What if I suggested that ‘control’ is an important factor in the mathematics performance of students? What if I went further and claimed that the amount of control students feel over mathematical tasks positively predicts future performance and various kinds of future motivation? This is a key prediction of ‘control-value theory’. Alongside the amount of control a student feels, the degree to which they value an activity, either for its own sake or as a means to an end, is the other key predictor.
I am not an expert in the longitudinal analysis that has been done to test control-value theory. This depend on specialist magic such as structural equation modeling that I have no experience with. However, from dipping my toes into this field, it seems to be pretty robust. I am therefore minded to accept the importance of control as a predictor.
This may seem like a surprising development. Am I about to start advocating for allowing students to select what activities they complete in mathematics classes? Was educational progressivism right all along? If we want motivated mathematics students, do we need to put them in the driving seat with student-centered learning, authentic problem solving and all that kind of a thing?
Well, before we do that, it’s probably best to back up a little.
Since completing my PhD, I no longer have an academic home and this means I no longer have library access. So, when my investigations of control-value theory led to this 2018 paper by Putwain and colleagues, I hit a brick wall.
I found a way to access the paper. That was not the issue. What I did not find was an easy way of accessing the ‘supplementary material’.
Why did I want to access this stuff?
There is a common problem we encounter in research. ‘Control’ is a psychological construct — a label we assign to what is usually a set of correlated behaviours. The problem is that when I write ‘control’, you think you know what I mean by that because it is a part of your everyday language. However, it is possible that researchers do not mean quite the same thing.
Unfortunately, many scientific papers discuss constructs like ‘control’ without fully explaining what they mean. Usually, these constructs are assessed via surveys. Sets of questions are then grouped together as representing ‘perceived control’ or ‘intrinsic value’ and students’ self-reports on these questions are used as the data in the study.
Contrary to the views of some, self-report measures of this kind can be quite useful. We have developed mathematical tests to see how reliable responses are and how well they correlate with other responses. This means that the surveys themselves evolve over time into powerful measuring instruments. It also means that sometimes these tests show us that certain sets of questions should be grouped together and we then have to generate a name for that group. We have to create a construct.
Unfortunately, accessing the surveys themselves can be complicated. Each survey should probably be supplied as an appendix to any study that uses it, but this must violate some law or regulation regarding intellectual property because these surveys are harder to find than you may expect.
I had good reason to believe that a set of survey questions sitting under the construct of ‘control’ were in the supplementary materials to the Putwain et al. study and so after an appeal on Twitter, a friendly source set me a copy.
Here are the questions used in the study to determine ‘perceived control’
I can learn things quickly in maths lessons
I have always done well in maths lessons.
Work in maths is easy for me.
If I get a maths question wrong I can work out why I went wrong.
I am not surprised these correlate with future mathematical performance and motivation.
These questions seem to be measuring whether a student thinks they are good at mathematics. To me, it is odd to label them as ‘perceived control’. I guess the label relates to the fact students answering these questions positively are not helpless — they can take charge and when the need arises, even figure out why they went wrong.
It would therefore be a damaging failure of communication to take such evidence about the desirability of ‘control’ and prescribe the clown-car festival of student-centered teaching methods.
As I have written about before, a similar issue arises when we start to look at research on conceptual understanding in mathematics. The first surprise for teachers swimming in progressivist waters is that it quickly becomes labelled, ‘conceptual knowledge’, and the second surprise is that it is often assessed by effectively asking for definitions.
The communication gap between well-designed, quantitative educational psychology research and teaching practice should be better known. If not, we risk teachers implementing the wrong practices for the right reasons.
We just need to teach students the correct answers to those four questions!
It looks like by control the researchers mean students feel in control of the results they achieve not the topics they are studying.