There is no such thing as a general skill of problem solving, above and beyond the strategies that we all possess and therefore do not need to be taught. Schools certainly can teach students how to solve specific kinds of problems. Schools can also teach useful heuristics for solving larger classes of problems but these seem to become less useful the wider the class of problems they are intended to solve.
The idea that general problem-solving cannot be taught may seem surprising for two reasons. Firstly, we have the term ‘problem-solving’ that implies one kind of thing. The spirit of problem-solving is also conjured into being in many curriculum documents and by countless education gurus. We are told that, in the future, the ‘skill’ of problem-solving will be more important than knowing particular content knowledge (even though it is specific content knowledge that is needed to solve specific problems).
It is worth being aware that this view comes down to us from the tradition of progressive education. Problem-solving is a key component of this tradition, taking it’s cue from the ideology of pragmatism. It is no coincidence that John Dewey was a leading pragmatist as well as a founder of the progressive education movement.
If you believe that problem-solving can be taught then the progressive view makes a lot of sense. Why not endow students with a skill that can be applied in almost any situation? What could be a more pragmatic aim for education? What could have more practical use?
The difficulty for those who advocate problem-solving is that there is no body of evidence that such a general skill can be taught. Such evidence would need to show that problem-solving is transferable; that improvements in problem-solving in one area lead to improvements in another. And it should come from randomised controlled trials so that we can be sure the improvement was down to problem-solving alone. I was reminded of this when reading a recent paper that showed that learning computer programming had no impact on students’ problem-solving skills in mathematics. This was despite the study having the sort of non-random design that might be expected to produce a positive result.
So why are we in this situation? Why are teachers constantly being urged to do something that is impossible?
The answer is that generic problem-solving is part of an ideology that has gripped large sections of the education community. Most of those who are in this grip are unaware of it and react pretty badly when the ideology is named or highlighted. This is because everyone likes to think that they have come to their own decisions in light of evidence and reason. People prefer to view themselves as measured and grounded, not prone to intellectual fancies.
But we are. All of us. I am starting to think this is part of our nature. We pick up thoughtworlds from those around us as a way of ensuring social cohesion. We don’t necessarily have to read John Dewey to be unwitting disciples of his philosophy. It just gets into the air. And the only way to fix this is to place the evidence in front teachers before they invest so much of their ego and professional standing in problem-solving or whatever else it is that they can no longer contemplate the possibility of being wrong.
Is it possible that a new teacher education course will be able to teach, in just twelve days, content that regular courses struggle to find time for in a year? This is exactly what a new programme offered by the BPP private university in the U.K. promises to do. To be clear, it is intended to be a top-up to a larger school-centred initial teacher training (SCITT) course, so nobody is claiming to be able to fully train teachers in six days. SCITT courses are a U.K. alternative to traditional university-based courses and my view is that Australia would benefit from new routes into teaching similar to these.
What’s the issue?
Currently, there is one dominant ideology in our education system and this is reflected in teacher education. This ideology has been described as student- or child-centred, constructivist or progressive education, although all of these labels are disputed. The key theme that emerges is that teaching should primarily be about initiating students into particular habits of mind; thinking critically, thinking like an historian and so on; something that is primarily achieved through doing (in the same way we acquire skills such as speaking and listening). These habits of mind are seen as at least partially independent of any particular content. Therefore, a mathematics lesson should be about students solving problems, the exact nature of which is less important than the act of problem-solving. Reading is about developing generic comprehension skills which can be applied to a range of texts. Indeed, the concept of a text (and literacy itself) is often expanded to incorporate everything from watching movies to surfing the internet. Sometimes, habits of mind take on a more political agenda, where teachers seek to encourage their students to challenge the establishment.
I have no problem with this ideology being taught to teacher education students. It is a legitimate if – in my view – flawed way of thinking about teaching. My issue is that it is presented as a consensus position as if there are no alternatives and as if it is supported by scientific evidence.
