom’s correctly identifies that facts and memory have to come first, as the analysis relies on having a good store of literary knowledge in your long-term memory.
However, it confirms for me that it is misguided to think that ‘skills of analysis’ or ‘skills of evaluation’ can exist in a vacuum, or that they are more important than a store of knowledge in long-term memory. If I couldn’t remember substantive points about any fiction/poetry I’d read, I doubt I’d even remember what I was told about fables on Saturday – there would be nothing to connect it to, and it would have seemed like a factoid rather than a revelation.
There is nothing ‘relevant’ about fables, or about abstract number problems. I suspect that the motivation to learn more is largely the motivation to connect more of what’s outside of your head with what’s already in there. The more that’s in there, the more there is to connect to, and the more enjoyable learning becomes*. If making one’s mind a more interesting place to inhabit is something we can offer to students, then that seems like a pretty worthy goal.
* The word ‘fabulous’ has the same root as ‘fable.’ How great is that?
** Incidentally, the easier remembering things becomes also – the more there is for a new idea to connect to, the more embedded it will be. It is odd when people say ‘Why memorise that [random thing] when you could learn [other thing]?’, as though there is finite space in our brains. If anything, it’s a Mary Poppins bag – the more that goes in, the more you can fit.