One well-known gambit that is used by those seeking math reforms in debates with those who take a traditional view of math education is to show how much both camps have in common. That is, traditionalists don’t rely solely on whole-class and direct instruction; they incorporate discovery and have students work in groups from time-to-time. And progressives don’t rely solely on discovery approaches and collaboration. The reformer will use this in arguments and say “I think we’re both saying the same things.”
Actually, speaking as a traditionalist, we’re not. Yes, some people have a lot of success using student-centered, inquiry-based techniques, and others have success using traditional approaches. But there is the question of “balance”: how much of each is being used. There’s also the issue of misrepresenting how traditional math is and has been taught: i.e., traditional math teaching relies on “rote memorization” without context or understanding, or connecting concepts to prior ones.
Another gambit used in the argument is one that is featured in a guest blog at Rick Hess’ “Straight Up” blog. In it, the guest blogger, Alex Baron, states:
[G]iven the multifarious nature of students, teachers, and school contexts, it seems clear that no single prescription would work for all, or even most, students. However, policymakers proceed with “research-based” inputs as if they would work for everyone, even though this contravenes our foundational sense that no two students are the same.
There are variations in effectiveness depending on the student. But that doesn’t negate research that demonstrates positive effects on large populations of students, such as Sweller’s “worked example effect”, scaffolding and “guided discovery”. Despite such evidence, there will always be those who claim “Ah, but there are exceptions.”
Yes, there are. One rather inconvenient exception is that students with learning disabilities seem to do better with explicit instruction than with discovery-oriented and other reform type approaches. And in fact, such exception raises the inconvenient question of whether and to what extent the reform-type approaches may be causing the increases in math learning disabilities over the years. And if that is the case, why not rely on the remedy in the first place? (See in particular this article, an updated version of which appears in this collection of articles on math education.) In addition, there are many exceptions to the approach that “understanding” must always come before procedure. With respect to the latter, many people have interpreted Common Core standards as requiring “instructional shifts” that place understanding first. (See this article.)
I am reminded of something said by Vern Williams, a middle school math teacher who served on the President’s National Math Advisory Panel in 2006-2008:
I have always stated that if a reform minded teacher produces competent, intellectually passionate students, they will absolutely escape any criticism on my part. But the opposite seems never to occur. Regardless of stellar results, the traditional teacher will always be criticized for being a self centered sage on the stage, controlling student learning and running a draconian classroom. Their students may be the happiest most accomplished students of all time but the teacher will never be good and pure until they cross over to the reform side.
I guess there is no end to the gambits of “we’re all saying the same thing” and “no one size fits all”.