They Really Get Motivation, Don’t They?

I’m working on a review of the anti-PBL / pro-PBL fracas of 2006 and I just had the wind knocked out of me by this line from Sweller & Cooper in 1985:

It was assumed that motivation, while reading a worked example, would be increased by the knowledge that a similar problem would need to be solved immediately afterwards. (p. 69)

This is their seminal study that establishes (finally!) the best practice for math instruction: I work out an example, then you work out an example from the same family as the first.

The straw man on which they premise their study (which, in turn, has been the premise of two decades of direct instruction advocacy) has to be seen to be believed. Even if I suspend disbelief for a moment, though, here’s the question I can’t find anywhere in the literature on worked examples:

What if you manage to create a perfect system of worked examples, a perfect lecture, a perfectly-wound informational system, and no one cares? What if the perfect lecture provokes students to truancy? What if a year of perfect explanation produces students who don’t want anything to do with math later in life, whether or not they’re proficient in the near term? (Boaler, 1998).

But the cost-benefit analysis of the perfect lecture is left to the teacher. Sweller, Cooper, and their modern-day acolytes totally punt the issue. “We know what works for an eight-question experiment,” they say. “You figure out how to make it work every day for a year.”

Sweller and Cooper don’t fully discount the issue of motivation but their answer – “You’ll be motivated to watch me work out this example because you’ll be doing one in a moment.” – is simply stunning. This is why teachers find it so easy to dismiss researchers.

2011 Mar 14: Sweller and Cooper’s straw man. In this study, the experimental group is taking a test on a problem while looking at an example of the same kind of problem worked out at the top of the page. The control group just takes the test. Unsurprisingly, the experimental group performs better. Surprisingly, Sweller and Cooper take this as evidence against any amount of guidance less direct than their worked examples.

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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. Joe Henderson

    March 14, 2011 - 12:43 pm -

    Kinda like building a straw man out of a study done in 1985?

    Here’s a question for you Dan: how do you square experimental design and cognitive claims with your WCYDWT? Do you expect that whatever you find with the WCYDWT research will be broadly generalizable across and within contexts? Is that one of your assumptions?

    Personally (keep in mind that I’m a qualitative researcher here), I don’t find these epistemological underpinnings compelling for making claims about the messy and irreducible nature of human teaching and learning. But that’s just me. This question is always in the back of my head when I read your blog, and the reason I push on the sociocultural aspect so much.

    My own suspicion is that “teachers dismiss researchers” so much because they often don’t meet them where they are…instead coming over their heads with generalizable claims about what teachers “should” be doing based on the research. Hence my own wariness about claims derived from experimental design. What say you?

  2. Joe: Kinda like building a straw man out of a study done in 1985?

    I admit I’m new to the grad school thing but I didn’t realize these things came with expiration dates, like milk or eggs. Sweller & Cooper was cited sixty times in 2010. Be reasonable.

    Joe: Do you expect that whatever you find with the WCYDWT research will be broadly generalizable across and within contexts? Is that one of your assumptions?

    I’m not at Stanford to study WCYDWT. WCYDWT is one solution to a single problem in math education: real-world relevance. I hope it doesn’t define my work.

    Joe: I don’t find these epistemological underpinnings compelling for making claims about the messy and irreducible nature of human teaching and learning. But that’s just me.

    I get that, and I’m sympathetic to a degree. But, like it or not, this is the playing field on which policy decisions are made and curricula are authored in my discipline. I need to know the game’s rulebook and the playbooks of both teams if I’m going to be of any use here.

    Joe: My own suspicion is that “teachers dismiss researchers” so much because they often don’t meet them where they are…instead coming over their heads with generalizable claims about what teachers “should” be doing based on the research. Hence my own wariness about claims derived from experimental design. What say you?

    Sure. I suppose communication – not pulling rank and coming in over their heads – has a lot to do with it. I may not see the situation as irreducible as you do, though.

  3. Of course, motivation is key to “wanting” to learn anything. But other things being equal, (1) will having good or “perfect” examples facilitate learning? (2) Will they facilitate motivation?

    On #1, Anderson’s ACT-R theory has decades of research showing how good examples facilitate learning. From personal experience, I can learn a software function that may take a hour or more of trying to decipher instructions but only a few seconds of observing someone’s example.

