Math Education

I stumbled across this video the other day:

It shows a middle-aged lady from Seattle talking about the state of math education in U.S. middle schools. She complains that students' abilities to understand and solve basic math problems is far below acceptable levels, and she obviously identifies didactic methods of contemporary textbooks as a major reason for that. She tries to prove her point by showing efforts to reduce the number and complexity of algorithms taught in school and to focus more on using reasoning and a structural understanding of the problems to come up with the solution.

One example that she gives is replacing the "standard" algorithm for multiplication of two-digit numbers (which I had never heard of, and which seems awfully complicated to me) with the so-called cluster method. This means, using reasoning to iteratively divide the problem into smaller parts which can be easily calculated. The textbook authors justify their approach by saying that the cluster method is more intuitive and easier to understand, and that everybody can use calculators for more complicated problems. The lady however thinks that these methods are the very reason why students don't understand math any more. She advocates going back to the old and established standard algorithms. In fact, one of her main claims is that "algorithms" are the way to go, instead of non-deterministic methods.

I don't think any reasonable person would seriously disagree with her statement that there is a lack of math skills in our society. From my experience, I can absolutely support this claim, both for the people in the U.S. and in Germany. Many times I've seen fellow computer science students which preferred to use a calculator to solve problems like 8 times 7. Every day I see politicians or advertisements using numbers in obviously misleading ways, and they always succeed in persuading people, even if their numbers don't even support their claim on second thought.

However, I do not agree that teaching children more algorithms in math classes would solve this problem. The problem is not that students are not able to solve "13 times 26" mentally, it is merely that people lack a structural understanding of number problems, and a "feel" for numbers. Knowing algorithms does not help too much nowadays, because computers and calculators are abundant, and they are so much better at solving such problems. The one thing that computers and calculators can't do is to reason about the numbers, meaning the ability to take one step back from the problem and think about whether the solution is reasonable, whether it makes sense. In my opinion, the cluster method for multiplication is a good step in this direction. It forces students to reason about what the solution would probably be, and not apply some algorithm and just accept the result.

Times change, and with the introduction of computers and calculators into our world, and with the vast amount of numbers that we are bombarded with every day, also our approach to numbers must change. Let the computers do the number crunching, and let's focus on interpreting the numbers, extracting their meaning and understanding what they actually say, instead of tenaciously holding on to algorithms which nobody ever uses after school.

Don't think in algorithms, think in structures. Computers can do the algorithms.

Starting my blog

I must admit, when my friend Nicola first told me about Blogs a couple of years ago, I didn't think that this form of communication would gain any major recognition beyond a bunch of computer geeks who spend most of their time reading Slashdot and, well, blogging about what computer geeks blog about.

But, obviously, I have changed my mind now. I was impressed by how major traditional news media report about blogs, cite from them and even introduce their own blogs. I was suprised when John Batelle at a recent talk at Google New York said that his Blog alone had about 20% as many readers each month as Wired Magazine, at what is probably a tiny fraction of the cost. I'm happy to see that blogs seem to become a significant ~~pain in the~~ nuisance for totalitarian regimes, and will hopefully help paving the way to more democracy and justice in the world. I'm glad that doing research online is constantly becoming easier and more effective, and that I frequently find answers to my questions on blogs. And finally, I'm (kind of) in the media business, and I'm not yet old enough to just miss major trends like that.

All together, I think it's time for me to give it a shot and see what happens. So, here it goes. :-)

Patrick's Blog

Math Education

Starting my blog