Quoting from Maths General, which is positioned in Lower School and Sixth Pure:
I have written webpages in places where one or more of these conditions apply:
• I have a different approach to what you find in a text book,
• where I never found enough exercises meeting the needs of my students,
• where the exercises available didn’t extend the subject sufficiently for my classes,
• where I found the textbook content only in university texts, which made them both rather difficult to read and hard to share with a class.
The readability of the English varies, depending upon who I was writing for at the time. If you want more or different, you might try writing to ask. If you modify my stuff, I’d like to know; if you disagree, I want to hear how and why and what you think is (more) correct. I have occasionally left what I think are answers nearby.
Frequently I have written theory in the dense language used in university texts. That is because, despite what I wrote in the earlier paragraph:
• I am trying to educate readers into coping with that sort of language
• I assume this content has been or will be taught in class.
For similar reasons I often look for different approaches to a topic. I believe understanding comes from several different approaches and I am sure that those student who benefited from my teaching were the ones who were prepared to find the same maths occurring in a different field.
Allegedly I specialised in Applied Maths. To all teachers I say that being good at a subject does not necessarily mean you can teach this to the reluctant, the confused and the less able. A subject you find difficult may well be one you teach better (but, in Maths, have more problems with doing test questions). I have no problem with admitting to that.
I remain confused why it is that so many of the topics in AS Mechanics are visited early in school science and yet so badly understood. This is to do with the ‘spiral’ approach to learning and I think it demonstrates failure. For example, the several equations for modelling constant acceleration (suvat) continue to be misapplied by those who have come through the school and really should have understood and corrected all historic errors by Y11. Friction is supposedly understood, as are vectors, ideas of dimension and so on. It makes sense to spiral around a topic, but less sense if so much is mis-understood. That is both a problem for teachers and for pupils; for the teachers in that their checking of progress—and any repair— has let problems slip through the net, and for students in that review of learning has not occurred. I suspect there simply is not enough resource, by which I mean the coincidence of time and interest.
I failed to find good texts in China for the teaching of Inertia and offer what I have produced as a short cut to a general understanding that also slowly extends that understanding to a good grasp of the topic. The classes that worked through these exercises were able to test answers for sense and this gave significant confidence that this was a topic (CIE FM Mech) they could get right, so we collectively judged this a success, if a little boring at times. The consensus was that they felt proofed against the unusual question and one comment was that the topic Inertia was as secure, after those exercises, as that of second order Differential Equations. Which would be good.
DJS 20151210