In reality, there are other ideologies, many of which may lay claim to a stronger evidence base. There is traditionalism, with its focus on academic subjects, the importance of knowledge and the transmission of this knowledge to students. There is behaviourism; the application of positive and negative external contingencies. Behaviourism is supported by strong evidence in the field of classroom management (even if the theory does not restrict itself to this). And there is the study of cognitive science with its roots in relatively small, randomised experiments that offer insight in to how we learn.
I don’t think these ideologies are deliberately ignored in teacher education. Instead, I believe that those involved simply don’t know what they don’t know. For instance, Project Follow Through was the largest experiment in the history of education and yet I have encountered many teacher educators who have not heard of it. Why? There are two reasons why it doesn’t fit; it was a large piece of empirical work, when teacher education tends to favour sociological theory, and it gave the wrong results.
What currently happens in teacher education is that conventional ways of thinking are simply reproduced. New teachers emerge unaware that there is a debate. When some of these mature into teacher educators themselves, they perpetuate these conventional ways of thinking. This is the pipeline.
What do alternative routes offer?
There is no reason to think that alternative routes into teaching will be any higher quality than traditional courses and it is quite possible that they might be worse. Programmes are going to have to draw from the pipeline in order to recruit tutors and design courses. Yet without the experience that universities possess in regulating such courses, we might see some of the worst excesses played out at scale. We may create a breeding-ground for learning styles theories and tech-fetishism.
We already have a number of alternatives in place such as Teach for Australia and, from all accounts, Teach for Australia is firmly situated within the dominant constructivist ideology.
So why bother trying to set up alternative routes? Because I see no other way out of the current thoughtworld. Teacher educators will not be persuaded by a few bloggers to take a broader and more inclusive approach to teacher education. Would this even be desirable? Should a course attempt to please everyone or should we have different, competing routes based in different ideologies? Given the limits to the amount of time available in teacher education, I think a good approach would be to plan for diversity.
Alternative routes at least offer the possibility of difference and change. There are enough people – just – in Australia to run perhaps one or two courses with a quite different take on teaching than the traditional models. In isolation, such courses will make little impact but they will open a discussion. Traditional routes may start to examine some of their a priori assumptions and respond through their own offerings, particularly in the localities where these alternative providers establish themselves.
The main barrier to alternative models in Australia is excessive bureaucracy. Teacher education courses need to demonstrate that they deliver on the Australian Professional Standards for Teachers, a woolly set of standards with a bias towards constructivist education that alternative ideologies would struggle to work with. Writing on the AARE blog, Susan Davis, Deputy Dean of Research for the School of Education & the Arts at CQ University notes that:
“While in the current version of national standards developed by AITSL (Australian Institute for Teaching and School Leadership) used in Australia there are 7 professional standards, underneath that are 37 focus areas and teacher education students must demonstrate evidence collected across all of these.
To be able to offer teacher education courses, teacher education providers must likewise provide evidence across a set of similarly numbered program standards.
In fact the instructions of what needs to be included takes up 42 pages in a guidelines document, which also emphasises that once a program is accredited no changes can be made to that progam. This type of approach encourages a compliance and tick box mentality.
It also means enormous energies and person power are devoted towards generating mountains of paperwork and which other poor reviewers must then wade their way through. While a so-called ‘light touch’ regulatory model was to be used for the re-accreditation of programs, one university education faculty recently reported that their accreditation submission amounted to over 1000 pages of documentation.”
It is unlikely that an Australian equivalent of BPP would wish to take this on. So those Australian teacher educators who took public offence at the BPP program can relax for now. Those of us who wish to see a change are going to have to wait a while longer.
This talk is from the researchED event at the ACE conference. It’s about explicit instruction and so it complements my first talk on project-based learning. The talk is filmed on a single camera and there is quite a lot of zooming.
You can download my slides here. You are free to use them in your school, including the diagrams, as long as you retain the original references and give me a credit with a link to this blog site.
