How people really learn

I ran into trouble with a few commentators last week. I wrote a piece for Spiked magazine where I referred to the children’s story “Fish is Fish,” and the way that it is used in the teacher education textbook “How People Learn,” by Bransford et al.

Of the story, I wrote, “The implication is that we cannot understand anything that we have not seen for ourselves; each individual has to discover the world anew.” Clearly, this is not exactly what is written in How People Learn because, the way I’ve stated it, it’s obviously absurd and people tend to avoid making obviously absurd claims. Also, note my use of the word, ‘understand,’. In education, some people are inclined to see understanding as something quite different to mere knowledge (which it isn’t, really).

So, have I misrepresented the book?

Some have suggested that the point of the story is simply to show that we must take into account our students’ prior knowledge when teaching them something new. If this is the point then it is a trivial one. Fish is Fish is deployed to illustrate something about constructivism. If you were to look for an educational approach that was as far away as possible from those inspired by constructivism then you may well alight upon Engelmann’s Direct Instruction. I was having a look at the manual for one of his writing programs recently and the first thing that he mentions is the use of placement tests to figure out what version of the program different students should be put in.

If this is all that Fish is Fish is meant to signify then it reminds me of Vygotsky and his Zone of Proximal Development; another underwhelming concept.

However, I hold to my view that Fish is Fish is there to tell us more than that; to tell us that it is basically impossible to transmit understanding from a teacher to a student. Instead, the student must be involved in some amount of direct discovery, particularly of the main concepts involved.

It has been pointed-out to me that the authors of How People Learn do suggest that there is a time for simply telling students stuff. This is true. For instance, they state that, “there are times, usually after people have first grappled with issues on their own, that “teaching by telling” can work extremely well (e.g., Schwartz and Bransford, 1998). However, teachers still need to pay attention to students’ interpretations and provide guidance when necessary.”

Note the whopping caveat, “usually after people have first grappled with issues on their own.” This is important, of course, if you want your students to truly understand. There is a whole area of constructivist research trying to prove the concept of ‘productive failure’, which is the idea that students benefit from struggling with problems prior to being given explicit instruction. It is the subject of some debate in the book “Constructivist Instruction: Success or Failure”, and, unfortunately, it seems that most of the key experiments have been poorly designed, with more than one factor varied at a time. I have a particular interest in this area – it’s part of my PhD research.

I think that the authors also reveal their views about the need for direct experience when they describe how it is quite impossible to explain to children that the world is spherical.

“When told it is round, children picture the earth as a pancake rather than as a sphere (Vosniadou and Brewer, 1989). If they are then told that it is round like a sphere, they interpret the new information about a spherical earth within their flat-earth view by picturing a pancake-like flat surface inside or on top of a sphere, with humans standing on top of the pancake. The children’s construction of their new understandings has been guided by a model of the earth that helped them explain how they could stand or walk upon its surface, and a spherical earth did not fit their mental model. Like Fish Is Fish, everything the children heard was incorporated into that preexisting view.”

If you are still unsure as to exactly what is being suggested then it is instructive to look at the exemplary lessons that the authors describe towards the end of the book. After informing us that history teaching should not be about learning facts – something quite at odds with my understanding of cognitive science that sees fact-learning as absolutely critical – they describe a maths class:

“Word problems form the basis for almost all instruction in Annie Keith’s classroom. Students spend a great deal of time discussing alternative strategies with each other, in groups, and as a whole class. The teacher often participates in these discussions but almost never demonstrates the solution to problems. Important ideas in mathematics are developed as students explore solutions to problems, rather than being a focus of instruction per se. For example, place-value concepts are developed as students use base-10 materials, such as base-10 blocks and counting frames, to solve word problems involving multidigit numbers.” [My emphasis]

It seems that this exemplary maths teacher has never heard of the worked-example effect.


