I met an erstwhile teacher colleague and we were discussing a student of his who was a bit of a mathematical genius – now comfortable amongst the elite of the elite in Cambridge. The colleague’s attitude was unassuming, that he could still guide the students whether they were better than him.
I replied with an answer that I now realise came from my time when I was a teacher. I said that because of the schools I taught in I never taught students that were “better than me”. Now that I have retired I want to unwrap any arrogance that is tied up in that comment so that I know what I should be ashamed of.
In maths there is a clear area of insight – problem solving, what could be called creative maths. It is this insight or spark that always has been most important for me because that spark is the path. I always wanted to push kids like this if I could find them. I would have liked to get them to learn about the path but that was not feasible.
Despite the schools I have taught in there are many students who have achieved more academically than I did, who have far more prestigious careers, some have even become famous. I was never arrogant enough to be measuring “better than me” in those terms. It was much more about the spark, and I answered the colleague in this way “there was only one student who had a distinctive spark and he was lazy”. I still have a vague facebook contact with that boy whose spark was “better than mine”. He is married, nice job, and from what I can tell not a path in sight.
I remember offending an ESN teacher 40 years ago. I told her that a boy in my first year class (now Americanised to year 7) was more intelligent in maths than she was. It was not my intention to be rude but she was offended, I was trying to get at the nature of intelligence. I remember it more because that night I was trying to score, my mouth got in the way and I lucked out. As an adult his maths achievement surpassed hers so I wasn’t wrong.
Spark and intelligence does not depend on achievement; for high-flying success you need both – creativity and application. But in terms of the path spark and intelligence is not enough either. I suspect the halls of academia are full of people who have spark, intelligence, and achievement – academic letters, books and papers flowing out of them, whilst at the same time having a deep frustration that they are missing out on something. They have not followed the path.
On this, Eckhart Tolle’s meme is interesting:-
Prerequisites for the path are usually meditation and spiritual teaching, I guess what he is saying is that these usually open the door. But suffering also does. My own upheaval was akin to suffering but whilst I was drunk and middle-class numbed I can’t say that I was suffering. There is far more suffering in the world than I experienced but suffering did not open those people onto the path.
So back to “better than me”. I always felt my maths had to be a level above the students, I had a maths degree so A level was my limit. One year I taught A level further maths and struggled with complex theory – something I thought I had once liked. I had gone past my limit.
An amusing story. One year I was working part-time, and got work at a polytechnic. The level of work was about A level standard – not too difficult but the students were two years older than I had been used to; I was also under stress in my personal life. I was teaching some maths for engineers, and an appalling pattern of behaviour (methodology) developed. I would prepare acetates to deliver the lecture, and the pattern that developed was that these acetates usually contained careless errors. Being engineers they loved to look for the errors, and this became the teaching methodology – acetates, errors and student engineer error-spotting and criticism. I tried hard not to make errors, was angry that I kept making them because it was embarrassing; but my excuse – I was under personal-life stress. I would prepare the acetates on Monday evening after a lecture finishing at 5.00pm. I would sometimes be there until 8.00pm (3 hours for a one hour lecture!!!) – and I was always waiting for a drink. I should have done the acetates and then checked them later with a fresh mind. BUT …. I didn’t, stress, drink, not enough professionalism and only one hour’s pay.
Here is the amusing thing about this story. My “methodology” had so motivated the students that they were doing well. Their exam results were significantly higher than previous years, so much higher that I was investigated for cheating. The investigation was concluded, the results stood, and the students were successful and happy. It wasn’t just my “methodology” that created this investigation, the institute was only interested in research funding – the lectures were only of secondary interest. As such the lecturers did not spend sufficient energy in “teaching”. Never again for this methodology though – the embarrassment.
Careless errors did occur after that but in such few numbers as there was rarely new material. I could pretend the errors were intentional and a teaching ploy – as a joke. Never a problem again. I am sure most of those engineers with their determination achieved far more “success” in the system than I did.
Back to the blog theme. Maths is linear – very linear. There are various stages of maths accreditation, key stages, GCSE and A level. Over time the syllabus content reflected the time it took for a typical student to achieve these levels, in other words two years to teach A level for students with a B or A at GCSE. This has changed recently (this century) because there is so much pressure to get students exam passes, teachers have focussed on areas that weaker students can do to improve their numbers. In maths this showed with A level students not being able to do algebra, and effectively ruining A level classes. GCSE students did not like algebra so under pressure careerist QA number teachers ignored the algebra.
Maths geniuses can jump the line only because they are able to do all the skills on the line so easily. The time frame of such students is far faster than the school standard linear time-frame described above. These maths geniuses clearly have a spark, but I suspect many of them failed to find the path because their success and likely ego will have got in the way. I never met such students and so was never able to measure my teaching ability against them.
So “better than me” is a fair description but what I don’t like about it now is how arrogant the phrase is. As I have evaluated it above my position is reasonable, but the phraseology is still arrogant. It is 12 years since I retired, it was clearly an assessment of my approach at the time, and in future, if it were to arise, I would be far more circumspect of the language I use.
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