Do you know the Khan academy? If you are not native English, you might never have heard about it. Otherwise, there are good chances you stumbled across it somewhere. A brilliant introduction can be found on TED where Khan gave the talk „Let us reinvent education with videos„. By the way, I recommend all TED talks, or at least most of them, if your English is sufficient. The talks are also a great model for talks you might give somewhere, and a relief from the often seen „presentations“.
So what is Khan doing? The idea is to provide sets of well made videos explaining stuff over the net. Many videos are about math, which is what caught my interest. The last time I saw a well made and attractive math video was when I saw Norman Wildberger talk about rational trigonometry. But educational videos have been around since ages. In the 60s there was a black and white series in Germany on TV with math related videos called Telekolleg. (See an example video on tangents.) So the idea is by no means new.
Does it work? Khan’s main argument is that with videos the learner can learn on his own path. He can repeat the video as often as he likes, or stop it to reflect about an argument (or simply to go to toilet). He can take the next video, when he is ready for it, not when there is time for it. He can take the test, when he feels he can pass it.
This is the very same idea of self determined learning that has been investigated in the recent years in connection with electronic material. We can add computer controlled tests to the learning environment, and Khan does just this over the net using computer generated problems. These are drill tests, which are good to teach those things that you can learn by drill.
Why videos? Didn’t we use books before just for the same purpose? That is not only a change in the culture of media consumption. In fact, videos are richer than books. They provide a social contact to the teacher that only very well written books can imitate. The human brain is very good in learning by watching. It is made like this. The fact that videos have not been around for 3000 years does not imply, that they are bad. Teachers have always been necessary to guide the learner. Why? Not only, because they can answer questions. Also, because they provide a paragon, a pattern to look up to, an example to imitate.
How to change Math Education?
Can we use videos and stop giving those classes in universities where the professor provides a one-for-all talk about the subject, with little or almost no feedback from the students? Can we replace them with a network page to work on, and assisted exercise sessions? Can we replace whole class instruction in schools by self determined learning and guided problem solving?
I think there is a lot we can change, but there are also problems.
First we need to agree: For a large part, math is not really a subject that can be learned by drill. Math is about understanding, intuition, visualization, and last not least about logic. The computational aspects are only one part of math, and its role is decreasing with the availability of computer algebra systems, statistical packages, or visualization software. Math needs to be learned by thinking about it, talking about it, and applying it to a wide variety of problems.
With that in mind, we can nevertheless try to stop some stupid things we did in the past. Partly, because we could not, and partly because we did not want to do better.
Stop reproducing Scripts!
If you are giving your lessons using a script, chalking it to a blackboard, back faced to the class with busily writing students, you might as well give the script to the students to work through. It is a waste of time, yours and the students. Even if you believe you give additional worthy explanations, your students are probably exhausted from writing, and thus completely unable to follow on anything you say. Most likely, they do not even listen.
Think about providing the script in printed form, and giving the lecture freely, enriching it with additional examples you do on the blackboard. I am doing that since years. However, I still do other mistakes. I am stuck in the old idea that a math course should be a complete, self-contained theory. I believe that this is not a good idea. Math must become dynamic, not a static theory. At least that should be the impression the students get. So we need not proof each and every theorem just to show that we can. We need to be teachers not text books. We need to guide the students on their very own path through the subject.
Give them Work!
We have been doing this in universities since the beginning. In seminars, students had to read material on their own, and present it. In math lessons, students get exercises to work on.
I feel that any kind of self study is more important than any talk I could give. So my talks become more and more motivational. I try to be no longer a human text book, but rather someone trying to motivate the students to study my material.
I do not always succeed. I am too much educated in the old way, where the web was not available, and sometimes not even good books. So I still feel like having to explain every little detail in the class. But with tons of scripts and exercises available in the net, with those videos, and hundreds of math text books appearing every year, this should be no longer my job. My job is to set students on the right track, and to give them the right problems to work on.