    On #2, from either a flow (Csikszmentmihalyi) or self-determination (Deci & Ryan) perspective, motivation is supported by competence, by activities that challenge without frustrating learners. From this viewpoint, examples support competence, which in turn supports motivation.

  4. Joe Henderson

    March 14, 2011 - 1:31 pm -

    Wow, didn’t realize it was cited that frequently. Good call on your part to critique it then. I’m also with you on the rest of your points. Thanks for the response.

  5. I haven’t been posting about my own stuff lately (bad, I know, I know) but one of the more interesting bits in the TIMSS data set is that teachers answer a questionnaire which includes asking how often students answer problems with no immediately obvious solution (essentially, not following a worked example, forcing students to think it out on their own).

    There was a negative correlation between that and the country’s test score, even when accounting for ‘worst case’ error. Ick. No wonder policy follows the path of least resistance.

  6. I think the issue of “long term” and “short term” is something deserving of all of our attention and critical eyes: Whether it’s a series of amazing individual lessons that amount to nothing in a year. Or a school with high gains in learning year-in-year-out that creates disinterested learners. How do we integrate meaning over time?

    Made me want to share this:
    FFullness of life as minimal unit

  7. @Dan “students who don’t want anything”

    Who’s to say that that WCYDWT problems will help motivate students who willfully fail or willfully choose not to do anything. I argue that even the best designed lesson, regardless of the strategies used, will motivate such students. These students are needing something that the teacher, classroom, or content can give them.

    Furthermore, is it possible that WCYDWT problems are not accessible for ALL students but certainly can be accessible to most students.

    Therefore, isn’t good teaching is to have a toolbox of instructional strategies to meet the needs of all students. Hence, WCYDWT problems become a tool in the box of tricks.

    @Joe “My own suspicion is that “teachers dismiss researchers” so much because they often don’t meet them where they are”

    I often have trouble implementing research because a lot of research is NOT PRACTICAL. I have found that some research, as great as it is on paper, does not work with my group of students. I don’t have the experimental ideal where as many variables are controlled for as possible. Teaching practice is very, very messy. A WCYDWT problem may work today, because the teacher and student variables were aligned enough to allow the problem to work. Tomorrow, I may need to use Direct Instruction. The next day I may need to do something different from the both of these things depending on the conditions. Real teaching seems conditional and there is no one-size-fits all method to teaching. This is where research is disconnected from teachers, in my opinion.

  8. @Michael I agree. I’ve always thought teaching was more like playing in a rock band than running an experiment; success is difficult to define or measure. Like, you can in hindsight point to things that made eg the Beatles famous, but it’s really hard to sit down and say “I’m going to make a world famous rock band” and have it work.

    There are a lot of techniques that amazing teachers I’ve seen have sworn by that, no matter how much I believed they would work, were disasters in my class. And vice versa. It’s weird.

  9. Joe Henderson

    March 14, 2011 - 3:17 pm -

    @Michael. You wrote, “Real teaching seems conditional and there is no one-size-fits all method to teaching.”

    That’s the point I was trying to make regardings the research design in the article that Dan referenced. As a qualitative researcher using anthropological methods, I’m trying to get at something different…the thing you’re mentioning.

    Many researchers (and policy wonks) would disagree with me, but I think it’s really problematic to “control” for cultural variables, and then claim to have an answer about “what works”.

    The really interesting research I see is trying to blend both the experimental with the sociocultural. I’m not sure it can be done, but many are trying. For motivational research, I highly recommend this work:

  10. I am reminded of something else I read:

    “Teaching, closely read, is messy: full of conflict, fragmentations, and ambivalence. These conditions of uncertainty present a problem in a culture that tends to regard conflict as distasteful and that prizes unity, predictability, rational decisiveness, certainty. This is a setup: Teaching
    involves a lot of ‘bad’ stuff, yet teachers are expected to be ‘good.’ ” (McDonald, 1992, p. 21)

    McDonald, J. P. (1992). Teaching: Making sense of an uncertain craft. New York: Teachers College Press.

  11. Clearly these researchers have an antiquated idea of “motivation” and lack knowledge in the many sources of motivation that span the age groups.

    But I have my own opinion of why teachers find it so difficult to take research seriously.

    A. Statistics are: 1. Easy to manipulate 2. Frequently proven erroneous (e.g. New York public school state testing debauchery)

    B. It’s too much work for someone who is just there to get paid, meaning, all present company excluded. Serious teachers try everything, and when it doesn’t work they adapt and try again.

