The Awful Truth About Teaching Math
Every time the power goes out, I have to re-install the driver for my wife’s printer. Every time, including (once again) today. I live in the country, beyond the suburbs into cow country, where it seems sometimes that the power goes out every time there’s a high wind. It doesn’t stay out for very long. Usually no more than ten minutes or so. That’s still enough to make me reinstall the driver. Oh! And VMWare player, which I use on my own computer. I figure that’s a bug that was probably fixed in a newer version but the last time I tried to upgrade, it completely hosed my network connections. After about 4 hours of fighting with it, I downgraded again. It works.
There’s actually a point to this other than just complaining about computers. I make my living (such as it is) with the things. Complaining about them is just part of the job. The bigger point is that, believe it or not, the computer age is still very young and there’s a lot we don’t fully understand about how to make software operate to our satisfaction. Things that should be easy aren’t always and benefits we think we should see sometimes don’t materialize.
Which brings me to the subject of a very interesting recent report (actually a thesis) summarizing studies of how students use software intended to help them learn to do arithmetic word problems. For a short article about the paper, see here. For the paper itself, go here. Three studies are considered. The purpose was to learn about how students interact with educational software when there has been a breakdown situation. That is, when they get the wrong answer, what do they do?
Anyone who has worked user support or who has even been around people who work with computers can probably answer that without the need for an academic study (or three). What do students do when they can’t figure out the answer to a problem given them by a computer? They do what everybody does: They blame the computer.
Specifically, when students entered the wrong answer to a problem and the computer rejected it, the first thing they tried was entering the answer in a different way – such as using a comma or fraction rather than a decimal point – to see if the computer had simply failed to recognize the syntax they used. I wouldn’t be too surprised if, when that didn’t work either, they tried rebooting the computer and starting over from the beginning. It’s what I’d do.
In another study, the researcher noted that students didn’t just read a problem and try to solve it, they tried to understand what the point of the exercise was in the context of school. That is, they didn’t think “What math concepts are needed to understand this problem?” They thought, “What does the teacher (in this case an unseeen teacher who wrote software) want me to do?”
Not surprisingly, my interpretation of these results is a bit different from that of the researcher, who talked about framing concepts and social understandings. None of that really has anything to do with math. What was going on in these studies was that the students didn’t have good enough math skills to see right off why their answers were wrong (if they did, they might have gotten the right answers in the first place), so they tried to game the system instead.
This could show a weakness in the software. It wasn’t giving them good enough feedback to understand that their answer really was wrong. From the sound of it, the only feedback the students got was a yes/no type response. Not even a hint as to how to do the problem correctly. Without feedback and with rudimentary ability to do the work, the students can be forgiven for feeling lost (And I mean the students can be forgiven. Many of the irate users I used to field calls from should have known better, but that’s an entirely different rant). The software used sounds more like it was intended to drill the students in (theoretically) already existing skills. It was not true teaching software. At the current state of development of the market, there is probably little of the latter. It seems likely that to really teach, software would need a quality of artificial intelligence that does not yet exist.
Another possibility is that there is a problem with math education in general, or more accurately in the things that need to be taught for most people to learn math well. Several times when trying to help people with their math homework I’ve seen that they had the wrong idea about how math problems are done.They thought that, since they could figure out 2+2 intuitively (meaning, with little or no conscious thought), they should be able to do all math the same way. They conjured answers out of thin air and hoped for the best. They relied on what worked in second grade, apparently feeling that anything harder than that was more trouble than it was worth. This may sound like an attitude that would be found mostly in children but I’ve found it in adults, too. Probably no one ever showed them the beauty of math.
Both of these explanations would tend to show that there is still no substitute for a good teacher. There’s another article about the role of teachers in using software as an aid to teaching math here.
The paper concludes with the common sense suggestion that the claims of companies that sell educational software should be taken with a grain of salt and the use of that software in the classroom thought through very carefully. This I agree with. Computers are wonderful things but they are not magic bullets. Even with computers, math is still challenging to learn.
Someday computers will be better teachers. Hopefully by then they will be able to reinstall their own #^*&$! drivers.
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I agree with your closing argument that computers are not magic bullets, and that teachers are vital to the learning process. However, it should be noted that math programs can be helpful in introducing new and interesting content to students to practice through repetition. Using the idea that 10,000 hours of practice give you a mastery of a subject, which Malcolm Gladwell wrote about in his book Outliers, any possible way that we can help math students reach the goal of 10,000 hours of math practice should be explored.
Good point. Math is one of the areas where good quality practice can make a terrific difference. And software never gets tired of walking students through the same problem or type of problem until they get it. I’m very optimistic about the possibilities.
It should also be noted that these studies were more interested in student behavior than any pros and cons of the software involved (which appears to have been a primitive kind of drill or flashcard type that is at the very low end of what educational software is capable of these days).
The big take away from that is that students found and exploited the weaknesses of the software. One example cited in the report was that students commonly tried entering random answers rather than re-doing their calculations.
I guess some students will always find a way to skip out on some of their work. That doesn’t make the work meaningless and it doesn’t mean the software has no value. As you pointed out, it can have a significant role in education.