Is productive struggle ethical?
The intention to cause difficulty seems a strange one for teachers to adopt
It is odd to think of teachers designing lessons with the intention of causing their students to struggle and yet this is a popular and pervasive idea, particularly in the world of mathematics teaching.
There are various justifications I can think of for the practice. Until a few years ago, perhaps the most popular reason was the theory of constructivism. The idea was that because we all have to construct our own mental representations of the world — true — we need to construct (elements of) the concepts we want to learn for ourselves. This appears to be false and suggests the easily falsified proposition that humans cannot directly communicate complex concepts to each other. If you are interested in this debate, there is an excellent book on the topic that gives equal treatment to proponents of both sides. Unfortunately, Constructivist Instruction: Success or Failure, is expensive.
A subgenre of productive struggle is the idea of productive failure, popularised by Manu Kapur. Productive failure involves setting students a problem that makes sense to them but for which they have not been taught the standard — or ‘canonical’ — solution method. Students then make up their own methods for tackling the problem with no expectation from the teacher that they discover the standard method. Finally, students are explicitly taught the standard method.
Recently, Twitter grew excited when Rod J Naquin posted a summary of a 2021 meta-analysis of productive failure by Tanmay Sinha and Kapur. At the time of writing, Naquin’s tweet has had 71k views. Perhaps unsurprisingly, Sinha and Kapur find that productive failure can be effective and there is clearly an appetite for this finding, so much so that their meta-analysis received a positive write-up in The New York Times in 2022.
However, following Naquin’s post, others pointed to some eccentricities in this meta-analysis (see here and here). I reviewed essentially the same set of studies for the literature review of my PhD thesis and did not find in favour of the efficacy of productive failure. When I reached out to The New York Times to offer a counterpoint, they were strangely uninterested. Nobody wants to publish the guy who says Santa Claus does not exist, I suppose.
The problem productive failure researchers, including me, face is what to compare it to. Ideally, we want to compare a productive failure sequence to explicit teaching, but explicit teaching is already part of the productive failure sequence. The solution is to flip the sequences and compare problem solving followed by explicit teaching with explicit teaching followed by problem solving. The issue that arises is that in many, if not most, cases, this leads to a comparison condition unlike anything you are likely to see in an explicit teaching classroom. From my thesis:
“One such study (Kapur, 2014) asked students in the explicit instruction – problem-solving condition to solve a problem in as many ways as they could, after being shown the canonical solution; a procedure with questionable ecological validity because it seems unlikely that teachers would choose such an approach in regular classrooms.”
In my own research, I resolved this issue by providing all students with multiple problems. The students in the explicit-first condition could then use these to practice the newly learned standard technique — a more typical sequence. I found an advantage for explicit teaching first rather than problem solving.
Zooming back out, in addition to constructivist theory, there are other conceivable advantages to asking students to struggle. It could confront them with the fact they don’t know how to solve the problem, making them more receptive to later teaching. It could provide a dispositional advantage — if students are used to struggle then maybe they will persist when struggling in the future. The process of struggling and eventually being successful may be motivating.
This latter suggestion points to a significant and for me, lethal problem with asking novices to struggle with new content. Some students may become motivated by success after struggle, but what of those who are not successful? And who are the unsuccessful students more likely to be? Logically, those students who are the least advantaged and bring the fewest resources to a problem are the least likely to be successful when struggling, but it is precisely these students who need motivation, not those who are already advantaged.
What is likely to happen — and I have seen this is practice — is that one student manages to solve a problem in a way the teacher has anticipated and probably even has a name for. This student’s solution is highlighted and the other students then copy* this approach. This will not make the majority of students feel better about themselves. It will not help them identify as mathematicians. Instead, they will identify the small group of students who usually come up with these solutions as the students who are ‘good at mathematics,’ despite their success being at least as much to do with prior knowledge as any natural aptitude.
This is when the struggling students start to get off the bus.
It is not by chance that when reviewing teacher effectiveness research, Barak Rosenshine noted that the more effective teachers obtain a high success rate.
Yes, of course teachers can help students more and give them more guidance when teaching using productive struggle. This will then mitigate the effects of asking them to struggle. Yet, struggle is the point. It is the original reason why we have decided to use this method. Intentionally causing struggle and then mitigating the negative effects is like intentionally making a hole in the bottom of a row boat and then grabbing a bucket to bail out the water.
I suppose part of the popularity of productive struggle is that it is a rebadging of teaching strategies that have long been associated with the philosophy of educational progressivism. As each new iteration of these strategies becomes discredited, a new name is needed for an old practice and everyone insists the new practice is not the old one — productive failure is definitely not discovery learning and so on. I suspect the paradox built into the name, ‘productive struggle,’ is also part of the appeal. We have to be an initiate to understand it. And yet sometimes, a paradox is just a paradox and doing the opposite of what makes sense is likely to be a bad idea.
Most children learning maths do not need their teachers to intentionally cause them to struggle because they are going to struggle anyway with this weird, unnatural subject. Over the course of their school careers, they will have plenty of opportunity to persist and be resilient with mathematics. What they need most when facing a new problem is strategies they can apply to solving it — which is why we have maths teachers. By equipping students with mathematical strategies, the students have more of a chance of experiencing success and the inevitable struggles of learning mathematics will not discourage them from studying the subject.
Given the foreseeable effects, intentionally causing struggle does not seem to be an ethical way to proceed.
*An interesting aspect of this debate is that opponents of explicit teaching often suggest it simply results in students ‘mimicking’ the teacher, yet when students copy each other’s methods, this is a profound and wonderful thing they would never describe as ‘mimicking’. This paradox highlights that it is not copying that is the issue, it is authority, and opponents of explicit teaching have a disdain for teacher expertise and authority. It’s basic romanticism.
Thanks for this.
I was watching a recent episode of Amazing Race where the contestants had to learn part of the Riverdance. I was thinking about explicit instruction, which all their tutors used. But, If their tutor said 'we'll let's figure it out the perfect configuration without me telling you' what would have happened? It would have been absolutely impossible and preposterous (though admittedly fun to watch). So why do we do the same for kids?
This reminds me of a recent post from Ben Orlin's blog Math with Bad Drawings, titled "Should math class be hard?" (https://mathwithbaddrawings.com/2023/12/11/should-math-class-be-hard/). Orlin's observation, which jibes with my own, is that more traditional mathematics education often favours a higher level of difficulty, while more progressive mathematics education tends to eschew this difficulty, but that given the philosophical underpinnings of traditional and progressive education, it should probably be the opposite. This opposite is what Greg illustrates here.
I'll admit that I don't mind it too much if the classes that I teach are harder than they could have been, but I teach at the postsecondary level and not at the primary or secondary level, and I also mostly teach future secondary school mathematics teachers. My role, as I see it, is to teach them as much mathematics as I possibly can, and to transmit to them the culture of doing mathematics. Given this goal, I don't think I can do "too much". But I will admit that it would be good to have actual research on what mathematics do future secondary school teachers actually need, and to develop a program to teach this material as seamlessly as possible. As for why progressive mathematics education often values the avoidance of difficulty (if we disregard the idea of progressive struggle), if I had to I would answer with something else Greg observed: many mathematics education specialists seem not to like mathematics very much, and their progressive orientation is part of their trying to do as little mathematics as possible.