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 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 students who benefited from my teaching were the ones who were prepared to find the same maths occurring in a different field.
None of these webpages will suit those who hated my lessons. These people (in my view) are those who want to be (demand that they be) spoon-fed. They want to know if each and every topic ‘will be in the exam’. Meaning that (i) they really have no use for this subject and (ii) quite possibly no use for school except as a means to stop needing education. I rate these minds as ‘closed’ and while I never stopped trying to open them, the resentment (of me, not by me) at such attempts was huge. I am as glad to have finished with school as they were to cease having lessons with me. I always hoped they would change their attitude at A-level, where at least in theory the subjects were chosen for positive reasons. If you are reading this you’re either a teacher or not in that group (or both).
Where I have written exam papers they are in the style of that board as I perceived it at the time. I was on a subject-specific committee for the MEI and contributed to conferences and, even though described astringently as ‘a lightweight’, often the only practising teacher providing a contribution. I marked for Cambridge (Further Maths, GCSE Computing) and [2015] inspected on their behalf (inspect what, I’m not allowed to tell, I think). While in Beijing I taught FPM (Further Pure Maths) to a rather good Y11 class on fewer lessons per week than the AS classes. We thought we were going twice as fast per lesson, which only made sense if all went on to do two A-levels in Maths, which I don’t think did happen. But then the pupils (and staff) turnover at BSB was so high, maybe 30% a year at the time, that it was the educational approach that mattered, one with which I thoroughly agreed. Throughout my China years we used CIE syllabi; these suit the Chinese temperament, light on language, heavy on maths. MEI differs, but the market should be diverse, so I view both approaches as healthy.
The long section entitled Lower School is the result of my generous HoD at Plymouth loosening the reins and letting me teach Y8 set 1 in my own idiosyncratic way and with no set syllabus content (though I did write it down so the department had a copy in case of enquiry). Many found my questioning of their assumptions would shake the fundamentals of their ideas of maths—testing the foundations, if you like— and most were the stronger for it. Those who felt differently all, at some point, threw away any regard for answers and reverted to what, for them, worked. Even when it didn’t, of course. Those who liked the approach found the subject exciting, challenging and rewarding — and perhaps still do enjoy applying the general thinking methods. Where Y8 and Y12 had adjacent single lessons in my room, the second would often ask what the ‘interesting stuff on the board’ was about.
Interested students: heaven.
DJS 20151210
