Dan Meyer doesn’t seem to understand what explicit instruction is

A while back, I found myself visiting my sister-in-law who had just moved to a new town. I decided to drive to the local supermarket and this seemed like a good chance to test out an idea that I had heard from David Didau and others. There is a debate about when feedback should be provided to students: should it be immediate or delayed? Feedback is a complicated issue in education and this is probably due to the fact that we are lumping together very different things under the one heading and so the answer to the question on timing is likely to be, ‘it depends.’

Didau had used the example of a car satellite navigation system or GPS in order to make a point against immediate feedback. GPS systems provide such feedback and it was Didau’s contention that this is why we don’t learn routes very well if we rely on them. Didau discussed using GPS to navigate a new city and not learning any of the routes.

So I decided to try and use GPS to learn the route to the supermarket. I paid attention to it on the way there and then tried to drive back without it. I learnt the route just fine and was even able to complete the same trip the next day from memory. I was using Google Maps on my iPhone – this shows a live map of the surrounding area and not only gives an indication of the next turn but the turn after that, something I find useful for ensuring that I turn into the correct lane if there are multiple lanes. I never suggested that this was the best way to learn a route – I was simply testing whether it was possible with GPS.

Dan Meyer picked up on my post about this and decided to relate GPS to explicit instruction in mathematics. He had found a study from 2006 where participants were given various different ways of navigating around a German zoo. Three conditions involved using handheld Personal Digital Assistants (PDAs) that gave various visual and auditory information (such as a picture of the intersection, an animation of the pathway and verbal instructions to ‘turn left’) when a participant reached an intersection. The fourth condition involved giving participants map ‘fragments’ i.e. maps of routes rather than of the whole zoo with photographs of the intersections in numbered order.

Participants were not told in advance that they would be tested on route and survey knowledge. When these tests were later carried out, all conditions showed learning but the map fragment condition demonstrated a statistically significant advantage over the others. Meyer then states:

“So your GPS does an excellent job transporting you efficiently from one point to another, but a poor job helping you acquire the survey knowledge to understand the terrain and adapt to changes.

Similarly, our step-by-step instructions do an excellent job transporting students efficiently from a question to its answer, but a poor job helping them acquire the domain knowledge to understand the deep structure in a problem set and adapt old methods to new questions.”

This is a non-sequitur. It is not clear that we can make any inferences from such a study and apply them to maths teaching. Even if we were able to, why does Meyer think the PDA conditions are more like explicit instruction than the map fragment one? In classic studies on the worked example effect the experimenters often made use of example-problem pairs. This is where a student is shown a whole worked example and then has to complete a similar problem themselves. You might argue that this has more structural similarity to the map fragment condition than the PDA conditions. I won’t be making such an argument because the link between German zoos and maths teaching seems tenuous and any conclusions we might draw about maths seem a little eccentric.

Many of those commenting on Meyer’s post made similar points to this and he added a coda in a comment of his own:

“The question that’s useless to us is “should we use [x] in helping students learn?” The answer for most values of x including worked examples is “yes.” The more interesting question to me is, “What kind of knowledge is easy and difficult to learn by way of worked examples?” And, “Under what preconditions are worked examples most helpful?”

The answer to those questions for some of the traditionalists whose blogs I tune into now and then seems to be “all knowledge for all novices” and “no preconditions are necessary.” That kind of maximalism is pretty easy to falsify. (See Greg Davies‘ comment for an example: “Surface structure always comes first.”) Even one datum falsifies a universal claim.” [sic]

I am not sure whether Meyer is referring to me here but I have certainly never claimed that “no preconditions are necessary” for learning from worked examples. To learn from a worked example you would need to understand a whole lot of prerequisite maths. If you don’t know multiplication tables, for instance, then algebra can be tricky – try factorising quadratics. This is a point I’ve made many times and actually sounds like a viewpoint that you might label as ‘traditional’.

