A response to Dan Meyer

Following my previous post, I have been engaged in a discussion on Twitter with Dan Meyer. I like Dan. He comes across as a nice guy and has the rare ability to stick to the issues without making things personal. There are a few people out there who could learn from that.

If you are unfamiliar with Dan then you should check out his blog and his TED talk. He is a big deal.

Dan has taken issue with me about a few points on Twitter and so I thought that I would take this opportunity to expand on my thoughts a little.


I do not generally describe explicit instruction as ‘lecturing’ so why not? Well, lecturing implies a lack of interaction. It is clear to me that effective instruction involves ensuring students’ attention. In my own teaching, I attempt to achieve this by peppering any ‘lecturing’ with questions. I decide which student will answer which question (I rarely ask volunteers) and so all of my students know that they could be called upon at any time. I find that this concentrates the mind. If I am presenting something new then I will ask students to tell me how to do the non-new bits e.g. the linear algebra that drops out of the end of a transformations problem.

This looks very different from a classical university lecture where the size of the audience militates against this kind of interaction. The problem with describing explicit instruction as ‘lecturing’ is that I find people then quote studies to me that show that university-level lecturing with interactive clickers or with short review breaks is more effective than straight lecturing, thus demonstrating that explicit instruction is flawed (See papers here, here, here and here that have been forwarded to me periodically by Doug Holton – note that a common problem in interpreting these studies is trying to figure out what the “interactive” condition actually means). Clearly, explicit instruction can be a highly interactive approach and so this evidence tells us little of relevance.

“Lecturing” also does not seem to capture the phases of a lesson where students are practicing independently whereas the way that explicit instruction is defined does cover this. Explicit instruction has a long track history and is often also referred to as ‘direct instruction’. However, the latter term tends to be confused with the highly-scripted programs developed by Siegfried Engelmann and others which are basically one particular type of explicit instruction. This is why I avoid this term.

Barak Rosenshine is something of an expert in explicit instruction. He was involved in analysing the process-product research of the 1950s to 1970s that aimed to uncover the differences between more and less effective teaching. His concept of explicit instruction / direct instruction was drawn upon my Engelmann in developing his own approach. Rosenshine provides an excellent description of explicit instruction in this AFT article although he doesn’t name it as such, preferring to simply discuss ‘principles of instruction’. He goes into more detail here, this time referring to ‘direct instruction’ (paywalled).

Why do teachers seek alternatives to explicit instruction?

If explicit instruction is as effective as I claim then why do teachers seek out alternatives?

I spent 13 years feeling guilty about the way that I taught; that I should be making greater use of whistles and bells. This is because the dominant view in education asserts this. Of course, in reality, many teachers will use forms of explicit instruction because the alternatives are often unworkable. I rapidly figured-out that if I taught in certain ways then I’d have to teach the stuff again later. But I thought this was a flaw in me.

Universities and teacher training materials instruct teachers that ‘constructivist’ teaching practices are more effective, even though the evidence does not really support this. Consultants, school leaders and Dan Meyer himself are all resources that teachers could be expected to consult if they want to improve their practice and they will get a broadly similar message from each. Where could a teacher even find out about explicit instruction and its effectiveness? Well, I am trying to do my bit in a small way but it hardly compares.

The sadness is that this means that teachers often miss out on training in how to make their default explicit instruction much more effective. One light in the darkness is the work of Dylan Wiliam around formative assessment (which was basically my route into a different way of thinking).

Indeed, teaching seems to suffer from the “How Obvious” problem that Greg Yates points to in his classic paper. When presented with the findings of research, teachers tend to declare them obvious. However, when student teachers are asked to identify the attributes of effective teaching that comes from this research they generally cannot. “Not a single student cited the effective teacher’s ability to articulate clearly, or to get students to maintain time engagement.”


I have briefly mentioned that the alternative to explicit instruction may be described as ‘constructivist’ teaching. I don’t want to become bogged-down in this – I am aware that constructivism is actually theory of learning and not of teaching and I have no problem with it in this regard; we link new knowledge to old etc. If it is true then, no matter how we teach, our students will learn constructively. However, some educationalists clearly do see implications for how we should teach.

Over the years, similar approaches have been described in many ways; discovery learning, guided discovery, problem-based learning, project-based learning (see William Heard Kilpatrick for an early description), inquiry learning and so on. Many of these date from a time before the constructivist theory of learning and so reflect a broader current in educational thought, epitomised by the progressive education movement of the early 20th century. Constructivism should really be seen as part of this tradition.

