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Friday, February 17, 2006

Redefining our major curriculum units

Early in April, our entire math department will be participating in a workshop on “redefining our major curriculum units”. At this point I have some very preliminary thoughts, some of which I’ve discussed here previously:
  • Many mathematical applications that are important at the beginning of the 21st Century receive short shrift from the high school math curriculum, even at intellectually progressive high schools such as Weston. For many years — at Weston and elsewhere — I’ve been beating the drum of cryptology, which has many claims on a significant place in a high school math program: it shows uses of linear functions, number theory, systems of equations, matrices, and exponential functions; it’s interesting and motivating for a significant number of students; it’s truly important in our current world of heavy Internet usage; and it provides ample interdisciplinary tie-ins. Nevertheless, cryptology is nowhere in the curriculum of most high schools, and at Weston it appears only in honors-level Algebra II.

    Similarly, it’s essential for future voters to understanding procedures and models of voting. But those topics appear nowhere in the high-school curriculum — neither at honors nor at college-prep level, neither at Weston nor elsewhere. We’re emphasizing mathematical models these days, as we should be doing, but some of those models ought to be of voting systems

    And then there’s game theory, another topic of increasing importance in the new century. Where does that occur in our curriculum? Only in a course taken by a tiny number of students who are not comfortable with the symbolic manipulations found in precalculus. This course, Applied Discrete Math Concepts, is a fine opportunity for the few kids who take it, but game theory ought to be found in the curriculum for all students.

  • At some schools, including Weston, math teachers invest a lot of time in thinking about themes, tools, and techniques. We talk about big ideas, such as representation and variable. And we talk about the details that are necessary to implement those big ideas, since the devil is in the details. And we talk about the tools and techniques that students ought to be learning as aids both in their future math and in other endeavors.

    Perhaps we need to place more emphasis on certain themes, such as transformations, which could weave their way into every year’s math course. And we should rethink our use of tools, whether they are mathematical tools such as matrices (applicable in many courses) or technological tools such as the graphing calculator or the Geometer’s Sketchpad.

  • We’ve made a valiant effort in our project of integrating computer programming into the regular math curriculum, but we still have far to go. In particular, programming is not integrated into enough units; it’s too scattered, and as a result a student may go a whole year without doing any. Last June, three of us delivered a paper at the TeachScheme Tenth Anniversary Workshop, in which we made the point that programming should be a regularly available tool at a student’s fingertips. But no one will develop enough facility to make this possible unless programming is a regular, not sporadic, part of the curriculum.

  • Finally, we always assume that honors curricula are a superset of college-prep curricula, and therefore an honors course is “better.” If a topic is in college-prep Algebra II, we know it will also be in Honors Algebra II, but not necessarily vice versa. Maybe this principle is wrong. Maybe college-prep and honors should be slightly different courses, where surely there’s something extra to be learned if you take honors, but where you also miss something if you do that. There would be a trade-off that would require some thinking; the honors course wouldn’t automatically be perceived as better.
I would welcome ideas from any students, teachers, parents, or anyone else who reads this blog — either additional ideas of your own, or feedback on the ones I’ve suggested. Let me know!

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