Constructivism and the Khan Academy

Not long after sitting down at my computer this morning, there was this tweet from David Wees:
“How would you explain constructivism to someone not (well) versed in pedagogy? You have 140 characters. #edchat #BCed”
I took David’s challenge and what followed was a pretty good conversation with David Cox, Ira Socol, and Jennifer Borgioli. For the sake of clarity, yet with an attempt at brevity, I thought a follow-up post would be good here. My goal is to share the kind of knowledge that David asked for -- a short explanation for someone who might be new or unclear about these ideas -- so please excuse me if I don’t touch on some of the nuanced bits (and there are many, trust me!) of the theory.

Before we talk about learning theory, we should take a step back and talk about epistemology - the branch of philosophy concerned with the nature of knowledge. There are multiple epistemologies, but two are important here.

Objectivism: An objectivist epistemology holds that knowledge and meaning exists independently of the learner. It is not just believing that “a rock would be a rock if we were here or not.” Instead, it is a belief that the rock carries some meaning of what it is to be a rock, and when we study rocks we are discovering that meaning. Objectivism is sometimes called empiricism or externalism.

Constructivism: A constructivist epistemology holds that there is no objective knowledge. This doesn’t mean that there aren’t objects, but that the knowledge and meaning we associate with objects is constructed by us as we engage and interact with the world. Constructivism can take several different forms, depending on the importance placed on social and historical interactions.

Hopefully you can already see how different epistemologies can affect a person’s view of teaching and learning. Now let’s compare three learning theories associated with these epistemologies.

Behaviorism: Behaviorist learning theory is often associated with an objectivist epistemology. Human actions, including exhibitions of our knowledge, are viewed as behaviors that respond to a stimulus. The process begins with a transmission of knowledge from the teacher (which can be a non-human source of knowledge) to the student. If the response is the expected behavior, the student is rewarded. If the response is not the expected behavior, the student is punished. By stimulating the student with rewards and punishments, the teacher encourages the student to receive the transmissions of knowledge.

Information Processing: IP theory still applies an objectivist epistemology, but differs from behaviorism in that learning is seen as an inner cognitive process and not just a response to a stimulus. The brain is seen roughly as analogous to a computer -- it has memory and processing systems that serve to store and analyze information, although the analogy doesn't extend to understanding exactly how those systems actually work. Application of this theory in teaching generally involves heavy doses of repetition to ensure that knowledge is retained in memory.

Constructivism: Not surprisingly, constructivist learning theory is associated with a constructivist epistemology. Because knowledge is constructed by the learner, the teaching/learning process focuses on creating conditions for that construction to happen. There is no "transmission" of knowledge. Depending on the form of constructivism, the teacher might facilitate the construction of knowledge through the inclusion of contexts and social interaction.

The science of education would be much easier if we could prove that some theories never work and one works all the time. But we can’t. However, I don’t know of an educational psychologist that doesn’t think constructivist learning theory (in at least one of its variants) works better than those based on an objectivist epistemology. So why doesn’t every teacher do it? Or do it well? Teachers in classrooms have resource, time, and other constraints that makes constructivism more difficult than we all wished it was. Also, it’s not always clear cut which theory is being applied by a teacher. Suppose you were to peek into a classroom and see a teacher speaking to the entire class. Maybe the teacher is trying to transmit knowledge in a behaviorist/IP way. Maybe the teacher is trying to help students get into a certain frame of mind and is a constructivist. You can’t tell at a glance because the learning theories don’t always present themselves as extreme opposite ends of the spectrum. But when there’s controversy, we like to pretend that they do. Enter Salman Khan.

There’s been a lot written about Sal Khan and the Khan Academy over the past several months, including a recent article in Wired Magazine that became a large part of this morning’s discussion on Twitter. The idea of learning by watching videos isn’t necessarily behaviorist or solely an application of information processing theory, but it’s more easily seen as a medium for the transmission of knowledge, not construction, and the point-keeping for problems right and wrong also fits the stimulus/response model. Phrases such as "Khan and Gates both admit there’s no easy way to automate the teaching of writing" also point at behaviorism and IP. (There’s an underlying assumption here that if teaching can be automated, learning will be automated.) The Wired article quotes parents and teachers who are amazed at the progress their kids are making, measured by problems completed, modules finished, and badges earned. Are those students learning? Of course they are, but exactly what they are learning and how well they understand it is at the core of the debate.