As every age invents a new name for it, so a new enthusiasm develops and, without much in the way of supporting evidence, armies of evangelists go out into the world and proclaim the new ‘effective practices’. A recent example can be seen in Canada. Around the year 2000, constructivist maths was pushed heavily in schools via public policy (see the WNCP) and consultants. Since this time, Canadian results in international maths tests such as PISA and TIMSS have generally declined (and I don’t mean relative to other countries, I mean in absolute terms). It is only a correlation but if this new approach was so effective then should we not have seen the reverse trend?

I am generally cautious about comparing different countries on these measures but I do think it significant when a single participant such as Canada or Finland declines relative to itself.

On the basis of quite thin evidence (see Kamii and Dominick and a nice replication from Stephen Norton which finds the precise opposite result or look at this poorly controlled study), teachers have been urged to abandon standard algorithms or to avoid drilling students in multiplication tables and number bonds. Cognitive load theory – of which I am a student – would predict this to be a disastrous move (see my slides from prior to starting my PhD).

So, if there is a lack of evidence then what justification is there for people to continue to support constructivist approaches? One example can be seen in the various reactions to Project Follow Through and goes something like this, “OK so Direct Instruction may be good for rote memorisation of basic facts but our kind of instruction does more intangible things over a greater period of time that cannot be measured”. Or, “Direct Instruction causes criminality”. Neither of these is true (see here and here).

Another approach is to say that people who favour explicit instruction neglect motivation; that motivation is key to learning and explicit instruction is just like really boring man!

Firstly, if motivation really is so important to learning and if explicit instruction is so demotivating then surely this would render explicit instruction ineffective. The evidence suggests otherwise.

For my second point, I need to be careful. The constructivists have set a rhetorical trap here that I might fall in. I will freely admit that entertainment is not my top priority when planning lessons. My top priority is that students should learn. However, this does not mean that I want my students to be bored. If they can learn something and I can make it interesting then I would always want to do both.

It is not clear to me why explicit instruction is intrinsically more boring than any other method. Yes, it can be boring but so can problem-based learning or anything else. I’ve observed students completing one of Dan’s activities who were not particularly turned-on by it. However, I would not conclude that it was therefore intrinsically boring. Perhaps it was pitched at the wrong level or the teacher hadn’t introduced it correctly. Motivation is a complicated thing.

I have written before in the context of science and asked which activity is more boring; completing an investigation to test the strength of different wet paper towels or a whole-class discussion of whether aliens exist? Advocates of alternative methods often make life harder for themselves by also insisting that all learning be nailed to mundane aspects of everyday life. For instance, I have noted that in David Perkins’ recent book he suggests, “students plan for their town’s future water needs or model its traffic flow.” Yawn! Boring! (see, I can do it too).

I have this little proof that I like to demonstrate to show that 0.999.. = 1. Every year, it provokes heated debate. What do I do? I show the students the proof, on the board, at the front of the room and then we discuss it. I suppose that I could ask the students to get into groups and try to come up with their own proof. I suspect that most would not and would also find the activity a bit boring.

The point is that nobody owns motivation. If your explicit instruction is boring then why not make it more interesting? Why does this problem have to imply a change of method? If that’s all constructivism’s got then it’s time for a rethink.


13 thoughts on “A response to Dan Meyer

  1. This is going to sound like bragging, but it really isn’t intended to be – I actually want to make a point about the assumption that explicit instruction is boring:

    I’ve been struck this year in particular by the large number of pupils (or their parents) commenting on how much they love English in my class. What struck me about it is that I genuinely can’t remember deviating from explicit instruction this year at all. I honestly don’t think they’ve got out of their seats once. I think they’ve enjoyed the subject because of the content of the lessons – they’ve learned and explored some fascinating texts and topics this year, in my opinion.

  2. Stan says:

    I wonder if math teachers worry about motivation more than teachers of other subjects. English teachers don’t seem to stress issues of relevance and motivation as much. You just don’t see the same angst over whether Romeo and Juliet is still relevant or interesting or has real world application. I know there are debates about which text to use but I have never seen a big debate about whether students in English class need to study fiction or need real world examples of the application of understanding literature.

