Motivation is a preoccupation of many maths teachers. If you listen to the prevailing maths reform rhetoric that comes out of the U.S., you will hear that maths needs to be made more relevant and engaging. Even if I could demonstrate that explicit teaching is more effective than inquiry learning in a way that satisfied inquiry advocates, they would likely reply that explicit teaching is less motivating than inquiry learning and what we really want is to induce is a lifelong love of maths. That way, students will persist in the face of difficulty.
I have never really bought this argument. Although we can all point to bad implementations of explicit teaching or inquiry learning, I see no reason to believe that one approach is intrinsically more interesting than the other. Any maths teacher will notice the correlation between motivated maths students and students who are good at maths, but this does not mean the former causes the latter. It is just as plausible that being good at maths motivates students about maths or that the interaction goes both ways. If this is true then the effectiveness of the teaching approach is highly relevant because effective approaches will be superior in making students better at maths.
I have written before about a long-term Canadian study that showed that earlier achievement predicted later intrinsic motivation but that earlier intrinsic motivation did not predict later achievement. At the time, I was pretty convinced that this was the direction of causation. However, after researching my book for new teachers, I rowed back a little to accept that there is probably a two way interaction, even if it does not show up in the Canadian study.
However, a recent German study seems to partly replicate the Canadian findings. Again, this was a study that tracked students over time and it found that ‘academic self concept’ i.e. self perception of how good you are at maths predicted later ‘intrinsic value’ i.e. level of interest as well as attainment, but intrinsic value did not predict later self-concept.
The researchers haven’t quite measured the same things here. It is possible, of course, that some students have high self-concept without being particularly good at maths, but that seems unlikely.
Interestingly, the researchers found the same pattern for learning English, but the reverse pattern for German, the students’ mother tongue.