Since most on this list probably work at the college level, as a high school teacher I'd be interested in the math expectations you'd have for incoming high school graduates today? In an age of ubiquitous computational technology, what should they know? What background skills should they have? Both in a traditional math sort of way, but also in a computational sense?
I may have an opportunity after winter break to discuss why creating a computational math course would be a really good thing to do, and I'd like to be able to back up what I say. I don't want to just make stuff up. These are some points I've come up with. Please correct me if I'm off, and please add anything else you consider essential. Thank you very much, - Michel Paul 1. Our secondary math curriculum arose in the age of handwriting and handcomputing (handcomputing includes the use of calculators), and most of what we teach has to do with the needs to express thoughts precisely and succinctly in order to minimize the number of hand calculations needed when evaluating expressions. I'd guess that's not the entire reason for our traditional syntax, but I bet a lot of it does have to do with those needs. 2. Our culture is shifting very rapidly because of technology, and literacy regarding it is important for general education. This need can be answered efficiently and quite elegantly via math classes. Computer Science classes are usually electives, but everyone has to take some math. 3. We often pay lip service to the assertion "Math is a language", but we really don't teach it that way. We teach it as a set of techniques to use for solving certain kinds of equations we might run into. We might 'use technology' to help us in that process, but we are still not thinking of math as a language when we do so. 4. In a computational age, it is more important to grasp relations between concepts than to memorize particular formulas. Better to learn how to analyze a concept as a set of inter-related concepts. Example - the quadratic formula. The traditional schoolish expression minimizes the number of hand calculations necessary. However, a more conceptually valuable expression might be to express it as h +/- r, where h =axis of symmetry, and r = distance to the roots. The traditional formula already does contain that relationship, but the structure of the related parabola is hidden for most students. I think it would be a good exercise for kids to think about it in this slightly more analytical way, spell it out, code it, and test it that way. Using Sage, it would be very easy to unite the articulation of the various components and the visual representation. Especially with @interact! Per the recent thread, even the ones who might not be able to code it could still interact with it and perhaps learn to understand the code that way. 5. With Sage, students could be creating their own mathematical papers. You want writing in the curriculum? Well, there you go! It's very easy to open up a text cell in Sage, so kids at many levels could create math reports that actually DID things. I don't even think it's that far fetched to have the more advanced kids learn some TeX. I just recently discovered the insert equation feature in Google docs. It's cool. Even if you don't know TeX, you can learn it just by using the editor. With this kind of stuff in the environment, I think this might be good for kids to experience. 6. There is always a tension between the use of calculators and 'showing ones work'. Kids hate having to write it all out if the calculator has already done it. All kinds of discussions go on about how 'much' work needs to be 'shown'. All of this becomes irrelevant if we instead focus on the 'work' being a functional decomposition of a problem or a concept. If one does ones 'work' correctly, the 'work' will then work for you! You can use it! 7. Instead of spending so much time teaching kids how to isolate variables in equations, perhaps it would be better for them to learn how to construct sutes of simple interacting functions? 8. China is already uniting Computer Science and math classes at the high school level. -- "Computer science is the new mathematics." -- Dr. Christos Papadimitrious -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
