To see the video in question, drop back here.
Meyer is a high school math teacher, and I believe at the time of this talk he had been teaching for 6 years.
Meyer suggests that the real problems besetting high school mathematics education is the lack of real-world sensibility in the work. He figures that questions where all of the relevant information is provided, or where the abstractions are beyond everyday experience are alienating for students. His solution is use digital technology to create problems that can be modeled in the classroom, and that will provide meaningful experiences for his students.
I can go along with this to a point. The first fact that Meyer avoids is that mathematics requires basic skills and that these skills require practice. It isn’t sexy. It isn’t fun for everybody. But without mastery of basic technique, math becomes significantly more difficult than it needs to be.
Second, the purpose of stereotyped problems is that they help students learn general procedures.
In this case we have a type of problem that is difficult for most students the first time they see one, but becomes easier with only a little repetition. OK for some students, once is enough; for others, 10 times or more might be necessary.
(For those who forget such things, the first hose fills 1/12 pools per hour and the second fills 1/10 pools per hour. Add them and you’ll know how many pools per hour they fill together. I’ll leave the rest to you.)
So now we have a matter for teacher choice. Some will teach only the textbook stereotypical problems. Some will teach stereotypes first, then maybe do a “real world” problem with incomplete and imperfect data. Others may start with the real world to motivate the development of technique necessary to solve the real world problem.
Meyers suggests skipping the stereotypical problems and jumping into the real world and staying there. If this is really what he does (and I doubt it) then I have a hard time believing that it’s successful.
Real world problems are interesting in lots of ways, but they are time consuming. The business of learning the technique has to take place somewhere.
Practice is important; but it isn’t everything. Real world engagement is important; but it isn’t everything either. What we require is balance. But how to balance?
The short answer is that there is no short answer. Teachers are professionals for a reason. Judgments have to be made about the students in the room before us. The reality is that not every student is the same as the others. Not every class or community or teacher is the same as the others. Often I will have two classes for the same course during the same term and find myself teaching the classes very differently from one another.
One size fits all solutions make for great TED talks. But they make for pretty sketchy classroom practice.