- The validity of an idea about mathematics education and the plausibility of that idea are uncorrelated.
- Mathematics education is much more complicated than you expected even though you expected it to be more complicated than you expected.
Begle coined those two laws in the latter half of the School Mathematics Study Group, a multi-decade project to figure this mathematics education thing out. I’ve heard those laws before but I hadn’t tracked down the original source until today. He seems weary in the speech. His list of tried-and-failed innovations is lengthy and disturbingly current.
Over forty years after Begle’s work with SMSG ended, those laws still offer us lots of comfort and at least a little humility. Math education is hard. My gut is probably wrong. Anybody who says differently is selling something.
Begle, E.G. Research and evaluation in mathematics education. In School Mathematics Study Group, Report on a conference on responsibilities for school mathematics in the 70’s. Stanford, CA: SMSG, 1971.
2016 Feb 28. Raymond Johnson cautions us not to read Begle too pessimistically:
I really do love the history of my subject and posts like Dan’s send me into hours of searching through old papers and citations. But, I must be mindful of our tendency to underestimate change when we read from our wisest predecessors. It’s too easy for us to throw our hands up and say things like, “Dewey knew it all along!” or “We’re stuck in the same damned place we were 25/50/100 years ago.” Is Begle’s 2nd law (“Mathematics education is much more complicated than you expected even though you expected it to be more complicated than you expected”) still true? I would agree it is. But, as a field, we’ve made enormous progress since Begle gave this talk in 1971. The danger, as individuals, is to not learn from this progress. To avoid reaching the same conclusions as Begle, we need to avoid starting in the same place as Begle. When I browse the pages of Begle’s final book, Critical Variables in Mathematics Education: Findings From a Survey of the Empirical Literature, I’m struck by the sheer number of things Begle and the field knew little or nothing about compared to what we know now. Don’t we owe it to ourselves, as individuals and as a field, to push past prior conclusions by starting farther ahead and taking more seriously work already done?