This title was inspired by a podcast interview of Professor Peter Harrison, but I used “maths” instead of “science” here. Prof. Harrison has published a number of books on the relationship between science and the Protestant Reformation, and suggested in the interview that to help people rebuilt their trust in scientists and their scientific expertise, it’s not to do with preaching the scientific orthodoxies, but requiring “the introduction of a humanity style understanding of what the science entails”. In other words, to educate people about science, not just in science.
We know there are people, out of their commercial motives or personal beliefs or negative experiences, tending to be sceptical about whatever scientific reports are about and to trust their own gut feelings rather. This is the predicament that the scientific academia is facing now. Well, as a maths person, the moment I heard of the distinction between “about science” and “in science” raised up in the podcast, I thought about the paralleling ideas in maths education: those things “about maths” and those “in maths” and the prevailing indifference towards this subject.
And these are the relevant topics “about maths” that I can think of:
- The history of maths. For example, when and why did mathematicians come up with the idea of “the complex numbers”?
- The sociology of maths. How was maths being operated in the past? How is it at present?
- The practical value of maths. How is maths applied to the real world? People always say that STE (science, technology and engineering) are indebted to M (mathematics), but can you show me?
- The principals of good maths. That sounds aloof, but I reckon basically, one of the fundamental rules of this subject is “the more concise the better” (see the adoption of the radian measure), another is “the more generalized the better” (see the shift from the Pythagoras theorem to the cosine rule), another is the pursuit of closure (see the introduction of fractions, then surds, then imaginary numbers)… In order to make sense of all these mathematical inventions in the long history, we need to understand, even buy into these principals. A lot of research is needed here, anyway.
- The anecdotes of maths/mathematicians. This part is related to the history part. But I would emphasize a more humanistic perspective here. We know that mathematicians are not saints, and they didn’t necessarily do maths with no self-interests. But they are also not just geeks or nerds. Hope I can collect many interesting stories about them so that to make maths less cold and elitist.
I am quite comfortable with discussing maths questions or concepts with my students — let’s talk about maths! But hold on, today’s teenagers need first to be convinced of the value of this subject, and the plausibility of being an agreeable maths learner rather than an eccentric nerd. Therefore, these topics about maths are what I am going to look into. But I am not the only one. Eddie Woo, the 2017 NSW hero, a dedicated secondary school maths teacher, has done all these topics about maths in his Wootube. When I watched his video of “Who Cares About Complex Numbers?”, it has really blown my mind! There are some ideas even new to me. In that video, he compared the invention of surds to that of the complex numbers, embedded a little bit history of 16th-century maths societies. With these, he successfully made me find it’s absolutely rational to invent “irrational numbers” and realistic to come up with “imaginary numbers”. That is awesome! Hope I can do the same thing one day in my career life.
I highly highly recommend the Wootube, and I myself will definitely keep learning from Eddie’s approaches and learn from other inspirational educators too, and harness my abilities to talk about maths.
Thanks.
Until then.
WS
Maths for us 