I have also written about the expertise reversal effect where the usefulness of worked examples fades as students become more expert. This is why explicit instruction gradually moves from explicit examples, through guided examples to independent practice. Rosenshine provides an excellent explanation of this process which is one that also makes objectives clear and is highly interactive. It is odd that Meyer links to Rosenshine but then insists on such a weird interpretation of explicit teaching.

The idea – dismissed by Meyer – that surface structure comes first is pretty well known in the field of cognitive psychology. I note that Meyer has recently become a fan of Dan Willingham and so he should perhaps return to this piece that Willingham wrote about the subject. Sadly, there are no pedagogical magic beans that we can buy that will helps us accelerate students towards apprehending deep structure. I am deeply sceptical that problem-based learning (PBL) can do this. I note that Meyer links to some Bransford and Schwartz pieces to support his view. I haven’t had chance to read these yet because I’ve been focused on the GPS study but I would be surprised if they draw upon well-controlled experiments that test strong explicit approaches against strong PBL ones.

We all want students to apprehend the deep structure of problems but we must recognise that this is hard work. The methods used by explicit educators might be to highlight non-examples to prevent students overgeneralising principles – a key source of many maths misconceptions – and providing deep explanations. Some have even tried to turn this into a science. Indeed, I find it surprising that those who are so eager to promote problem-based approaches to mathematics are also keen to see explicit instruction as simply a set of step-by-step directions, ignoring the role of explanations altogether: “Do this. Now do that. Don’t ask why.”

Actually, it’s not that surprising because it is much easier to knock-out a straw man than a heavyweight boxer.


5 Comments on “Dan Meyer doesn’t seem to understand what explicit instruction is”

  1. Gary says:

    Regardless of efficacy, I find the discussion of discovery vs DI seems to lack a consideration of efficiency.

    I would argue that doing a science PhD is the ultimate example of discovery learning. Nobody even knows the answers to the questions you’re trying to answer or the problems you’re trying to solve, so people can’t guide you or tell you the answers even if they wanted to.

    It took me 3 years to solve the main problems that went into my thesis. I could now explain the main concepts behind the problems I solved to you in about 15 minutes.

    Would you rather have the 3 year version, or the 15 minute version?

    Not to mention discovery learning is extremely demoralising. See e.g. http://www.ibo.org/ib-world-archive/september-2014-issue-70/its-not-about-the-numbers/ and this quote:

    “With my PhD students, I think I spend 50 per cent of my time on their psychology, giving them the mental strength to tackle areas of research where nobody’s been able to find answers,”

    Many of the arguments seem to revolve around the fact that experts use discovery learning to learn new things.

    But they only do that because they have to; they have no choice. There is no other way.

    I actually spend much of my time as a scientist learning about other people’s work and teaching myself knowledge that is already known, not discovering that knowledge.

    The discovery part is only left for parts where people don’t already know the answers.

    Making students discover stuff that is already known, that took the discoverers themselves years to discover, is bordering on cruelty, frankly.

    The route to expertise is knowing and understanding ever more stuff, and practice. You can’t short-cut the process. There are things I know and understand that I can barely even imagine how I could articulate to somebody else; it has simply come from thousands of hours of practice.

    The most amazing thing is that this is frankly common sense, but something has been hijacked along the way.

    Did somebody just give Andy Murray a tennis racquet and tell him to get on with it? Or did he have a tennis coach Mum and then go the world’s best tennis academies at a young age?

    Did the Polga twins just get given a chess set and become grandmasters as teenagers by chance, or did they have a Dad who himself was a decent chess player and who set out to turn them into chess prodigies?

    Did Mozart become a virtuoso by himself, or did he have an accomplished composer for a father who taught young Mozart everything he knew?

    How the education debate ever got to the stage where we decided that giving students the ingredients but not the recipe was the best, most efficient, and quickest way for them to bake a great cake, I do not know.