    C. Teachers need to see it to believe it. Model the model. Check out the charter school in NY featured on 60 minutes last night. Great ideas. Poor implementation. Not worth replicating. If I can’t see it. I don’t believe it.

    When researchers are ready to walk into a classroom themselves and show the rest of the teaching population that their theory works indisputably, under ever condition possible, then they will be taken more seriously. But this admittedly difficult to do in a soft science.

    The characteristics of inspiring teaching are in many ways as hard to define as those of our favorite actor and actress…they are just as subjective. Objectively, a great teacher is one that continues pulling every resource they can find in the most flexible and fluid fashion that every student can not help but demonstrate proficiency in the content whether they “like” math or not.

  12. “a review of the anti-PBL / pro-PBL fracas of 2006”

    For those of us who missed that movie, can you tell us where to get it on DVD? (Which is to say… are there a few key references you’d point us to?)

  13. A. Real-world math doesn’t come with examples to follow, as everyone reading here knows. A couple decades ago I worked in unearthing bank fraud and you found it by working around procedures. Hmmm….the way math is taught kinda explains how the hedge fund managers and bankers get away with so much, eh?

    B. Roland Barth now estimates that whereas students used to leave school knowing 75% of what they need for life, they now leave knowing 3%. We have to produce lifelong learners, making true motivation beyond test grades even more essential.

    C. You need a deeper understanding of math to teach flexibly and that is where much of the trouble lies. Most teachers teach how they learn, or how they learned, not out of laziness or inattention to best practices but as clearly shown above by lack of clear research to support change from what is working for them–the evidence that something would work better isn’t all that obvious. But…as a math coach, if I can give them experiences that engage they themselves in other ways of teaching (thanks, Dan, for some of the problems I use!!), they are quick to incorporate it into their teaching.

    D. Deborah Ball’s work on “the particularity of math knowledge” is key here–there’s a great set of slides from her presentation at the 2010 NCSM conference that shows how much knowledge a 4th grade teacher needs to pull off more exploratory methods of teaching. The methods work if you have the knowledge but we keep debating methods rather than examining how to make what is needed in real life math work in a classroom.

  14. Maybe it’s just that I have a really nasty respiratory virus kicking my lungs and head to pieces, but I’m finding some of what I’m reading lately in the comments on this blog truly disturbing.

    One thing that’s always been clear to me from early on in reading what Dan writes is that he isn’t preaching a one-size-fits-all sermon. Rather, he’s sharing HIS practice in a public way and inviting folks to comment, critique (hopefully in a constructive manner) and adopt from what he’s doing that which makes sense for any given teacher. He’s not “selling” a panacea and never has.

    So while I’m all for helpful questions about specific things he’s doing, there’s this recent run of “gee, this won’t work with every kid” and “where’s your gold standard, double blind study to prove that what you’re doing works or is better than teacher-centered, lecture-driven instruction?” commentary that, frankly, gets my blood boiling.

    Here’s a news flash: no classroom teacher is likely to be able to do that sort of study on her/his own practice. It’s damned difficult, in fact, for ANYONE to do that sort of study, and the fact remains that when anything that vaguely looks like a methodologically-sound study is published, the nay-sayers in Direct Instructionland NEVER are satisfied with the results or the methods or the subjects or the fact that the researchers won’t violate standard practice by disclosing names and exact places (which, of course, is against a host of grant and human subjects protocols that guarantee anonymity). In brief, the reality is that NOTHING (and I really do mean nothing) will ever sway a DI (or d.i. – the capital letters refer to the program out of U of Oregon, while the small letters are the generic ‘direct instruction’ in which it’s grounded) advocate from the notions that A) there IS in fact one BEST way to teach ALL people for ALL time in ALL places about ALL subjects; and B) that that way is, of course, Direct Instruction (or direct instruction).

    I’ve seen good folks with excellent materials, methods, or teaching practices turn themselves inside out trying to argue with such people and it is, ultimately, almost always a complete waste of time (if the goal is to change the minds of those people). Once in a Purim, something happens and a Diane Ravitch has a major philosophical epiphany. But then, Diane never worked at University of Oregon as far as I know. Try arguing with, say, Zig Englemann or some of his U of O colleagues on these issues and you will understand in short order what I’m talking about.

