In my second year (January-April 1971) the family, consisting of myself, Sue, 4 year old Rebecca and 3 month old Christopher travelled to Princeton where I was a visiting research fellow working with Michael Atiyah. It was here that I met Hassler Whitney, a highly respected mathematician who had turned his attention to teaching young children. It was here I decided to turn fully to being a mathematics educator. I first met cherry ice-cream too and ate it by the gallon (An American gallon is actually only 4/5 of an English gallon, so it was not as much as all that.) The result was that I put on some weight. Hassler took me into New York to visit a project he was involved in in Greenwich Village. We travelled to Penn Station and he asked what method I would like to use to get down to the Village. I said, the same as he used himself. As we walked out of the station he said, “In New York, I run!" and sped off down the avenue. I puffed along in his wake doing my best to keep up with someone who was about twice my age as New York policemen looked twice at this perspiring fat guy chasing after a skinny old man. This was long before the days of fitness and long-distance running.

During my time in New York, I visited several times to see operas and broadway shows. It is an exciting but often unfriendly town. On my first visit I took Rebecca. Having promised her I would take her earlier in the week, I could not let her down when the temperature dropped to 6°F. It was windy and freezing cold. I stopped a New York policeman and asked him the way to the Rockerfeller Center (which happened to be about 50 yards away). He looked and said, “Ya gotta dollar?”, to which I replied, “Yes.” He turned on his way and called over his shoulder, “then buy a map!”

Back in England, I now began my task of converting myself seriously from a mathematician to a mathematics educator, which was difficult at the time because the only relevant research was either Piagetian stage theory, or psychological stimulus-response. More general materials about teaching and learning mathematics did not exist, at least, not until Richard Skemp published his famous little book on The Psychology of Learning Mathematics. In the mid-seventies, I started investigating students’ conceptions of university mathematics and this eventually led to my conversion into a mathematics educator.

In 1976 I attended my first ever overseas conference, paid entirely by the department. This was the International Congress of Mathematics Education at Karlsruhe in Germany. I saved money by staying in a student room instead of a hotel and there met a group of friendly German students. One of them had sold his motorbike to a wine-maker who had paid him in wine. He sold a good Riesling Kabinett for one mark 70 and a great Auslese for two marks 70. I bought loads and was the purveyor of my own wine at parties, where mine was far superior to that provided by the conference. I formed links with mathematics educators in Montreal which led to me going to Canada on study-leave.

The best part of the conference was the formation of the International Group for the Psychology of Mathematics Education which held its first meeting at Utrecht in 1977. There I met Shlomo Vinner who invited me to Jerusalem. It was the true beginning of my transition from mathematics to mathematical thinking. However, I am getting ahead of myself. Before going on to more academic developments, I need to return to my music.