Sunday, November 28, 2010

Rethinking Math Education

I just watched Conrad Wolfram's (WolframAlpha) TED talk called "Teaching kids real math with computers" and thought he had some great ideas. Wolfram advocates teaching kids to solve math problems like they will in the real world, with computers, instead of stressing learning how to calculate by hand which in today's world is more or less useless.

The topic of math education reminds me of my own experience with public school math. In 3rd through 6th grade I was in a "gifted" program where, among other things, we were allowed to go at our own pace in math. The minimum amount of assignments that needed to be turned in a week was set, but you could complete as many as you wanted beyond that. As a result, I was working on the 6th grade math curriculum in 4th grade, and by 5th grade had finished it and worked through books on algebra, geometry, and trigonometry. In 6th grade, my teacher, having run out of books, assigned me and another student to build a scale model of the school - which was a little too much freedom for a couple of 6th graders, because we never actually got anything done that year.

After 6th grade, the system started to fail me. In 7th grade I easily tested into an "honors" math class, which consisted solely of arithmetic and some "pre-algebra." For the next several years I took pre-algebra (again - after moving and switching schools, this was once again the most advanced option), geometry, algebra, and pre-calculus, covering very little material beyond what I had taught myself in elementary school. In 12th grade I took AP Calculus, dropped the class halfway due to boredom and still managed to pass both parts of the AP test - because I understood the fundamentals, and didn't need to spend half a year drilling them.

The lack of advanced options for smart students, in my experience, turns them into slackers. There is absolutely no merit in doing three years' worth (or even a single year) of drills in "pre-algebra" once you grasp the concepts you're working with. It becomes grunt work, and this is why, until college, I viewed math as something that I was naturally good at but found dreadfully boring.

Anyway, I think that Wolfram's suggestions have a lot of potential for keeping advanced students more involved in learning about math. I liked the idea of being given free reign to solve a real problem - for example, "what type of car insurance should I buy?" This is a real world application of math that will stick with a student much longer than quadratic equation drills. Give the students some parameters (what type of car, mileage) and let them gather data and solve the problem on their own. I think this type of approach to education is needed to generate students that are computationally literate - which is more important in today's world than being able to crunch numbers by hand.

Saturday, November 27, 2010

Eliminate the Computer Science major

I believe we should do away with Computer Science as a field of undergraduate study - at least, the way it's implemented right now.

It's a given that, generally, a Geology major is studying to be a geologist. Likewise, a Biology major is training to become a biologist, and an Art major will probably end up an artist of some kind.

Computer Science students, however, don't go to college to become computer scientists. They go to learn "programming."

Theoretical computer science involves complex math and theory that is useful and interesting and takes a sharp mind to fully comprehend; most undergrads don't care and increasingly are not being exposed to it. Instead, popular languages are being taught in undergraduate courses, with the intention of preparing students for future work (see Joel Spolsky's The Perils of JavaSchools for another take on this phenomenon.)

The sad thing is, having worked one-on-one with several recent Computer Science graduates, I don't believe that they're learning much about programming, either. Students with a passion for programming study it in their free time, work on their own projects, and do most of their learning outside of the classroom. Fresh graduates with a BS in Computer Science and no real experience programming just don't have the skills they need to do anything but grunt work. As an undergraduate Biology student, my first CS course was on bioinformatics algorithms and had several Masters students, and when I was able to implement the algorithms quicker and more efficiently than CS students, I saw how lacking my school's curriculum was.

Solutions thus far have been to dumb down the CS degree by using higher level ("easier") programming languages and teaching less theory and advanced math. I think that aiming to dumb down the curriculum in order to prepare students for a corporate programming career is killing off the pool of intelligent academic computer scientists. The solution? Accept that there's a difference and offer two distinct majors: Computer Science and Programming.

The immediate result would probably be a huge shift of students from CS to Programming. Maybe some CS departments would cease to exist due to lack of interest. Programming students would learn the basics they need to succeed in the corporate world (similar to some "Information Systems Management" programs, but with a more straightforward focus on the technical aspects of development.) But smart CS students wouldn't be hampered by the dumbing down of their programs of study. They'd be exposed to more current topics in research and have the opportunity to take more advanced courses. They'd be allowed to choose from emphasis areas more in line with the current directions of academia. The Computer Science department would be a fraction of its current size but the per capita ability and motivation would go up, and these students would go on to be the brilliant researchers of the future. Their peers in the Programming department could get the high-paying job at the corporation of their choice, or start their own companies.

Let's accept that there's a difference between the two types of student, and start treating them differently.

Edit: Based on comments from several readers, I think "Software Engineering" is a much better name for my proposed vocational split-off than "Programming." Also, this pattern has already been implemented at some Universities, including Purdue (see CS vs. Computer and Information Technology) although as of yet it's hardly pervasive.