To make a long story short, I won. I'm very happy to be able to say that. It was an unbelievable roller coaster ride - at one moment it seemed like it would happen, at another I got kicked in the teeth. Round and round. I started on the very first day of school this year, and it's taken until now, but finally, it's going to happen. I get to create a computational math analysis course for next year.
Here are some things I've been thinking about - it seems that in the PreCalc texts used at our school, sequences, series, combinations, probability, etc. are all handled towards the end of the second semester. However, in a computational approach, it seems that sequences and series should be done early first semester, as all kinds of things can then be constructed from them. Thinking in terms of lists created from other lists is fundamental. That stuff should be done early. And I think there should be more emphasis on number theory. Our traditional texts don't really get into that. The fact that the primary types of number are programmable data types in Sage I think is really cool, and I'd like to make good use of that in an analysis course. I also think matrices should be done early. Again, in our current texts this is a later topic. But in a computational approach it's easy to think of and create a list whose elements are other lists. Does it make sense to say that our current secondary curriculum is organized as it is because it evolved in an age of handwriting? When doing things by hand we tend to emphasize single letter variables, but when doing things computationally it makes a whole lot more sense to use descriptive variables and function names. One of the big points I made in presenting a computational approach is that all kinds of lip service is paid to the theme of 'writing in the math curriculum', but no one is quite sure what that entails. Well, that's what programming is! Programming is using language to describe unambiguously how to solve problems of a certain type. I would be very interested in practical suggestions anyone might have for a computationally organized high school math curriculum. Ultimately I think an entirely new kind of high school math curriculum will be necessary, but at the moment, here in the trenches, it's one step at a time. Thanks very much, Michel -- "Computer science is the new mathematics." -- Dr. Christos Papadimitriou -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