9 thoughts on “How people really learn

  1. Stan says:

    The two examples given, the fish and the frog and the student and the sphere shaped Earth, are examples of what Stephen Pinker refers to as the curse of knowledge. He describes this problem in his book A Sense of Style. His context is the writer who has to communicate with no means of feedback. This curse is the problem of not appreciating how difficult being on the receiving end is without the knowledge the writer has. The term and idea is not Pinker’s but comes from economic theory.

    Pinker points out that for the writer simply being aware of the problem and trying harder is not a very effective means to avoid it. Instead he argues for careful attention to the use of jargon, my chunks are not your chunks, and how an experienced person thinks of an idea differently from a novice. Everyone should read every book Pinker writes and this is no exception. He applies his fix to various examples making it all very clear.

    The problem is also more subtle than described in the reference here. What does it mean to say “Everything is incorporated into that preexisting view”? How could that not be the case? How could people learn about the shape of the Earth and not incorporate that into their existing view of the Earth as the thing they have been walking around on all their lives? The problem is not that learning involves incorporating new ideas into a preexisting set of ideas. That is a tautology. The problem is that the person communicating the new ideas will not be aware of the gap between the preexisting ideas and the way they are trying to impart the new one. Worse, even if they are aware of this issue that is not enough to remedy it. They have to take specific steps to resolve it.

    You can find more about Pinker’s book at

  2. Pingback: Why Linda Darling-Hammond is wrong (and why this matters) | Filling the pail

  3. You have a very interesting and strongly held position that I tend to agree with in a lot of ways. I see your argument here as essentially a response to the argument (in my words): “There are very few situations where direct instruction is an optimal teaching strategy.” I get that there is a debate as to whether you are creating a red herring here, but I want to learn more about your thinking by approaching from the other side. Do you support the position that “there are very few situations where constructivism/productive failure/etc is an optimal teaching strategy?” Do you believe it is ever appropriate to pose new problems to students and ask them to work on the problem without showing them an example solution? By ‘new problems’ I mean problems like the kind Dan Meyer asks where there is either new mathematics involved or the synthesis of mathematics in new ways.

    If not, how do we prepare students for solving problems outside the classroom? Is it reasonable to expect that many of the problems faced outside the classroom will be new problems, where there will not be a teacher present?

    I think this debate is really hard to evaluate analytically. Unlike many constructivists, I think the evidence is pretty strong that direct instruction or explicit instruction is better than most other standard methodologies for teaching if the goal is to teach students to solve well stated and well defined problems from a relatively small pool of example problems (If I want to get students to quickly and efficiently find roots of a quadratic, my fastest teaching method is to show them how to do it and then have them practice.). That said, this situation is not what I am trying to address when I utilize constructivish methodologies. I am trying to prepare students for curve-ball breakdown questions that do not match a known pool of example problems. Assessing this ability is obviously very hard. As soon as I write down a question to assess the ability, it becomes a problem that can be explicitly taught.

    Personally, I believe that a reasonable blend between the two positions makes the most sense. In fact, I think the Common Core’s notion of rigor got things approximately right. 1/3 fluency, best achieved with directish instruction, 1/3 conceptual understanding, best achieved with constructivish instruction and 1/3 modeling, best achieved by ???? (I have no idea how best to teach modeling, probably a blend of both).

    While I’m going, I may as well ask you another couple of questions that I couldn’t find answers to on your blog:
    How do you feel about proof/conceptual understanding and the teaching of proof in elementary and secondary ed?

    How do you feel about modeling and the role of modeling in the math classroom as opposed to the science/etc classroom?

    • Firstly, I think proof has been neglected.