    Again, Dan isn’t offering us a miracle cure, which is one of the reasons I trust him (though that’s only the tip of the iceberg as to why I find him so very credible). I despise those who do, and a quick look at anything coming from DI people will give you an education in charlatanism and those who think they can cure every educational and social ill with one inspired method. See, for example, the latest from Professor Englemann:

    If that letter isn’t the work of a huckster, I don’t know what is. And if you can’t see the difference between his mindset and Dan’s, you’re wasting your time reading this blog.

  15. For my part, I have seen traditional teachers change. It is hard but it is all in how you do it. Perhaps researchers would be more successful, if they had degrees in motivation and persuasion as well. :)
    Personally, I think Dan should earn one just for being as motivating a public speaker/writer as he is.

    My experience as a math specialist is that if you take something new and tell a DI teacher to do it, they won’t do it. BUT If you go into their room and do it for them over and over again (they are happy to catch a break from teaching), let them try with your help (they are happy for the in-class support) and in the process show them that the new practice is actually easier and more effective than the old practice…the DI teacher WILL change their practices.

    This is where I believe administrators can adjust their professional development practices. The things that teachers need to learn how to do can’t be taught in a lecture, a professors classroom, or by reading a book or on the internet. Teachers have to see in being successful within their context before they will buy into it. Which makes perfect sense, doesn’t it?

    The climate created by the administration also must make teachers feels comfortable trying something new & failing. Innovation, regardless of success, needs to be celebrated. No teacher wants to take a shot in the dark, only to have it fail and make them look bad.

    The assumption that some teachers can’t change is similar to the assumption that some students can’t learn. The approach & presentation are always key.

  16. I’m not a math teacher, but I follow this blog because I find it one of the best examples of leading with relevance. Meaning, the instruction is based on topics that students can relate to and that are credible.

    What struck me about this post is the idea that worked examples are the solution rather than a tool in a well-stocked toolbox. I see the instructional designer “engineering” a classroom experience or learning event using multiple tools, weaving many forms of motivation (ARCS) into the mix.

  17. Lovely, intelligent words all around. It’s tough to know which way to go with this one: discuss why research is tightly wound and teaching ain’t; or how motivating others to put stuff in their heads is tricky business. I’ll pursue the latter.

    Recently read yet another article about how incentives (cash or otherwise) helped raise standardized test scores. Really? Yep, dollars for points on the SAT works and it is known by more than BF Skinner et al. At least for a semester. Students given the choice between doing a problem that is similar to other problems, or going to lunch consistently choose lunch.

    I taught in a community for years that was openly hostile to education. Nonetheless, I worked along side successful folks who did not give the perfect lecture, and did not follow the research in the field, nor, to my mind, would it have helped who motivated batter than Dale Carnegie.

    Just as your terrific musings share, perfect isn’t good enough, because of the human condition. Research tries to work extraneous variables out the equation. If one teaches middle school math, it’s variables all the way down.

    I saw teachers in the trenches who understood motivation deeply. They were drawing evidence-based conclusions all day for 20 years, with countless variables, where n=150 per semester. Yeah, motivation counts, while, sadly, research often does not.

  18. ” … how often students answer problems with no immediately obvious solution (essentially, not following a worked example, forcing students to think it out on their own).

    There was a negative correlation between that and the country’s test score, even when accounting for ‘worst case’ error. Ick. No wonder policy follows the path of least resistance.”

    It is good test-taking strategy to answer the obvious problems first. Perhaps in the countries with low test scores, the students are incapable of distinguishing between the easy problems and the hard ones, and so are more likely to attempt the hard ones. The question should also look at how often they get the hard problems right when they attempt them. Random flailing is not a laudable goal, even if risk taking is valued.

  19. I saw this post a bit late, I was catching up on blog posts over spring break.

    As I read your post I was caught off guard by the authors of the article, Sweller and Cooper. I was caught off guard as I much of my graduate research (in physics education) was based on some of Sweller’s work. After some deep belly-breathing, I remembered that I often had my own conflicts with Sweller, both in what he said and the general lab rat style of educational research. In particular I remember an article talking about the failure of inquiry based learning…

    (pdf) –>

    My advisor had to talk me down after reading that article. I felt as if the rug had been pulled out from under me.

    However, much of what I read from Sweller is certainly compatible with your approach and my own general lean towards inquiry. I was often in awe or at least disbelief in the general willingness of researchers in general to leap to conclusions based on 10 or 20 paid volunteers.

