Ten years ago a randomised controlled trial (RCT) took place in the U.S. The trial pitted four early years maths programs against each other. Two of these programs, Saxon Math and Math Expressions, used explicit instruction. The other two programs, Investigations in Number Data and Space (commonly known as ‘TERC’ after its developers) and Scott Foresman-Addison Wesley Mathematics, did not, preferring a ‘constructivist‘ approach. For instance, TERC encourages students to ‘develop their own strategies for solving problems and engage in discussion about their reasoning and ideas’. This stands in contrast to teachers explicitly teaching students how to solve problems.
The RCT found that the explicit programs were more effective than the constructivist ones. This is hardly surprising given the wealth of evidence we have in favour of explicit instruction generally, as well as specific experiments that have found that explicit maths is superior to constructivist maths.
Eric Taylor, an assistant professor of education at Harvard, has now reviewed the data from the original study and completed an additional analysis that seems to show something pretty interesting (thanks to @Smithre5 for pointing this article out to me).
The teachers in the study were all assessed on something called the “Mathematical Knowledge for Teaching” test (MKT). This essentially assesses teachers’ maths knowledge but through the lens of teaching maths. For instance, some of the questions provide sample student responses and then ask questions about those responses.
Taylor found evidence that when teachers had a low score on the MKT test, it did not really matter whether they used the explicit or constructivist maths programs. Instead, it was for teachers who scored more highly that a difference emerged in favour of the explicit approach.
There is a common sense explanation for this. In a program where the teacher has to stand up and actually teach maths, their maths skills matter, but when the students have to figure things out for themselves then the more skilled teachers have no way of making use of their greater skill level.
If this finding stands across other studies then I think it has three implications:
- Primary teachers must pass a maths skills test if they are to teach mathematics (schools could perhaps reorganise so that maths was taught by specialists to get around the problem of getting all teachers to this level)
- Primary teachers who lack maths skills should be given training in this area
- Explicit programs for teaching maths should be adopted in primary schools
We already have masses of evidence for point three and it seems that education systems might be waking up to points one and two.
This finding perhaps explains other interesting results. For instance, the literature is full of studies that seem to tell contradictory stories about the effect of the level of teacher education on student results. This might be expected if bad teaching methods cancel out any gains from having better qualified teachers.