1911 ~ 1979

Tim Rowland continued:-

Nevertheless, the Guides did seem to want to bring into primary mathematics some joy and some breadth, such as I had experienced with the students on the games and puzzles course, and it is for this reason that I regret the loss of most of these topics from school mathematics. I resisted Diane's suggestion that I should be drawn into teaching a primary mathematics curriculum (quaintly-named ‘Basic Mathematics') course. Remarkably few limitations were imposed by others on what I might be expected to be able to do!

I recognise how much I learnt from all sorts of people in staff room conversations, especially when everything stopped for mid-morning coffee. It is regrettable that such opportunities are now relatively few and far between. In the absence of any formal training to teach, I learnt a great deal by osmosis – about philosophy of science, about child development, about dance and drama education, about the rationale for the new middle schools. I would say that what I learnt most of all were ideas and principles. I developed a kind of idealism, a philosophy of learning that turned out to be hard, initially, to implement in the ‘real' world, but which nevertheless remained unshaken in the face of pragmatic constraints. I do not look back on my own experience as an Assistant Lecturer as workplace training for teaching. One could construe it in that way, but that would stretch my own sense of what I was doing somewhat too far.

After three years, there followed a year's secondment to a secondary comprehensive school, to teach the school's first-ever A-level mathematics class. I enjoyed the advanced teaching and survived the rest. The fact that the Head only realised that this was my probationary year in the week that I left the school had everything to do with a breakdown of communication and nothing to do with my competence with the 15-year-olds in the seventh mathematics set. On the other hand, I did teach A-level mathematics to Vicki Kellett, who that year became the first pupil from the school to gain a university place - to study textiles, at Leeds University.

I returned to the College as a ‘proper' lecturer, resigned to teaching how-to-teach, having just been made painfully aware of my own shortcomings when it came to managing 11- to 15-year-olds. David Moore had cornered the secondary curriculum area anyway, so there was no opening for me there. That fact probably determined the direction of much of the rest of my career.

So it happened that I became Jack's Apprentice in primary mathematics curriculum. Jack Ashworth took retirement when the College closed, and has since passed on. He was a down-to-earth, thoroughly likeable man, paternally kind to me. His previous post had been at Bulmershe College in Reading , where he had been thoroughly infected with Dienes, doubtless due to the influence of his colleague, later HMI, Peter Seaborne. The Basic Mathematics course was based on a strong diet of Logiblocs and Multibase Arithmetic Blocks (Seaborne, 1975). We did all the Nuffield stuff with sets. We made them, we sorted them, notated them, found their union and intersection.

We were amazed to see that common denominators of fractions were merely the intersections of sets of multiples. I may have forgotten, and probably have, but I don't think we talked too much about children, their learning (they would get that in education ‘theory') or how one might organise them to do and reflect on these activities. As I remarked earlier, mathematics education was at that time in its infancy as a research domain. Many years later, we realise that mathematics pedagogy is informed by both understanding of mathematics per se and by theories of child development - not to mention theories of knowledge, understanding of social factors, and much more.

When my apprenticeship came to an end, I was set loose with my own Basic Mathematics classes. I tried to do what Jack did, and for good measure threw in some fun with binary arithmetic and punched cards. I had also discovered tessellation, and we did some of that too. I take pleasure in pointing out that I managed to acquire two degrees in mathematics without learning that every quadrilateral tessellates in the plane. About six years ago, I mentioned this to a distinguished Cambridge Professor of Geometry as we climbed the staircase towards his College rooms. He stopped in his tracks and asked me, “Is that really true?” I think our Basic Mathematics courses engaged the students' interest and raised their awareness that (for better or worse) there was more to primary mathematics than they recalled from their own experience.

I made no visits to students in schools in my first incarnation at Bingley, as an Assistant Lecturer. In my second coming I was, of course, obliged to do so. Time has kindly blotted out all memory of my ‘supervision' of students in schools, with one exception. I supervised a PGCE student called Alan Barnes at Eccleshill Upper School . Alan had a PhD in relativity, and did far more to further my career than I could possibly have done for his, as I indicated at the time (Rowland, 1994).

On the national scene, there were some tremendously exciting ideas in the air. One of the earliest uses of the term ‘investigations' is in a report on College of Education mathematics main subject studies (co-authored by Alan Bell) produced for the mathematics section of the Association of Teachers in Colleges and Departments of Education (ATCDE, 1967). In the same year, the ATM published Notes on Mathematics in Primary Schools . It is probably true to say that we did play down the skills of arithmetic in our curriculum courses, at the expense of enquiry-based approaches to learning. No doubt some of it rubbed off, but when our students got into school they, like most of their school mentors, depended heavily on ‘Fletcher Maths'. It was all undeniably exciting, if somewhat chaotic. Perhaps this teacher training environment did for many of these students much the same as it did for me, their ‘teacher' – the inculcation of some ill-defined but passionately-held ideals and values.

All good things must come to an end and, without doubt, it was a good thing for me that this one did. Seven years after I had arrived, I left Bingley for a school teaching post. Three years later, I read that the College had been closed. The boom years had been followed by a dramatic decline in the allocation of student numbers in response to demographic trends. In common with a great many others, the College became a victim of local government reorganisation and the delightful remoteness of its moorland location.

Tim Rowland is Senior Lecturer in Mathematics Education at Cambridge University