      On your main point, I don’t believe that there is a general ‘ability to solve novel problems’ that can be trained. There are no domain general problem solving skills that can be identified other than means-end analysis and we all possess this anyway. Tricot and Sweller are good here:

      Click to access TricotSweller_revised.pdf

      In the real-world, professionals are usually required to solve variants on well-known and well-defined problems. Where this is not the case, they will need to draw upon experience to look for something that might help – episodic knowledge. If a novel problem requires the use of a quadratic equation, for instance, then a solution will not be clear to someone who had not mastered quadratic equations in the way that you describe. It will also help if this someone has seen them used in a range of situations. If we are lucky, the new problem might be close to something that our problem-solver has seen before, increasing the chance that a solution will be spotted.

      I tend to think of constructivism as an aspirin in search of a headache. Initially, it was thought that it would boost academic gains. This doesn’t seem to be the case. Others claim it is more motivating. Sometimes the claim is made that it increases the ability to solve novel problems. Any such propositions are in need of evidence.

      • I agree strongly that the world would benefit from more good research in education (as well as many other things). That said, we have students in front of us and we are stuck making decisions with limited information.

        The paper you linked is fascinating. I’ve read the first half and look forward to finishing it. I am interested in reading responses to it. At the same time, I think the specific question they are looking at (domain specific vs. domain general) may be a bit orthogonal to what I’m trying to get at. I believe that the ability to solve new problems is mostly a domain specific skill. I agree completely with you that solving a new problem typically requires, as a necessary condition, a large body of facts. In talking about a new problem though, I am by my definition asserting that the facts are, on their own, not sufficient to solve the problem. The missing ingredient is not domain general knowledge (though I don’t doubt that domain general, biologically primary, knowledge is important and I am not ready to accept that it cannot be taught through teacher crafted experiences.). Instead, the missing ingredient is other domain specific/biologically secondary knowledge that doesn’t quite fit the standard definition of fact. I would maybe like to associate this other missing ingredient with heuristics. It isn’t a truth statement that is missing it is a probability statement/induction that can then, after the fact, back fill the truth statement/deduction.

      • This comment really threads between another of your posts and this one and maybe fits better in the other post. I’m leaving it here for continuity.

        I like the article you referenced about the Five Meanings of Direct Instruction. I feel that few constructivists would argue against the efficacy of many of the teaching methods described as direct instruction in the article. I know you have said recently that you prefer the term explicit teaching. I heard Deborah Ball’s talk and saw the slide you referenced. I interpreted the slide as a contrast between definition 5, what she was calling direct instruction, and her vision of explicit instruction which is more like definition 3. She spoke the day before and really stressed a couple points that I think you’ll generally like: 1. We need to do a lot of research into actual teaching methods and get truly reliable data around effectiveness, and 2. Teaching is too important to continue the eduction wars and picking sides. I took this to be her saying that we have the research technology to get much more specific than constructivist vs. direct instruction and thus the obligation. And here I am engaging in the kind of battle she was warning against.

        Assuming we can come up with something specific and clear that we still disagree on, I think it’s important to look at what we are using to assess the effectiveness of the instruction. If we are using problems that fairly closely match problems that students have seen before, then we are not really assessing the domain specific skills that I am pointing at. How do we assess student ability to effectively struggle on problems that will require them to use their skills in new and unexpected ways? Do modeling problems address this somewhat? What teaching methods would you use if you expect that problems will have ambiguity about the appropriate model and ambiguity about the implications in the real world? If there are many different correct answers and a big part of what we are assessing is the precision and effectiveness of the argument? Where we reasonably will expect that very few if any students will get perfect scores on the problem, instead, we expect students to effectively generate mathematical arguments and reasoning in the absence of certainty?

        Personally, I would use a lot of teacher modeling, as described in definition 3. I would make sure that students have solid fluency, largely through doing examples on the board and having students repeat similar problems enough times to generate confidence. I would also give students many opportunities to actually play the game. They would encounter many problems that they didn’t know how to solve, that would require flailing and failing and perseverance.

        I think proof problems, especially when grades carefully, provide similar opportunities. Of course, grading like this is impractically laborious. Which calls for much better automated grading.

  4. Pingback: Gotcha? | Filling the pail

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.