I filmed this video at the researchED event held on Saturday 1st July at Brighton Grammar. Stephen Norton is someone who I have wanted to meet and hear speak for some time. This particular presentation does not lend itself well to filming – Norton eschewed PowerPoint and had more of a discussion with the people in the room, some of whom challenged him on a number of points. You can hear these interventions on the audio track. As Norton walks around, he bobs in and out of the video and you can’t always see what he is doing. There are also a couple of errors in places. However, I still think it is well worth viewing if you want a sense of the debate around teaching elementary maths in Australia.
Stephen Norton gave a keynote on Monday 3rd July. This is a more traditional kind of presentation and I hope it is available soon.
I filmed this video at researchED Melbourne on Saturday 1st July 2017. I have now uploaded it to the researchED YouTube channel. It was great for someone of Hattie’s standing to come and support an event like researchED and his talk was fascinating. Hattie was the discussion topic of the day and many of the subsequent speakers refered to this talk. The video quality isn’t quite good enough to clearly read all of Hattie’s slides but, even so, you can fully understand his arguments. I don’t agree with everything Hattie says but it would be churlish and prejudicial to expand on that here. You can also find Jen Buckingham’s talk here and my talk here.
The Cambridge-Somerville Youth Study was a ground-breaking piece of research. It followed a mentoring initiative for boys from deprived suburbs of Boston that ran from 1939 to 1945. At the time, this initiative was almost unique in the field of social sciences because it also followed a matched control group of boys who did not receive the mentoring intervention. Through the efforts of researchers, the subjects were traced over a long period of time so that outcomes such as involvement in crime and stability of relationships could be compared.
The study was the subject of a recent Freakonomics podcast that serves as a warning to any of us who wish to intervene positively in the lives of young people. The boys who were given the intervention were overwhelmingly positive about it. And it’s not hard to see why. According to the criminologist, Brandon Welsh:
“The counselors would meet every couple of weeks with the boys, interact with them, help them with homework, take them to the YMCA. During the summer months, some of the treatment-group boys were able to go to summer camps and so were sent out of the city.”
Yet when the data was analysed thirty years later, the boys who received the intervention had fared significantly worse than the control group on a whole range of outcomes related to criminal behaviour, health and work.
Clearly, good intentions are not enough when it comes to social interventions. We cannot fool ourselves into thinking that the worst that can happen is that we have no effect: Sadly, it is possible to do harm. As Denise Gottfredson, professor of criminology and criminal justice at the University of Maryland, states in the podcast, “People just assume that if you do something that sounds good, that it’s going to have positive effects. But it’s actually more complicated than that.” She then goes on to explain that the somewhat counter intuitive result may be due to students in the intervention providing a form of validation for each others’ behaviour.
This is just one example of why there is a clear, ethical imperative to collect quantitative data. We cannot simply rely on our own good intentions or on interventions that are based in theory. It is quite wrong to simply dismiss calls for empirical evidence as, ‘positivism,’ while continuing to intervene with young people in ways that might actually be harmful.
This is why I am so concerned about particular models of differentiation that have become popular in schools. As I have previously written, Universal Design for Learning (UDL) is such a model that lacks evidence to support a positive effect on academic outcomes. One UDL website promotes the program with spurious images of brains. A partner website has a section on the evidence for UDL. However, this section asks visitors if they have any evidence to support these claims. Seeking confirmatory evidence is basically the opposite of science.
One of the features of these forms of differentiation is that they often allow students to present what they have learnt in a variety of different ways. This may be appropriate if a student with a disability simply cannot complete a certain type of task. However, I am deeply concerned about the practice of offering such alternatives to students who have difficulties with a particular task. If a student habitually avoids writing, for instance, then she is never likely to improve at writing and will be severely disadvantaged as a result as the gap grows ever wider between her and her peers. Instead of planning for alternative ways of demonstrating learning, we should be focusing our efforts on intensive and explicit writing instruction.
I might be quite wrong about this, but how would we know?
