For thousands of years, human beings have been trying to figure out why the world they live in works in the way it does. But it’s only been in the last five hundred or so that a coherent picture of those explanations has begun to emerge. It’s as if people have long had many of the pieces of the jigsaw, but there was no picture on the box. Because a few crucial pieces were missing, it was impossible to put the puzzle together so that the whole thing made sense.

Some of the puzzle pieces that began to make sense to the ancient Greeks involved mathematics – notably geometry. They assumed that if the consistent principles of geometry could be reliably applied to the real world, then it was likely other mathematical principles and the principles underlying mathematics (logic) could too. So philosophers started to use logic to study the fundamental nature of things.

Unfortunately for the mathematicians, logicians and philosophers the real world didn’t always behave in ways that mathematics, logic and philosophy predicted. And that’s why we developed science as we know it today. Scientific theories are tested against observations. If the observations fit the theory we can take the theory to be true for the time being. As soon as observations don’t fit the theory, it’s back to the drawing board. As far as science is concerned we can never be 100% sure of anything, but obviously we can be pretty sure of some things, otherwise we wouldn’t be able to cure diseases, build aircraft that fly, or land probes on Mars.

**unknown unknowns**

Mathematics, logic and philosophy provide useful tools for helping us make sense of the real world, but those tools have limitations. One of the limitations is that the real world contains unknowns. Not only that, but as Donald Rumsfeld famously pointed out, some unknowns are unknown – we don’t always know what we don’t know. You can work out the unknowns in a set of mathematical equations – but not if you don’t know how many unknowns there are.

Education theory is a case in point. It has, from what I’ve seen, always been a bit of a mess. That’s not surprising, given that education is a heavily derived field; it encompasses a wide range of disciplines from sociology and politics to linguistics and child development. Bringing together core concepts from all relevant disciplines to apply them to education is challenging. There’s a big risk of oversimplifying theory, particularly if you take mathematics, logic or philosophy as your starting point.

That’s because it’s tempting, if you are familiar with mathematics, logic or philosophy but don’t have much experience of messier sciences like genetics, geography or medicine, to assume that the real world will fit into the mathematical, logical or philosophical grand scheme of things. It won’t. It’s also tempting to take mathematics, logic or philosophy as your starting point for developing educational theory on the assumption that rational argument will cut a clear path through the real-world jungle. It won’t.

The underlying principles of mathematics, logic and philosophy are well-established, but once real-world unknowns get involved, those underlying principles, although still valid, can’t readily be applied if you don’t know what you’re applying them to. If you haven’t identified all the causes of low school attendance, say, or if you assume you’ve identified all the causes of low school attendance when you haven’t.

traditional vs progressive

Take, for example, the ongoing debate about the relative merits of traditional vs progressive education. Critics often point out that framing educational methods as *either *traditional *or* progressive is futile for several reasons. People have different views about which methods are traditional and which are progressive, teachers don’t usually stick to methods they think of as being one type or the other, and some methods could qualify as both traditional and progressive. In short, critics claim that the traditional/progressive dichotomy is a false one.

This criticism has been hotly contested, notably by self-styled proponents of traditional methods. In a recent post, Greg Ashman contended that Steve Watson, as an author of a study comparing ‘traditional or teacher-centred’ to ‘student-centred’ approaches to teaching mathematics, was inconsistent here in claiming that the traditional/progressive dichotomy was a false one.

Watson *et al* got dragged into the traditional/progressive debate because of the terminology they used in their study. First off, they used the terms ‘teacher-centred’ and ‘student-centred’. In their study, ‘teacher-centred’ and ‘student-centred’ approaches are defined quite clearly. In other words ‘teacher-centred’ and ‘student-centred’ are descriptive labels that, for the purposes of the study, are applied to two specific approaches to mathematics teaching. The researchers could have labelled the two types of approach anything they liked – ‘a & b’, ‘Laurel & Hardy’ or ‘bacon & eggs’- but giving them descriptive labels has obvious advantages for researcher and reader alike. It doesn’t follow that the researchers believe that **all **educational methods can legitimately be divided into two mutually exclusive categories *either* ‘teacher-centred’ *or* ‘student-centred’.

Their second slip-up was using the word ‘traditional’. It’s used three times in their paper, again descriptively, to refer to usual or common practice. And again, the use of ‘traditional’ as a descriptor doesn’t mean the authors subscribe to the idea of a traditional/progressive divide. It’s worth noting that they don’t use the word ‘progressive’ at all.

**words are used in different ways**

Essentially, the researchers use the terms ‘teacher-centred’, ‘student-centred’ and ‘traditional’ as **convenient labels for particular educational approaches in a specific context.** The approaches are so highly specified that other researchers would stand a good chance of accurately replicating the study if they chose to do so.

Proponents of the traditional/progressive dichotomy are using the terms in a different way –** as labels for** **ideas**. In this case, the ideas are broad, mutually exclusive categories to which all educational approaches, they assume, can be allocated; the approaches involved are loosely specified, if indeed they are specified at all.

Another dichotomy characterises the traditional/progressive divide; **teacher-centred vs student-centred methods**. In his post on the subject, Greg appears to make three assumptions about Watson *et al*’s use of the terms ‘teacher-centred’ and ‘student-centred’ to denote two specific types of educational method;

• because they use the same terms as the traditional/progressive dichotomy proponents, they must be using those terms in the same way as the traditional/progressive dichotomy proponents, therefore

• whatever they claim to the contrary, they evidently do subscribe to the traditional/progressive dichotomy, and

• if the researchers apply the terms to two distinct types of educational approach, *all *educational methods must fit into one of the two mutually exclusive categories.

Commenting on his post, Greg says “to prove that it is a false dichotomy then you would have to show that one can use child-centred or teacher-centred approaches at the same time or that there is a third alternative that is commonly used”. I pointed out that whether child-centred and teacher-centred are mutually exclusive depends on what you mean by ‘at the same time’ (same moment? same lesson?) and suggested **collaborative approaches** as a third alternative. Greg obviously didn’t accept that but omitted to explain why.

Collaborative approaches to teaching and learning were used extensively at the primary school I attended in the 1960s, and I’ve found them very effective for educating my own children. Collaboration between teacher and student could be described as *neither* teacher-centred *nor *student-centred, or as *both*. By definition it isn’t *either* one *or* the other.

**tired of talking about traditional/progressive?**

Many teachers say they are tired of never-ending debates about traditional/progressive methods and of arguments about whether or not the traditional/progressive dichotomy is a false one. I can understand why; the debates often generate more heat than light whilst going round in the same well-worn circles. So why am I bothering to write about it?

The reason is that simple dichotomies have intuitive appeal and can be very persuasive to people who don’t have the time or energy to think about them in detail. It’s all too easy to frame our thinking in terms of left/right, black/white or traditional/progressive and to overlook the fact that the world doesn’t fit neatly into those simple categories and that the categories might not be mutually exclusive. Proponents of particular policies, worldviews or educational approaches can marshal a good deal of support by simplistic framing even if that completely overlooks the complex messiness of the real world and has significant negative outcomes for real people.

The effectiveness of education, in the English speaking world at least, has been undermined by the overuse for decades of the traditional/progressive dichotomy. When I was training as a teacher, if it wasn’t progressive (whatever that meant) it was bad; for some teachers now, if it isn’t traditional (whatever that means) it’s bad. What we all need is a range of educational methods that are effective in enabling students to learn. Whether those methods can be described as traditional or progressive is not only neither here nor there, trying to fit methods into those categories serves, as far as I can see, no useful purpose whatsoever for most of us.