I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. If my students were all fully engaged, fully motivated, and directing their attention to the problems at hand, I daresay I could leave the room entirely and they would still learn math. And as soon as I completed 2 worked examples, they would no longer be part of the engaged group, so I could throw out their data. Self-fulfilling prophecies are my favorite.

  2. Jeremy Millington

    April 4, 2012 - 1:02 pm -

    What about students who ARE motivated? Typically those in advanced (e.g. Honors, AP, and high-level college courses) are motivated to learn. Would CLT and the Worked Example Effect work better for these students compared to unmotivated students?

  3. John Sweller is a cognitive scientist, making claims about scientific problems like how the brain works, not practical problems like how to run an engaging classroom.

    Chemists put elements on the periodic table even if they’re poisonous. Physicists provide theories of gravity even though it would be fun float around all the time.

    Cognitive load theory is a rare case where we get some fundamental limits about what is physically possible or impossible in the moments of actual learning, at the second-by-second level. It may even be at a low enough level to be not worth a teacher’s consideration. But as a contribution to the body of cognitive science knowledge, it certainly seems useful.

    Now, you may accept Sweller’s specific scientific findings but then say that he shouldn’t try to make arguments for or against broad types of learning. Here I would say that you might find the arguments more palatable if you think of them as arguments about these microscale moments of learning rather than, say, how to organize a day in a classroom. I’d even say that CLT isn’t necessarily prescriptive for worked examples — they are chosen as an embodiment of certain properties, and contrasted with an embodiment of certain other properties to demonstrate that learning does not occur when particular properties exist (i.e. those that violate cognitive load theory).

    Of course, with the tone of the some of those articles, it’s tempting to take sides…

  4. Ryan: John Sweller is a cognitive scientist, making claims about scientific problems like how the brain works, not practical problems like how to run an engaging classroom.

    It’s hard to square the Sweller you describe (the unassuming cognitive science who keeps carefully to his own jurisdiction, letting his chips fall where they may in the classroom) with the Sweller who wrote this and this. In those pieces, Sweller translates the implications of CLT directly into prescriptions for classroom organization.

  5. I have been focused on how to motivate my high school math students since I began teaching high school math. True, the cognitive load theorists do not consider the unmotivated students – they are concerned with how and when learning occurs. That being said, I got to thinking about why so many of my students are unmotivated, and after listening to Sweller and doing a bit more research into the cognitive load theory, I came to the possible conclusion that these students have spent years in classrooms that do not take cognitive load into consideration. These students have been expected to learn in an environment where their cognitive load is exceeded time and time again, creating huge gaps in the scaffolding of their schema. Seems to me that a student in this situation would eventually say “who cares?”, not because he doesn’t care, but because to care is too painful. I do not believe there to be a greater motivator than success, nor a greater de-motivator than failure. Look at the motivated students in your classrooms. Are they successful? Now ask this question: are they successful because they are motivated,or are they motivated because they are successful? Suppose the latter is true. What if all students understood cognitive load theory. What if they understood that their failures stem in large part from faulty teaching or curriculum design. Could they then ask useful questions that would eventually lead to the necessary repairs in their scaffolding? Here’s an example: I ask the student, “what don’t you understand?” and the student typically responds something akin to, “I don’t get any of it.” Okay. Not helpful. Instead, what if the student understood that his schema was lacking some integral platform upon which this new information could be built. In other words, what if the student could say, “you’ve gone beyond my working memory, and you have to take a step back.” Then we could talk intelligently and usefully about what he does know and find the pieces he doesn’t, thereby creating the pathway to understanding. I am thinking that if a student understands how he learns, he will be able to advocate for his learning. And if he can advocate for his learning, he can ensure understanding. And if he understands, he will experience success. And success is the ultimate motivator.

  6. I had the fortune to grow up in a country where math education was in top 5 in the world at that time. I know what I am going to write is not going to be very useful, because it is incompatible with the way education is set up in a normal independent school district, but maybe someone can find a good idea in it. So here goes nothing, the motivation we had in order to pay attention was basically this:

    1) Fear :) You will need all this for your maturity exam (something like SAT)

    2) Coordination: When we learned log, pH calculating came up in chemistry class, when we learned about % we had mixing problems. Problems in physics and chemistry gave a strong motivation to learn math. Without this it would have been very difficult to motivate us.

    3) PBM tournaments: lots of problem solving tournaments where you had to mail in or put you solutions in a dropbox, which was teaching us a clear way of presentation of our thoughts. Students on different levels of understanding participated in different tournaments for extra credit in the school, but there were city, county and statewide tournaments too. The important point here is that the problems were too complex for a test, this is what forced the written presentations into a clear form. (we had good guidelines for them too)

    4) Ideo locator: the “you are here” mark. Constant feedback from teachers, so we always knew how far we are in the curriculum, where we are compared to the other students. Teachers gave personal opinion on our work: good, OK, I expected more. This didn’t have anything to do with the grades. The self image has to reflect the student’s abilities. Especially if the performance level does not match the student’s ability, because for one reason or other he under-performed lately. Teachers did talk to us often, they talked to the parents on monthly basis. ( But they did not have more than 60 students in a semester. )

    5) Success: We got the extra credit from the tournaments. We got partial credit if the written presentation of our solution was clear and logical, and the method was good, even if result was wrong (calculation errors). We got the feedback from the teachers whenever it was possible.

    6) And after this if someone was staring out of the windows, teachers let him be. In junior high the teachers got us into the habit of coaching each other. If someone didn’t listen in class, he just generated a whole lot of work for himself and some of his classmates.

    7) I have to add that teachers had way less workload than they have here in the US, even including afternoon programs that they had to provide. Math teachers had various optional math coaching classes at all levels at least once a week for each level. For the real good students these were really challenging problem solving classes, for the really bad students these were basic problem grinding classes.

    As homework problems go, we had very little compared to what my kids get here in the US.

    This is not something that could be adopted in a single classroom without a deep change to the entire way education is handled in an school district. It also creates a lot of aggravation, and stress among students, so this might not be what you want to aim at. The implementation can not be successful in a school district, because this system is honed to provide for the educators’ professional needs, unlike ISDs it is not an administrators’ paradise.