    My research was designed around taking some of the ideas from Cognitive Load Theory (John Sweller, being a key player there) and applying it to a large classroom (200+ college students) over a longer period of time (half a semester). Unfortunately, I was only in for the junior graduate degree (masters) and didn’t get a chance to refine and repeat. We saw potentially great results (nearly 7-8% improvement, almost a letter grade!) but still nowhere near lab quality results…

    This year I successfully brought in “completion problems” into my physics classroom. (I have not tried them with math. Which might be a different beast.) The ability for my students to solve problems, traditional and no so much so, seems to be greatly improved, but it is a different group of kids…

  20. Jeremy: However, much of what I read from Sweller is certainly compatible with your approach and my own general lean towards inquiry.

    Thanks. I doubt Sweller would agree, though. Two of his titles from the last five years:

    Why Minimal Guidance during Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching

    And in case you’re wondering if that paper is too general to apply to math education in particular:

    Teaching General Problem-Solving Skills Is Not a Substitute for, or a Viable Addition to, Teaching Mathematics

    They’re very clear that if it’s anything less explicit than worked examples, it isn’t good learning.

  21. Hey Dan,
    Long time fan, first time poster.
    These last few years, I have been working on increasing motivation in my classroom and I have stumbled on a few things I thought I would share. Most of the things I have been testing out in my room have come from Daniel Pink’s book Drive. In it he discusses the different motivations used in some businesses (bonuses, money, power, etc) to other groups that promote autonomy, mastery, and clarity of purpose as motivating factors. He states that rewards based incentives (carrot and stick style) are good for tasks that have a clear reactionary out come: if I do this, then I will achieve this. But once the task becomes less clear, or there is no guarantee of success, the rewards based incentives become a hindrance. This seems to hold true in my Math class and the topic you are describing here. If a student is given a series of examples that they know will lead them to success and that there is only slight variations, then they will find some amount of motivation to continue. The motivation is usually based on the student’s feeling or belief of possible success. However, when the student is given a problem that may not have a clear solution or a problem with less guidance on how to find an answer, the motivation changes. Autonomy, mastery, and a clear purpose become the motivators.
    Autonomy is the desire we all have for freedom. How often do students get presented with problems where they have to find the length of something using math and the student says to themselves, “I would just measure the other side”. The problem not only becomes less interesting to them, but it also offends this idea of autonomy. The problem is telling you, you can’t measure the other side. If enough of these offenses exist for a student, then they will become disinterested. So, this hatred for math is actually a hatred for static problems that aren’t interesting. There is no challenge to their creative side. Students aren’t allowed to use the tools which they have become accustomed to using, to solve the problem.
    Mastery is the innate desire we have to be good or competent at a task. Pink talks about hobbies and the like. Things humans do to not make money, but to feed their desire to improve and become better at something. This is where Sweller and Cooper may have gotten their simplistic idea that people shown examples will be motivated even more if they know they will be asked to solve a similar problem afterwards. The true motivation is to do well at something, which explains why students actively oppose the act of learning. Usually there is a history of failure that needs to be overcome. Those students that show themselves as apathetic learners are usually that way because they don’t believe they can accomplish it and the pain of being reminded of their failure is too much. So, it becomes easier for the student to fall back on the showing of apathy. This allows them to say, they are smart enough to do the problem, but they don’t want to. This is a defense mechanism that helps the students externalize their feelings of failure.
    Clarity of purpose is the end purpose to the process. Why do I want to solve this problem? Why do I want to learn about Math? There needs to be a purpose there that a student can believe in. For example, I am obsessed with photography. My passion for it extends beyond the word hobby. The initial purpose for me to improve my photography skills were to improve the pictures that I would be leaving behind for my children and their children. Now my purpose has moved beyond this one, but I hope the point is clear. Without my purpose, I wouldn’t have pursued further understanding of the concepts and art of photography.
    Now, how this relates to your comments. The problems that you propose to your classes allow students to honor their autonomy, promotes their own purpose (to solve a real problem, become a better problem solver, etc), and allows for a students desire of mastery. Giving students example after example followed by their own attempts to solve problems can still be motivating to students, but how useful is it to them? This style is easier for some students, but not as fulfilling for most students. It is like comparing a job in a factory on an assembly line to a job at a tech firm charged with improving user experience. One of them has a definite if/then nature to it and the other is more open ended and challenges creativity. In my own education the things that have stuck with me the most have been of an inquiry nature. They were labs in science, assignments that left me with the autonomy and creativity to decide how they would be presented, and open ended research and discussions of topics.

