My friend and coauthor Joshua Gans has two blogs. When he’s not blogging about new innovations in economics on Core Econ, he’s offering new insights on parentingÂ at Game TheoristÂ (which has led toÂ a book, Parentonomics, forthcoming in August 2008).
One of my favourite of Joshua’s parenting suggestions is this one:
A few years ago, while trying to teach my then 3 year-old daughter some mathematics, I hopped on a similar Why Not? moment in reversal. She had always been pretty quick with numbers and could easily count to 20 and beyond. So I set about teaching her how to add. Now the way to do this is to make liberal use of fingers. This is all very well when the numbers you are adding are less than 10 but is a problem after that. Then it requires breaking up the problem; a conceptual advance that is pretty daunting for a child. Of course, you could move on to toes as my son is want to do but that involves taking off shoes.
So I thought, stuff this! How about we start with subtraction first? The idea there was that you could take any number up to ten and subtract any smaller number and still not exhaust your finger options. That dramatically opened up the possibilities and, what is more, I noticed how damn easy it was for a child. They were used to having and then not having and seeing what was left. It was a natural part of their day. When they eat, the food on the plate shrinks. When they paint, the clear bits of the canvas get smaller. Subtraction was a far more natural part of everyday life for children.
But how would we know if Joshua’s observations are applicable only to his children; or if they would benefit all children? A new article in Science suggests one way we could test the competing theories. Here’s the NYT writeup:
[M]any educators in recent years have incorporated more and more examples from the real world to teach abstract concepts. The idea is that making math more relevant makes it easier to learn.
That idea may be wrong, if researchers at Ohio State University are correct. An experiment by the researchers suggests that it might be better to let the apples, oranges and locomotives stay in the real world and, in the classroom, to focus on abstract equations …
â€œThe motivation behind this research was to examine a very widespread belief about the teaching of mathematics, namely that teaching students multiple concrete examples will benefit learning,â€ said Jennifer A. Kaminski, a research scientist at the Center for Cognitive Science at Ohio State. â€œIt was really just that, a belief.â€
Dr. Kaminski and her colleagues Vladimir M. Sloutsky and Andrew F. Heckler did something relatively rare in education research: they performed a randomized, controlled experiment. Their results appear in Fridayâ€™s issue of the journal Science.
The advantage of this approach is that it used a gold-standard evaluation approach (a randomised trial). The disadvantage is that although the main policy question is about how best to teach school students, the experiment was based on university students. Clearly if we’re going to test Joshua’s theory, we would need to try it on younger children. But the experiment need not last years – a few months would be enough. For my own part, I would be quite happy to have my own son as part of the experiment, knowing that he would be randomised to either the treatment group (learning subtraction then addition) or the control group (learning addition then subtraction).