    Compare that to the sometimes tortured attempts to create motivation by real world application with math. Most students will never see the quadratic formula after completing their education. Ask students to survey their parents for how many use the sine function in the last year and you won’t get a lot of real world support to motivate its importance to high school students.

    • It is interesting that you mention quadratics. In his book, David Perkins uses the fact that most adults never see them as a reason to suggest that we shouldn’t teach them. He suggests statistics instead. The thing is, you don’t have to know anything particular in order to survive in life and statistics would succumb to the same logic. Instead, it is useful to generally know lots of stuff over a broad range of topics – this is what aids reading comprehension, enables you to make connections and so facilitates analysis and creativity.

      People do make similar arguments about English. They point at Shakespeare and note he’s dead, white and male. Again, you don’t need to know any Shakespeare to survive. However, I agree that maths seems particularly prone to this sort of argument. My hypothesis is that there are a large number of influential people in education who never mastered maths in the same way as they mastered the arts and humanities. It is human, in such a circumstance, to look to blame the way that maths is taught rather than any lacking in oneself. The easy trope is to talk about how useless and abstract it all is.

      However, it is an odd idea that by tying maths to mundane real-world applications we will somehow make it more interesting.

      • My hypothesis is that there are a large number of influential people in education who never mastered maths in the same way as they mastered the arts and humanities. It is human, in such a circumstance, to look to blame the way that maths is taught rather than any lacking in oneself. The easy trope is to talk about how useless and abstract it all is.

        I have a similar hypothesis. I argue here, for instance, (http://www.textsavvy.blogspot.com/2015/06/the-curse-of-novice.html) that this “novice-hood” can cause us to view expertise more superficially.

      • Paul Hartzer says:

        James Grime (of Numberphile) is excellent at repeating in several videos that the reason for working on obscure math problems is to create tools that will then be available for other math problems. So what if most people don’t use quadratics? Exploring quadratics allows us to explore important mathematics concepts, such as roots of a function, lines of symmetry, and extrema. Some further recent thoughts of mine: http://paulhartzer.com/teachblog/why-are-we-teaching-this/

      • Stan says:

        I know there is some discussion on Shakespeare for example, but the difference is it is hard to find an English teacher who spends time worrying about this or an English curriculum that spends time justifying learning Shakespeare with real world examples of its utility.

        My favorite essay on the topic of why to teach math is by Underwood Dudley http://www.ams.org/notices/201005/rtx100500608p.pdf . Well worth a read if you find the typical real world math problem given to students a bit lame.

        I suspect that beyond arithmetic learning math is a bit like learning another language. Studying some verb forms is not of its self hugely useful. It is just a necessary step to the useful end of fluency.

        The problem for math teaching is that for most students fluency in high school math is less obviously useful than learning Spanish or French. Most will never need to know a trig identity ever again. Same with the quadratic formula.

        A solid justification for teaching everyone the quadratic formula is that it is a necessary step to becoming a mathematician, physicist, or engineer and no one should miss the opportunity for that. Another justification with some merit is along the lines of Dudley’s. That is that it is a very effective way to develop thinking skills. Another would be that it is important to demystify math so that it is not seen as something available only to a certain priesthood.

        Most people justifying some piece of high school math seem to try for some more immediate necessity for every topic. Not for them the long term fluency goal of the French teacher, who can say fluency is the goal so it’s verb conjugations for the next two weeks.

        So you get examples like Dan Meyer’s recent blog post where he wants to describe the headache that understanding what a function is as compared to other relations solves. I really could not follow how his suggestions would motivate anyone. All the posters there had their favorite example or analogy of relations that are a function and those that are not. These might be great teaching ideas but none provides a high school student with a motivation for learning the distinction and taxonomy of functions as a subtype of relations.

        In the case of functions the real motivation is not their ubiquity or that they are like vending machines or somehow more certain than other relations. It is that there are more mathematical tools for working with functions. The most obvious of these are differentiation and integration which don’t seem to be available as justifications at the point where the taxonomy of relations is taught.

  3. I have just spent a half term teaching an intervention group to memorise their times tables and get faster through the use of x tables tests (which involved them beating different superheroes – x2, x5 and x10 was batman, x3 and x4 was hawkgirl and so on). We have also focused on number bonds to numbers to 10 and a lot of rapid fire questions and dictating missing number questions. The point being that it was explicit instruction, children in their seats and head down doing their work. But they have absolutely loved it. The first lesson was not as good as they were not used to it but by the time they left, they loved each lesson.

