Today, a study immediately reminded me of a classic, frequently cited study. Oh, and also of the importance of having high expectations in education. Of course, expectations are about what you think students can achieve. But perhaps you can see them even more clearly somewhere else: in the tasks you give your students.

This is shown by a study by Marilyn DePietto and Bruce Torff of mathematics teachers and so-called problem-posing tasks. In these tasks, students are not only given a mathematical problem to solve but also asked to formulate their own problem or question based on the information provided. The researchers were interested in a simple but crucial question: does it matter whether teachers think such a task is intended for high- or low-achieving students?

The same tasks, a different label

A total of 157 certified secondary mathematics teachers participated in the study. The researchers created two versions of the same questionnaire and randomly assigned participants to one of them. Both groups were shown the same eight mathematical tasks: four standard problem-solving tasks and four problem-posing tasks. Among other things, they had to indicate whether they found the tasks conceptual or procedural and how likely they were to use them in their lessons.

There was only one difference, but it was a crucial one. One group of teachers had to imagine that the tasks were intended for students whom the researchers described as high-achieving. The other group received the same question, but were asked to tailor it for low-achieving students. Of the 157 participants, 72 ended up in the first condition and 85 in the second.

Who do we save the hard thinking for?

In the experiment, the teachers themselves made a clear distinction between the two types of tasks. Problem-posing tasks, for example, were considered much more conceptual than ordinary, routine math problems.

But which tasks would the teachers want to use with their fictional students? Teachers who were asked to think about teaching high-achieving students were somewhat more inclined to use standard problem-solving exercises than those who were asked to think about low-achieving students.

With the more conceptual problem-posing tasks, however, that difference became much larger. Teachers in the high-achieving condition scored an average of 29.57 on the scale measuring willingness to use these tasks. In the low-achieving condition, that was only 20.22.

On the other hand, when teachers had to take into account low-achieving pupils when choosing tasks, they preferred routine problem-solving rather than problem-posing. In cases where teachers had to consider high-achieving students, the opposite was true.

In other words, merely changing the label attached to the students was associated with the level of difficulty the teachers were willing to assign to them. I don’t think you’re very surprised now.  At the same time, it can mean that you challenge some students less precisely because you have lower expectations of them.

Pygmalion in the classroom?

Reading this study immediately reminded me of Pygmalion in the Classroom, the famous study by Robert Rosenthal and Lenore Jacobson from the 1960s. They suggested that teachers’ expectations can influence student performance. Their research became world-famous, but later also received considerable methodological criticism. We should therefore treat the simple version of the Pygmalion story with due caution. It’s much more complicated than “tell a teacher that a student has a lot of potential and that student will perform better as a result”.

This new study makes a much more limited, safer claim. The researchers do not demonstrate that students ultimately learn better or worse. There were no students participating in the experiment at all. What they do show is a possible intermediate step in the process through which teachers’ expectations can help determine learning opportunities.

If you think certain students won’t be able to handle something, you may be less likely to let them try. And then they also get less practice in developing precisely those knowledge and skills. In this context, the authors speak of the risk of an opportunity gap: students who are already achieving less may subsequently receive fewer opportunities to practise higher-order skills.

It is important to note, however, that this study concerns what teachers say they would do, not what they actually do in their classrooms. No lessons were observed, and, as said, no real, flesh-and-blood students were involved. Furthermore, it is a convenience sample. So we do not know whether these differences in intentions translate into differences in the actual classroom, let alone into learning outcomes.

High expectations are also a teaching choice

This brings me back to the importance of high expectations, which I mentioned in my introduction. It’s not about the vague sense that you just have to believe in every child. This study shows high expectations can be very concrete. It’s not only about what you think students can do. No, the crux also lies in what you ask them to do.

All of this also touches on a tricky point about differentiation. I do believe differentiation is usually done with the best intentions. You try to align your teaching more closely with what a student needs at that moment. However, this is exactly where a danger may arise. If differentiation by level means assigning less complex tasks to poor-performing pupils, it may actually widen the gap in learners’ educational opportunities. It is something I have described often on this blog. Differentiation can also increase inequality, even when well-intentioned.

The authors point out that problem posing, in which students come up with questions or tasks themselves, offers an opportunity to differentiate within the same assignment. Students can devise questions of varying complexity based on their own level of knowledge. So: the same task for everyone, but with room for different levels of complexity. Handy.