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calc. reform
Posted:
Jun 2, 1997 1:28 PM


I have been reading the posts in this group with great interest and it is good to see teachers with such a genuine passion for their student's education. However, I think many of you are terribly misguided with respect to this calculus reform issue.
The Harvard Calculus (HC) text and ones like it are very one dimensional and dangerous. They emphasize a few types of conceptual problems which are based on calculators but (1) it omits almost all theory and some of the theory and definitions which it contains are wrong  for example a wrong proof of the quotient rule  with no explanation (2) it omits a huge number of topics  see the MC web site for a list of about 20 serious omissions (3) it suffers from a deemphasis on algebraic manipulation and calculation in general. A world famous mathematician  Donald Passman of the University of Wisconsin once told me, in his negative evaluation of calculus reform  "at least with the traditional calculus course we knew the engineering majors would know algebra by the time they graduated college  now we don't even have that" (4) Because of (1) and (2) the HC text is useless as a reference book.
Several of my friends in areo space and computer animation pointed (4) out to me. BTW These people hated the book and thought it would be terrible to use for CS and engineering majors. My neighbor is an aerospace engineer and I gave him the HC book to look at  his reaction was " they can't possibly mean that this book could be used for scientific majors". These people  who use computers on a regular basis  laugh at the way calculators are integrated into the material. They all say they would feel better having colleagues who could compute by hand and who know enough theory to be able learn a new topic if needed.
Here is some history: The calculus reform movement started in the mid 80's when it was found that about 50% of American students were flunking calculus the first time they took it. One would have thought that, as a first step, we look at what is happening before calculus. It was known that algebra skills were weak. Instead of looking into this the reformers said "hey, here is a good idea, let's not make calculus as algebra intensive and take out the theory."
Now this is bad for several reasons (1) Calculus without algebra, computation and some theory is not calculus and becomes useless for all scientific majors and (2) it stops people from looking into the real problems in education.
None of the reformers took the time to research educational issues  such as studies done by E.D. Hirsch who found that reform like ideas in education have been around for decades and are to blame for huge amount of what is wrong.
I can see the immediate appeal of the HC book to HS math teachers. Because it doesn't require facility with algebra and because it involves pushing buttons it will have a kneejerk appeal to students and the teachers get excited. But you are missing the big picture. What is important for success in college is that students have a firm base of knowledge which must include a solid understanding of algebra and trig. Furthermore students need to have good study skills. It is this last thing which differentiates the good college students from the rest. Good students will tell you that the act of learning isn't fun  it requires sacrifice and struggle. Students who don't know this are not prepared for college. Of course the rewards are great but a price must be paid. If calculators are getting in the way of this I would advocate not using them at all. I used to think they coul be used in HS, but reading these posts is making me think otherwise.
As a math professor at CSUN I see hundreds of students who have received a significant portion of their math training under reform programs  the California Framework, as instituted in 92, is very reform minded. These students are lacking in prerequisites and have know idea how to study independently. Since the inception of reform my students have gotten much worse.
While I know many of you have the best interest of your students at heart, I can tell you, from a college professor's perspective, you are harming them if you don't develop their ability to do hardcore calculation and give them dexterity with all the transcendental functions and their inverses. Furthermore, you must develop their ability to accumulate knowledge independently. If they are coming to you weak in the basics this is a problem. But getting them to push more buttons is not the solution and only masks the problem until a later date.
Some of you mentioned there has been no long term studies. This is no argument to defend reform. Just because an idea is pushed (and in the case of reform, some of it's biggest pushers, are those who are making a profit off it) doesn't mean it deserves to be studied while it is being forced on millions of unsuspecting students.
WLL was used for over a decade and we have now discovered that it has ruined the reading ability of tens of thousands of children.
What if the problems our children have had nothing to do with the traditional education that the reformers are so quick to attack? I and every math professor I know had a traditional education. Many of my friends from NYC had a traditional education and have gone on to highly successful careers. Face it, millions of people in this country and abroad were welltrained in a traditional manner.
What if the real problems in education were caused by schools of education through pushing programs which are based on the very ideas in common with calculus reform.
We would be in big trouble. We are in big trouble. If you are not profiting from reform then I urge you to consider this very carefully.
Jerry Rosen CSUN



