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 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.
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 (chi2(1) = 82.14, p < .001).