Archive for the 'Uncategorized' Category

Calculus Crank

August 17, 2006

Thanks Chris for your comment on my last post. There was a lot there and it stirred up memory of one of the biggest sources of advice for this project: a book review by Underwood Dudley from nearly twenty years ago that is repringed on talldarkandmysterious’s site. Before starting to write last summer I sent Dudley an email asking if his views have changed since 1988 and he said no that his objections are pretty much the same.

So what triggered this memory was Chris’ note about geometry. Dudley’s second conclusion is that Calculus books need more geometry. I think that Calculus can be taught as a nice combination of calculation and intuition and that driving the geometry out of it makes the intuition less – umm – intuitive.

It is Dudley’s first conclusion that is the biggest risk in Calculus books. It is easy for Math practitioners to be dismissive of a book on Calculus that doesn’t do something in a particular way. But, as Dudley notes, Calculus books should be written for students and not for professors. In fact, I think that students should be able to read and learn from the book as a supplement to what the instructor is presenting. If the instructor is merely re-teaching exactly what is in the book (which is done way more often than you would like) then there seems to be little value in the student owning a copy of the book.

This memory was spurred by Chris’ note that we shouldn’t be teaching Calculus for that one in 100,000 that is going on for a PhD in Math. There was a conference at Breadloaf in the 1980s at which the point was made that the PhD requirements for Biology helped drive the science we teach first graders. The arguement was that undergraduate curriculum in Biology was designed by Biologists who, among other things, wanted to ensure that students would be prepared for grad school in Biology. The High School AP program and hence standard Bio courses were therefore designed to adequately prepare students to take Biology in college. These high school teachers told middle and elementary school teachers what science the younger kids would need to come in with. The result was that the science taught in first grade was not necessarilly the science that would be taught without the constraints of beginning the preparation of preparing a small percentage of that population for work as a professional.

No longer Head First

August 12, 2006

I got the letter of cancellation for the Calculus book. It is no longer going to be a Head First book. I’ve been spending some time trying to figure out what it will be. This is a bit confused by my misunderstanding of what it was.

Without providing details, there seems to have been a disagreement among the too many editors involved in the book (I count seven who have so far weighed in with opinions). Some have found it to be very Head First and very good while recently a senior voice said it was not at all Head First and would have to be story-boarded and rewritten.

So it will be something else and that’s ok. It was initially something else. The Head First elements and philosophy is wonderful and this would have been a great book. Maybe they will sign someone else to write the book they want. I need to figure out what happens to this one.

I’m open to suggestions. Also – I’m looking for idea donations. What would you call the series that this book appears in?

Limits

June 8, 2006

I returned to writing a week or so ago. It’s been inconsistent but I am now writing about limits.

To me, a limit is all about expectation. The limit of f(x) as x approaches a is all about a guess of what should happen at x = a. What actually happens is not relevant. Maybe f(a) is a different value than this limit. Maybe f(a) doesn’t exist. None of that matters. We don’t worry about reconciling expectation with reality until we discuss continuity.

I’m in this whole “Harry Potter” thing right now in this chapter. I don’t know if it will stay in. I’ve also got this Abbot and Costello “who’s on first” routine about the sum of the limits is the limit of the sums and so on. Writing a head first book is both scary and liberating. It’s like a drugless trip. The boundaries of traditional books don’t restrict us.

In any case, this is just a brief post to say thank you for your support these past months and that I’m back trying to write each day.