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calc. reform
Posted:
Jun 4, 1997 9:42 AM


Let me give an example illustrating some points from my last message.
My first job after getting my doctorate, in 82 and was at the University of Iowa in Iowa City. At that time the University of Iowa did some recruitment of undergraduates from Japan. The first course I ever taught as a professor was three quarters Japanese. Every one of these students knew traditional precalculus material backwards and forwards and they were all hard workers.
We did very little "drill and kill" stuff  it would have been a waste of their time. Instead I proved a lot of things  but not everything and did a lot of conceptual stuff. But the conceptual stuff was tied into the theory. For example, I would try to explain why a continuous function would have extreme values on a closed interval. Then after a physical motivation for Rolle's theorem, it and the MVT could be proved.
Now the reformers say  "you have to assume the completeness property of the real line, so you're not really proving the MVT"
But this is where reformers miss a few BIG points by a mile
(1) It isn't the logical presentation of the MVT that matters here, but rather it introduces the students to a proof which can be motivated physically and geometrically
(2) The MVT may be the most important theorem in analysis and it is crucial that many students know it. Theorems are always understood better when they are proved.
I also spent a lot of time motivating derivative through instantaneous velocity and we approximated this by hand  nobody had calculators and it didn't matter  they could compute better than me  after all I was American educated.
WE also spent a lot of time solving the hard word problems. Who care if they were realistic or not  many were  I can not imagine better training for a scientific career.
Also I didn't have to lump problems into types. For example, when doing curve sketching we didn't do parabolas then cubics then quartics then rational functions and later on transcendental ones. Since these students truly knew precalculus I could "mix it up". This was also true for word problems.
It was a real challenge to teach these students and it was a total joy. The traditional book had a good balance between all these things. One of the big lies of the reform movement is that the traditional programs we heavy on rote stuff and left out conceptual stuff. The older Calculus texts were not heavy on rote stuff at all  check out Courant and John or many written in the '50's. Even those written in the '60's were not heavy on rote. But even if they were, so what? Some students may need a lot of rote stuff. In any case, many of the traditional texts could be used to give several types of courses.
Someone in the group mentioned to me that he uses the HC text successfully. This may be true and the people in this group seem very intelligent and may be able to supplement it where necessary  of course, it leaves out so much I doubt it can be successfully supplemented  this is definitely the case if it is used in a mainstream college calculus course. But I seriously doubt whether many future HS AP calculus teachers will be able to give a good course out of the HC or books like it.
Here at CSUN the prospective HS math teachers are not required to take advanced calculus (it was taken off the required list in 82 by the math education people in my dept. at that time) and they take a watereddown version of the math major. Half of our majors use the HC text and many of the "feeder" JC's use it too. Hence it is safe to say many future AP Calculus teachers in the Valley and the greater LA area will not know what a limit is, will not know what a series is and will have a huge number of topics  including L'hopital's rule, parametric equations, polar coordinates, sequences, MVT (which is not mentioned until towards the end of the HC book, etc. ... omitted from their education. How can such people teach an honest APCalculus course? Reform educated teachers all over the country will not have the background for teaching AP Calculus and will lack the ability to "make up ground". Since the HC text and ones like it are so lacking in topics and proofs they are also useless as reference books and many future teachers won't even have proper Calculus books in their personal libraries.
This is why I think all of you should oppose the HC text and similar reform texts. I truly believe you can cover the conceptual problems from a more traditional book. I know Dan Hart has had some success with Saxon for AP Calculus. In any case, the intense negative reaction against HC will result in different books being written and perhaps you will find one which won't need supplementation. Perhaps some of you can get involved in writing projects with college teachers  this would be valuable for all.
But if AP teachers get caught up in this reform bandwagon then progress will be slower. Also, as I indicated in my last message, the reform stuff just masks the bigger problems which start in K8. I teach our math courses for prospective K8 teachers and believe me there are some very serious problems here which need to be dealt with.
I appreciate the comments I have gotten from this group. Everyone here seems open to different points of view. Like you, I experience a certain amount of displeasure in teaching and the nature of my teaching has changed drastically since I started at CSUN in 84.
I know that the appeal of the HC text for HS teachers and college teachers is, in part, due to the fact that it is different and people may feel that any change is good. But as with my Japanese students, teaching a group of motivated students who are prepared and know how to study will always be fun and with such a group new things can be tried from time to time.
But this reform calculus is highly detrimental to anything good happening in the long run as well as the not so long run. I notice some of you discuss including and omitting certain topics  at least you are aware of various topics. Your successors will not be if they have gone through reform minded programs.
I have great respect for HS math teachers and in fact it was such a teacher who got me interested in math and in being a good student. I owe a huge amount to this person (as well as to a school system which had standards and assessment).
Like the Whole Language Learning movement, the Calculus Reform Movement is completely lacking in balance in the direction of dumbing down. The HC text is extremely bad for all science oriented students including future teachers. I hope I can convince some of you to see my point of view.
Jerry Rosen