    • gregashman says:

      Your criticisms of discovery learning are spot-on but if you were to explain them to a proponent of problem-based learning, constructivism or whatever then you are likely to be dismissed with a comment that their preferred method is not pure discovery and contains a lot of guidance. This is the substance of many responses to Kirschner, Sweller and Clarks’s 2006 paper on ‘minimal’ guidance. The paper’s argument does not apply, PBL advocates claim, because their methods provide more than ‘minimal’ guidance (although anyone sensible and who has been in a classroom knows exactly what the authors meant).

      I think what we need to establish is the advantage of *any* element of discovery with novice learners or, conversely, the disadvantages of fully guided instruction. Some have sought to do this by running often poorly controlled studies that generate small effect sizes for PBL when compared to some non-optimal form of explicit instruction. Others shift the goalposts and insist that explicit instruction delivers on academic aims but an element of discovery delivers on more nebulous objectives that can’t be measured. This is, of course, unfalsifiable and is therefore a form of pseudoscientific argument.

    • Chester Draws says:

      Did somebody just give Andy Murray a tennis racquet …
      Did the Polga twins…
      Did Mozart become a virtuoso …

      Maybe it’s just me, but I find the advocates of discovery learning tend to have a distaste for that sort of excellence, although they rarely admit it openly.

      If you point out that the best results tend to come from schools with an emphasis on explicit methods, you get told that they “don’t understand” what they are doing, just following “rote” procedures. Never mind that they clearly do understand what they are doing, because you really cannot fake Maths ability once you reach the top end of High School. Never mind that books written by auto-didacts are mostly quite poor (often the traditionally skilled editor goes unseen).

      Their exemplars of excellence are the likes of Zahar Hadid — never mind that she designed buildings that were expensive and impractical — Tracey Emin (ugh!) and Jacques Derrida — who is mostly incomprehensible if you forget to be in awe of him. They are creative, and against traditional excellence.

      So pointing out that excellence comes from solid basics and hours and hours of practice really won’t work. That is not how they define excellence.

    • Ronda says:

      Oh, the time thing! Yes!

      I’ve been thinking this recently myself. The other day I did SOLE/inquiry hybrid kinda thing with my kids, because “that’s the way we do things now”. It took almost 2 hours for each group to (poorly) research one topic each, grapple (poorly) with unfamiliar vocab and content, miss key concepts or “construct their own [flawed] knowledge” and present to their peers. At least one kid in each group spent the whole time doing pretty headings and pictures for their presentation. It was fine for a few of the more highly motivated, higher achieving kids, but by and large, it was a waste of time for most.

      I reflected on it afterwards – modelling how to locate that info, explicitly working through it to identify/understand key vocab/concepts and taking a more modelled/guided/independent approach would have not only covered MORE concepts, but it would have been done in less time and I could have been sure that the salient points were understood.

      I can see the benefits of these choose-your-own-adventure pedagogies as capstone events or for certain content areas, but as a holus bolus “paradigm shift”? Nuh.

  2. David says:

    What’s interesting about the map exercise, is that anyone who has served in their country’s armed forces has gone through some form of map training, which usually entails the equivalent of explicit instruction. This has usually been done on a paper map, with emphasis on specific geographic features, important grid coordinates, etc. Thus, a context is built up prior to the “discovery” aspect when one is on the ground.

    In the US Army, we were introduced to GPS in the Gulf War–it was cool, but did not replace the old way of doing things. It would be unacceptaple for a soldier not to have a good sense of his/her surroundings and how to place these on a map. GPS simply augmented previously learned info. If you’re interested, see here or the Army’s 2006 edition of the manual for map reading and land navigation. https://fas.org/irp/doddir/army/fm3-25-26.pdf

    There’s also the issue of whether the technology can be hacked or disrupted, which is why the US Navy is teaching its officers how to use a sextant…https://theconversation.com/is-technology-making-us-dumber-or-smarter-yes-58124

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