Jóhann Örn Sigurjónsson's PhD study looked at cognitive activation in mathematics classrooms in the Nordic countries, with a particular focus on Iceland.
We asked Sigurjónsson what his research can tell us about how mathematics is taught, and where there are opportunities for improvement.
Can you say a bit about the background for your study?
Following the educational discourse in my home country of Iceland, it is clear that mathematics teaching has been under some criticism in the past years.
A lot of the discussion is related to these international measures like PISA, where Iceland’s average has been the lowest among the Nordic countries in mathematics.
But PISA is just one measure of student achievement, there are other studies that look at the instruction itself, ‘what does mathematics teaching in Iceland actually look like?’ and these studies show it's not too different from what we see in the other Nordic countries. It’s mostly individual work lessons, where students have a plan with a number of exercises to work on.
So part of what I set out to do with my study was provide some examples of more dynamic mathematics instruction that balances the procedural focus with a focus on conceptual understanding and justification. I wanted to give concrete examples of ‘this type of instruction does exist in the Nordic countries, and this is what it looks like.’
You’re looking specifically at ‘cognitive activation’ in mathematics classrooms. Can you explain that concept?
Cognitive activation is a dimension of teaching quality that has to do with the extent to which the teacher engages with the educational goal of student understanding. So for example, how well the teacher creates opportunities for students to engage with the concepts being taught in mathematics lessons, through their selection and implementation of challenging tasks.
How did you go about studying this?
I drew on the LISA-Nordic data, and in order to study cognitive activation I looked at three things:
First of all I looked at the teaching itself, which could be observed through the video-recorded lessons.
Secondly, I identified the tasks in the lessons that the teacher set for the students.
And third I looked at the student surveys – what the students said on a survey about the teaching.
Your thesis consists of three papers, can you give an overview of those?
In the first paper I looked at 10 lower secondary mathematics classrooms in Iceland, three to four lessons from each.
The main finding was that in the majority of the lessons that we observed there was limited evidence of ‘intellectual challenge’, which is one of the metrics I’ve used to study cognitive activation.
So across one school week of mathematics teaching, half of the classrooms we observed scored constantly at the 1 or 2 level (out of a possible 4) on the PLATO* measure for intellectual challenge. Now, a question that arises here is; how often would you expect to see high levels of intellectual challenge in a lower secondary mathematics classroom?
There was one teacher who consistently scored at a 3 or 4 level, but that’s not something we would expect to see every teacher do. But I do think it's reasonable to expect that at least one lesson segment during a week’s worth of lessons scores higher than a 2. As we did not see that in half of the classrooms, there seem to be clear opportunities for improvement.
In the second paper you looked at the students’ perspective. What did you find?
Yes, for the second paper I connected the observation of the teaching to the student surveys.
An interesting finding from this paper is that the instances of intellectual challenge and classroom discourse have a weak connection to what the students’ report in their surveys about the lesson. The correlation is virtually zero.
It's kind of a paradox, the students don't perceive the quality of the lesson the way that the researchers do.
Which is a problem, because the first thought is ‘oh, one of these measures must be wrong. Either our measurement tools are wrong or the students are wrong.’
A more probable answer is; maybe it's some combination of the two.
As researchers, we observe just one week – three to four lessons – but the students are there for the whole school year, so they know much more about what goes on in these classrooms.
On the other hand, you can also ask; to what extent are the students – who are 13 or 14 years old – capable of grasping and reporting on the aspects of teaching that we’re trying to measure?
I’ll actually be talking more about this in an Observation System Seminar in April.
What did you find out in the third paper?
In the third paper, I selected some specific lessons that had high PLATO scores in the ‘intellectual challenge’ element. This was across Iceland, Denmark, Sweden and Norway. I wanted look closely at what actually goes on in those lessons.
One of my findings from this paper is that there's no recipe for a cognitively activating lesson, but even though there's no recipe, there are some common factors.
The lessons all tended to focus on whole class discussions and group work. None of them were dominated by individual work, though individual work was also present in some of them.
Looking at the interactions that happened in these lessons we see that the teachers seemed to shift frequently between types of interactions. So they provide feedback and then they prompt the students for an explanation, for example.
The teachers also focus on connection-making in mathematics; both connecting concepts to a real world context and also making connections within the world of mathematics, so to speak.
What has it been like to be part of the QUINT Centre?
I think it has helped a lot to be part of QUINT. In particular, being part of a bigger project (LISA-Nordic) means that the data collection is a collaboration between many people, and in this case collaboration between eight universities and five countries.
Just the data from mathematics in Iceland is 34 lessons, more than 20 hours of video, so it was very helpful to already have a baseline analysis of the lessons from the other countries in the LISA-Nordic study in the form of the PLATO scores. It let me know which lessons to focus on for a closer analysis.
Also, having the opportunity to work with the LISA-Nordic data and the PLATO training – it give me a lot of insights that I probably would otherwise not have had.
*PLATO (Protocol for Language Arts Teaching Observations) is a classroom observation system designed to capture features of classroom instruction.