  22. I’m really sympathetic with this line of criticism of Sweller. He also assumes a definition of math that is incredibly limited, i.e. the ability to solve problems.

    For all the noise about whether inquiry is the best way to learn how to answer mathematical questions, does anyone deny that problem-solving is the best way to learn mathematical problem-solving?

    Wouldn’t the worked-examples/practice model, when applied to learning how to solve new problems, involve receiving an explicit model of how to solve a new problem and then being given the chance to engage in lots of genuine problem-solving?

    And don’t the CCSS require that kids learn how to solve new problems?

  23. The CCSS implicitly assesses on “the ability to solve problems absent previous worked examples.” Teaching that through worked examples seems self-defeating.

    I suppose it’s no surprise I agree with you here. But catch this exchange with commenter Kevin H. He has a good command of the research and seems every ounce a reasonable broker of these ideas. I’ll ping him on this thread and see if he wants to weigh in.

    (Even setting aside problem solving, how many worked examples comprise “Algebra 1”? I read a paper that quoted 97, though the citation eludes me. 97 worked examples times 3 instances of each example times 20 practice problems. My word.)

  24. Jeremy and Dan, typing with one hand while holding baby in other, so sorry for typos. Here goes. Citations linked at end if this post.

    While people tend to debate which is better, inquiry learning or direct instruction, the research says sometimes it’s one and sometimes the other. A recent meta study found that inquiry is on average better, but only when “enhanced” to provide students with assistance [1]. Worked examples actually can be one such form if assistance (e.g., showing examples and prompting students for explanations of why each step was taken).

    One difficulty with just discussing this topics that people tend to disagree about what constitutes inquiry-based learning. I heard David Klahr, a main researcher in this field, speak at a conference once, and he said lots of people considered his “direct instruction” conditions to be inquiry. He wished he had just labelled his conditions as Condition 1, 2, and 3 because it would have avoided lots of controversy.

    Here’s where Cognitive Load Theory comes in: effectiveness with inquiry (minimal guidance) depends in the net impact of at least 3 competing factors: (a) motivation, (b) the generation effect, and (c) working memory limitations. Regarding (a), Dan often makes the good point that if teachers use worked examples in a boring way, learning will be poor even if students cognitive needs are being met very well.

    The generation effect says that you remember better the facts, names, rules, etc that you are asked to come up with on your own. It can be very difficult to control for this effect in a study, mainly because its always possible that if you let students come up with their own explanations in one group while providing explanations to a control group, the groups will be exposed to different explanations, and then you’re testing the quality of the explanations and not the generation effect itself. However, a pretty brilliant (in my opinion) study controlled forvthis and verified the effect [2]. We need more studies to confirm. Here is a really portent paragraph from the second page of the paper: “Because examples are often addressed in Cognitive Load Theory (Paas, Renkl, & Sweller, 2003), it is worth a moment to discuss the theory’s predictions. The theory defines three types of cognitive load: intrinsic cognitive load is due to the content itself; extraneous cognitive load is due to the instruction and harms learning; germane cognitive load is due to the instruction and helps learning. Renkl and Atkinson (2003) note that self-explaining increases measurable cognitive load and also increases learning, so it must be a source of germane cognitive load. This is consistent with both of our hypotheses. The Coverage hypothesis suggests that the students are attending to more content, and this extra content increases both load and learning. The Generation hypothesis suggests that load and learning are higher when generating content than when comprehending it. In short, Cognitive Load Theory is consistent with both hypotheses and does not help us discriminate between them.”

    I will continue in a separate post below..don’t want to lose what I wrote so far.



  25. OK, diaper changed.

    Factor (c) is working memory load. The main idea is found in this quote from the Sweller paper Dan linked to above, Why Minimal Instruction During Instruction Does Not Work [3]: “Inquiry-based instruction requires the learner to search a problem space for problem-relevant information. All problem-based searching makes heavy demands on working memory. Furthermore, that working memory load does not contribute to the accumulation of knowledge in long-term memory because while working memory is being used to search for problem solutions, it is not available and cannot be used to learn.” The key here is that when your working memory is being used to figure something out, it’s not actually being used to to LEARN it. Even after figuring it out, the student may not be quite sure what they figured out and may not be able to repeat it.