I have criticised forms of differentiation in the past and it has resulted in some pretty unpleasant commentary. I have been accused by Dr Linda Graham of disregarding the Australian Disabilities Discrimination Act, something I strongly dispute. This kind of authoritarian stance can only serve to silence criticism. Yet as an education community, we desperately need to think more critically. With UDL gaining in popularity to the extent of featuring in an Australian Senate report as an example of good practice, we need to ask whether it is possible, just possible, that it does more harm than good.
I was struck by a post by John Kenny who wrote about a presentation he had recently attended. Advised by the presenter that he should let students with Language Processing Disorder present their learning in the form of a video rather than in writing, he questioned this. According to Kenny, “When I raised this concern with the presenter, she simply stated that it was not fair to make students constantly do what they are not good at, that they should be given the chance to shine at things they are good at.”
It is clear that such views come from a place of deep compassion and concern for students; of this there is no dispute. But what if compassion and concern not enough? After all, there were not enough in the Cambridge-Somerville study. What if, in our rush to apply ideas that we think are sound and that suit our ideological outlook, we are actually doing harm? We will never know if we focus on silencing criticism and refuse to support the kinds of quantitative trials that could answer these questions.
Problem-solving is one of those twentieth century skills that schools are supposed to be teaching in order to prepare students for jobs that haven’t been invented yet. It is a key component of the ‘critical and creative thinking’ general capability of the Australian Curriculum. Yet problem-solving is a tricky concept. I certainly don’t believe it is a discrete skill like a golf-swing that can be developed through teaching and practice.
David Geary’s distinction between biologically primary and biologically secondary knowledge perhaps offers a useful way of thinking about problem-solving. General problem-solving skills are biologically primary because they have evolved alongside the human mind: we have always had to solve problems in a general sense. Tricot and Sweller suggest that mean-ends analysis is a good example of such a strategy. This is essentially the tactic of working backwards from the goal in order to assess your progress towards it. We all possess this strategy already and so there is no need to teach it to children.
Biologically secondary knowledge builds upon primary knowledge. Means-end analysis is at the root of maths problem-solving (unless we engineer its absence) but we then complement this by teaching a series of domain specific strategies. For instance, knowing how to factorise a quadratic is really useful if you need to solve a problem involving quadratic equations, yet it’s not much help in solving other kinds of maths problems, let alone the problem of a blocked drain.
One of the difficulties that maths teachers encounter is in enabling students to transfer problem solving procedures from one context to another. For instance, a student may be able to factorise a quadratic equation but may not realise that this is what is required in a particular problem. My approach to this is an explicit one where students begin work on problems that look very similar to each other but then gradually work through problems with varying contexts. At a later stage, different problem types need to be interleaved so that students may learn to spot the deep structure and therefore the type of solution required. All of this proceeds with lots of teacher guidance and demonstration and plenty of formative assessment to keep the trains on the track.
However, what if we could develop more general problem-solving strategies that could shortcut this process? These may be completely general skills like means-end analysis that can be applied to any problem or they may be intermediate strategies that apply to a broad range of problems within a particular domain. There is little evidence available that we can learn general problem-solving strategies but what of these more middling kinds of strategies?
For instance, ‘draw a diagram’ is a reasonably useful strategy to help solve a very broad class of physics problems. It might not help much in other kinds of problems but it has a general applicability in physics. Nevertheless, it is nowhere near as useful as a specific strategy for solving a particular problem. It works as a cognitive aid to enable us focus on the deep structure.
Some intermediate strategies have potential and they seem similar in nature to reading comprehension strategies. Research suggests that reading comprehension strategies produce a quick boost in reading performance but that they don’t really function as a skill in the sense that repeated practice of these strategies increases their effect. Perhaps ‘draw a diagram’ is a useful heuristic that operates in a similar way.
I can’t see any value in some intermediate strategies. For instance, ‘solve a simpler problem’ only works if you already know the deep structure of the problem because the two problems need to share structure for the simpler one to be useful. Yet if you already knew the deep structure then you would not need a more general problem-solving strategy.