According to Dan Meyer, the problem with a steady diet of TV sitcoms is students learn to expect easy problems resolved in twenty-two minutes “with a laugh track.” We have now raised several generations of “impatient” problem solvers, and typical math textbooks pander to the syndrome instead of challenging it.
Mr. Meyer has a prescription for what ails our math teaching.
According to Mr. Meyer, there are two kinds of mathematics: computation, or “the step you forgot” and math reasoning. Within computation, there are a lot of tricks and gimmicks, like counting decimals places. The tricks work because of the underlying math reasoning. We teach the tricks, the non-math, and call it math. Good grades for non-math amount to “congratulating students for following the smooth path and stepping over the cracks.” No wonder our students display symptoms of impatient problem solving syndrome:
Lack of Initiative,
Lack of Perseverance,
Lack of Retention,
Aversion to Word Problems, and
Eagerness for Formulas.
The older your students the more likely you can be teach math reasoning well and still encounter not only the symptoms, but also resistance to the cure. Your students have been so conditioned by previous experience, that like chemical tolerance, they do not believe they can function mathematically any other way. It might be a good idea to show this video the first day of class to shock their systems into even entertaining the idea that math could be different.
His description of his presentation of the water tank problem is very like the way Japanese elementary teachers have been teaching math for decades (that I know about). They can easily spend a whole period on a single problem, but they actually save time, because they are not wasting it practicing forgettable procedure on twenty problems. They invest the time it requires to think about math, for as Mr. Meyer says, “Math is the vocabulary for your own intuition.”
Mr. Meyers suggests a five-part prescription:
Encourage Student Intuition,
Ask the Shortest Possible Question,
Let Students Build the Problem, and
Be Less Helpful.
Teachers ignore many features of a problem as irrelevant without discussion as if we expect students to figure it out on their own. Many do, some do not. Asking what matters, says Mr. Meyer, id probably the most underrepresented question in math curriculum.
After, and only after, students have acquired the math reasoning should we give them shortcuts, tricks and mnemonics.
This video is an excellent example of a math teacher receiving accolades for teaching non-math.
And finally, just for fun.