    The progress they made astonished me and each of them grew in confidence. I found the same thing when I taught a literacy group the different word classes.

    The superhero times tables was simply times tables with a picture on it – it ‘prettied’ it and gave them a sense of competition. If it were another group then it might not work. Constructivist approaches have worse outcomes in the end as children do not progress as quickly or develop their self esteem in the same way.

    The truth is not one the education establishment wants to swallow – which is that they have spent the last 40 years promoting an ineffective way of teaching because it appealed to them.
    They don’t want to accept that they have got it wrong and the methods they moved away from have proven to be more effective.

  4. The think that irritates me about this contention about lecturing is that it is typically raised in a discussion about teaching small children. The university-hall lecture studies with many tens or over 100 students in a hall, and completely unlike direct instruction in a primary grade classroom, in almost every respect — including that of lecturing itself.

    Further, a university class consists of adult learners. Meyer himself lectures adults. That, after all, is what a TeD talk is: a LECTURE. Further, he is now a circuit speaker. On his site he has an impressive list of speaking engagements. Guess what? By all accounts … he LECTURES adults.

    Lecturing is an appropriate form of instruction for adults. Is it the most effective approach? Well, these studies are showing that it is quite effective WHEN combined with some element to ensure engagement. But not when isolated in its purest form. No big surprise there. There are numerous reasons, from brain science to attention span to social dynamics that make lecturing a useful way to instruct adults … and a terrible way to instruct small children. The issues are very different. There is, as far as I know, no disagreement among the various camps on this.

    Yet educationists persist in dragging out these studies on adult classes at university as if they had some implication about DI as it is used in primary-grade elementary school. Sorry, it’s completely irrelevant.

    Meyer tweeted just the other day to characterize as a group (yes, making things “personal”) those — explicitly referencing Anna Stokke — who think anything other than “lecturing” is “building birdhouses”. This is an unfair characterization. Stokke does not advocate lecturing (and certainly not university-style as in the studies) as a form of direct instruction to small children and did not use the word “lecture” in either the interview upon which the referenced article was written or in the CD Howe report she had written, which sparked the interest that led to the article http://www.theglobeandmail.com/news/national/old-school-or-new-math-teachers-debate-best-methods-as-canadian-scores-fall/article25224581/

    Meyer apparently understood the writer’s assertion that “Anna Stokke … is a staunch defender of lecturing and practice” with something coming from Stokke’s own mouth. It did not. It is a complete misrepresentation of Stokke’s position on the matter! When she wrote the author and the editor in charge, they showed their level of disregard for the very point of the discussion by insisting that it was “fair game” to use “lecture” as an abbreviation for “direct instruction”. What is one to do when so badly mischaracterized, and the media outlet refuses to make a correction or retraction?

    So Meyer is perhaps not completely to blame for this, although treating the writer’s statement as coming from Anna is a nonsequitor. It changed the nature of the discussion completely onto a completely irrelevant point. And it propagated and magnified that error, probably leading ultimately to your discussion of “lecturing” with Meyer as if that’s what DI was about.

  5. Stan says:

    Robert is too generous to Dan. Stokke was quite clear that she saw a balance and gave her view of what that should be, 80/20. Dan continues to argue against a view that is 100/0 and where the 100% of EI has no ability to motivate. As Robert points out Dan routinely gives talks that are pretty close to a lecture format and yet Dan probably believes he is quite capable of motivating his audience in that format.
    So Dan is arguing against a strawman on two counts instead of addressing the actual points made by those he is debating.
    In his latest twitter debate he argues that a good movie that raises questions in the viewers mind is somehow supporting his argument despite a movie being very much a one way communication – just like DI/EI. He seems to be unwilling to accept that a good teacher doing EI could aim for and get this effect or that a good teacher doing EI would find X% discovery has hit the point of diminishing returns.

    It’s an example of the classic false argument described in How not to be wrong. Assume a relationship is linear, point out one extreme is bad and conclude the other extreme must be good. Sad to fail on that one when the subject is math.

  6. vlorbik says:

    the system prescribes methods that are good *for the system*.
    not for the individual human beings… teachers and students…
    that make up its physical… and social… substratum.

    draw careful distinctions or roll around in the gutter of confusion.


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