This page can be safely omitted by those able to read a novel without first having to read a biography of its author, a habit that I find perverse, if not pernicious. On the other hand, it is sometimes helpful to know the background of an author in order to form an opinion on her/his credibility. Certainly, were

I came from France to the University of Pennsylvania in the Fall of 1965, on a Fulbright, with an ABD in Mechanics, a discipline that, in Europe, traditionally sits between Mathematics and Physics. It was both

That I would switch from research in

At my request, the School of Education at the University of Pennsylvania set me up working an hour every morning with lowest track third-graders at an associated Elementary School with Dienes' Attribute and Multi-Base Arithmetic blocks. However, fascinated by the children's reaction to my very clumsy efforts at letting them go through the Dienes four-cycle, I immediately forgot what I had meant to investigate and let myself be carried by the experience. The results were of course diverse but two incidents have stayed in my mind. Once, I had left the classroom for a few minutes to find at the door, on my return, a very agitated administrator who explained to me that what I had done was completely irresponsible and quite dangerous as such students as I had could, left to their own devices, be expected to do just about anything, including setting the school on fire. Looking through the window, though, it seemed as if the students had hardly noticed my absence and were just continuing to do with their blocks whatever they had been doing when I left. That did not mean much for the agitated administrator but may have perhaps accounted for my not being thrown in jail. The other incident was my visit to the principal, towards the end of the academic year, because Russell, a quiet loner, had written down, completely on his own and not even at my suggestion,

The next year, after my wife and I decided to stay a while more, I got a job teaching at Community College of Philadelphia which had half started just the year before. The "open door" concept was a fascinatingly new one to me and completely in accord with my political views. In France, if education was free, including beyond secondary education, and theoretically reserved to talent, it was in fact almost exclusively for the bourgeoisie. To be sure, in France, the elite did not coincide entirely with the privileged classes as, historically, the latter has always been very keen on recruiting a managerial class from the lower classes. Lebesgue for instance was the son of a blacksmith whose elementary school teachers got him a cost of living scholarship for him to go to a secondary boarding school in the provincial capital. His teachers there got him a cost of living scholarship for him to go to the university in Paris. But, at least in the 1960s, students of blue-collar origin still accounted for only about 1% of all post-secondary students.

It didn't take me long, though, to realize that what we were teaching at Community College of Philadelphia was what appeared to me to be, at best, a very watered-down version of the first two years of 4-year colleges. Yet, dealing on a day-to-day basis with these students rapidly convinced me that there was no need for the inanity of the Mathematics for Liberal Studies that we were teaching them and I proceeded to write a text,

In the meantime, I had learned some

From almost the first day, my obsession had been to make the "open door" concept a real one as opposed to the revolving door that Community Colleges turned out to be for the most part. So I went back to the idea of starting basic arithmetic with Dienes'

I was also convinced, as I still am, that the lack of continuity inherent in semester courses was part of the problem. So I wrote a text for a

Then I thought that a systematic use of

By defining the tangent line as the best linear approximation to the graph of a function near a point, [Bivins] has narrowed the gap, always treacherous to students, between an intuitive idea and a rigorous definition. The subject of this article is fundamental to the first two years of college mathematics and should simplify things for students.....I also pointed out the difference in the usual definitions of the derivative in dimension 1 and in dimensions 2 and 3. Nothing would do and my colleague remained steadfastly unconvinced. You might say that he had a vested interest, though.

After running repeatedly into this kind of, let us say, lack of support, I thought I would keep to myself and just take care of

After the first couple of tries I was convinced that it would never get funded [by the NSF], but I continued to submit 12 times in all as an experiment on how the system works. I found that there was always a split opinion on my proposal that typically fell into three groups. About one third dismissed me outright as a crank. About one third was intrigued and sometimes gave my proposal an Excellent rating. The other third was noncommittal, mainly because they were not sure they understood what I was talking about.

And then, as before, the sequence came under heavy fire from the Physics/Engineering Department and, somehow, it just so happened that academic advisors started discouraging students from taking the integrated sequence on the grounds that taking Precalculus I, II and Calculus I in 8 semester hours

Of those attempting the first course in each sequence, 12.5% finished the [conventional three semester 10 hour] sequence while 48.3% finished the [integrated two semester 8-hour] sequence, revealing a definite association between the [integrated two semester 8 hour] sequence and completion (chi^{2}(1) = 82.14, p < .001).

So, I though that, if I were to keep on working on unconventional things, this would henceforth have be completely on my own and within the framework of the conventional courses that I was now teaching, Arithmetic, Basic Algebra and Precalculus I. After all, that is what tenure was for.

Eventually, though, a report on a