    Does this mean asking students to figure stuff out for themselves is a bad idea? No. But it does mean you have to pay attention to working memory limitations by giving students lots of drill practice applying a concept right after they discover it. If you don’t give the drill practice after inquiry, students do WORSE than if you just provided direct instruction. If you do provide the drill practice, they do better than with direct instruction. This is not a firmly-established result in the literature, but it’s what the data seems to show right now. I’ve linked below to a classroom study [4] and a really rigorously-controlled lab study study [5] showing this. They’re both pretty fascinating reads… though the “methods” section of [5] can be a little tedious, the first and last parts are pretty cool. The title of [5] sums it up: “Practice Enables Successful Learning Under Minimal Guidance.” The draft version of that paper was actually subtitled “Drill and kill makes discovery learning a success”!

    As I mentioned in the other thread Dan linked to, worked examples have been shown in year-long classroom studies to speed up student learning dramatically. See the section called “Recent Research on Worked Examples in Tutored Problem Solving” in [6]. This result is not provisional, but is one of the best-established results in the learning sciences.

    So, in summary, the answer to whether to use inquiry learning is not “yes” or “no”, and people shouldn’t divide into camps based on ideology. Still unanswered question is the question when to be “less helpful” as Dan’s motto says and when to be more helpful.

    One of the best researchers in the area is Ken Koedinger, who calls this the Assistance Dilemma and discusses it in this article [7]. His synthesis of his and others’ work on the question seems to say that more complex concepts benefit from inquiry-type methods, but simple rules and skills are better learned from direct instruction [8]. See especially the chart on p. 780 of [8]. There may also be an expertise reversal effect in which support that benefits novice learners of a skill actually ends up being detrimental for students with greater proficiency in that skill.

    Okay, before I go, one caveat: I’m just a math teacher in Northern Virginia, so while I follow this literature avidly, I’m not as expert as an actual scientist in this field. Perhaps we could invite some real experts to chime in?








  26. Thanks a mil, Kevin. While we’re digesting this, if you get a free second, I’d appreciate hearing how your understanding of this CLT research informs your teaching.

  27. The short version is that CLT research has made me faster in teaching skills, because cognitive principles like worked examples, spacing, and the testing effect do work. For a summary of the principles, see this:

    But it’s also made me persistent in trying 3-Acts and other creative methods, because it gives me more levers to adjust if students seem engaged but the learning doesn’t seem to “stick”.

    Here’s a depressing example from my own classroom:
    2 years ago I was videotaping my lessons for my masters thesis on Accountable Talk, a discourse technique. I needed to kick off the topic of inverse functions, and I thought I had a good plan. I wrote down the formula A = s^2 for the area of a square and asked students what the “inverse” of that might mean (just intuitively, before we had actually defined what an inverse function is). Student opinions converged on the S = SqRt(A). I had a few students summarize and paraphrase, making sure they specifically hit on the concept of switching input and output, and everyone seemed to be on board. We even did an analogous problem on whiteboards, which most students got correct. Then I switched the representations and drew the point (2, 4) point on a coordinate plane. I said, “This is a function. What would its inverse be?” I expected it to be easy, but it was surprisingly difficult. Most students thought it would be (-2, -4) or (2, -4), because inverse meant ‘opposite’. Eventually a student, James (not his real name), explained that it would be (4, 2) because that represents switching inputs and outputs. Eventually everyone agreed. Multiple students paraphrased and summarized, and I thought things were good.

    Class ended, but I felt good. The next class, I put up an similar problem to restart the conversation. If a function is given by the point (3, 7), what’s the inverse of that function? Dead silence for a while. Then one student (the top student in the class) piped up: “I don’t remember the answer, but I remember that this is where James ‘schooled’ us last class.” Watching the video of that as I wrote up my thesis was pretty tough.

    But at least I had something to fall back on. I decided it was a case of too much cognitive load–they were processing the first discussion as we were having it, but they didn’t have the additional working memory needed to consolidate it. If I had attended to cognitive needs better, the question about (2, 4) would have been easier, and I should NOT have switched representations from equations to points until it seemed like the switch would be a piece of cake.

    I also think knowing the CLT research has made me realize how much more work I need to do to spiral in my classrrom.