Behaviorism and information processing aren't mentioned by name in the article. Perhaps they don't need to be; it’s a style of education that most all of us are familiar with and perhaps it doesn’t need much explaining. Constructivists are named as Khan’s critics, and the theory is described using terms such as "play around" and "fumbling around," the latter of which was probably an unfortunate choice of words by a constructivism supporter. Saying that "it’s better to give kids activities that let them discover the principles of math and physics on their own" doesn’t give enough credit to teachers in good constructivist learning environments. When done well, teachers don’t just "give" activities and students aren’t "on their own." Instead, there’s a careful orchestration going on and the teacher is with the students 100% of the way, asking questions, providing feedback, provoking the student to look at tasks in ways that help students construct deep understandings. Can a video do this? Obviously there are severe limitations -- not limitations that prevent all learning, but limitations that might be preventing the best kind of learning.

Look for an upcoming post about what happens when the instruction is based on objectivism but the student, a kid we'll call "Benny," constructs knowledge in his own, incorrect way. The "Benny" paper by Stanley Erlwanger in 1973 had huge ramifications for research and teaching in mathematics education, and has interesting parallels to learning via the Khan Academy.

I'd like to give great thanks to Jackie Hotchkiss for helping review a draft of this post. (Any final shortcomings are solely mine, of course.) When in doubt, talk to an educational psychologist!


  1. Really interesting post - I have done a lot of work recently on constructivism, this has been extremely helpful. Thank you

  2. "I don’t know of an educational psychologist that doesn’t think constructivist learning theory (in at least one of its variants) works better than those based on an objectivist epistemology."...

    I think the key word here is "works". Depending on the outcome, all of these theories probably "work", they just produce different outcomes. For example, if your goal is to be able to shift gears in a manual transmission car, then information processing theory would suggest that you first have to think about every single action, and through practice, the individual actions become automatic. This is the value of "repetitive practice" -- through practice, we automaticize particular sequences of actions. Information processign theory calls this type of knowledge "procedural knowledge", and if your goal is to gain automaticity in a particular procedure, then information processing theory "works".

    However, if your goal is to _understand_ how a transmission works, or to be able to _create_ a new type of transmission, then simply automaticizing the practice of shifting gears in a manual transmission is probably not going to get you there. This type of knowledge might be called "conceptual" knowledge, and is probably better acquired through constructivism.

    In other words, I would argue that we first have to consider the _type_ of knowledge that we want students to have before we make pedagogical decisions, or discuss what "works". Furthermore, we have to understand that all types of knowledge -- declarative, procedural, and conceptual -- are important for students, and hence, there is probably not one particular pedagogy that will "work" in every situation.

    This is why Realistic Mathematics Education is so appealing to me. It's a mostly constructivist theory whose overarching goal is for students to understand mathematical concepts (well, the real goal is for students to constantly be engaged in _doing_mathematics -- that is, mathematizing). But it doesn't ignore the value in algorithmic skill, or the importance of practice in acquiring such skill. There is a time for discovery, a time for construction, and a time for practice.

  3. Regarding my comment above, and the Khan academy, this comment by Keith Devlin is apropos:

    "I may not have K-12 classroom experience, but I've done enough math teaching in my life to know that good teaching is a matter of helping students figure it out for themselves. This, incidentally, is why Kahn Academy (which I have endorsed elsewhere and will continue to do so) does not teach anyone how to do math (i.e., how to think mathematically), any more than a dictionary, thesaurus, and grammar book can teach someone how to write a novel. What Salman Kahn does is provide an excellent instructional resource for some of the tools you need to do math. A particularly gifted and motivated individual could likely use it to learn mathematics on their own, particularly if they had access to a mathematician who could assist them when they are stuck. Thank you for doing that, Sal. Your site is valuable, and you deserve all the attention it has garnered. The danger I see in all the media coverage of late is if people think that the provision of a tool that can play a part in improving the nation's mathematical abilities is actually the entire solution. (As far as I am aware - and I have met Sal a few times and we have talked about his material - he himself has not claimed that, though others seem to have come close.)"

  4. Fred: I hadn't seen that comment by Devlin, but I think it's spot on. I certainly think there's room for enthusiasm about the Khan Academy, but perhaps we ought to stick with "bridled" instead of "unbridled" enthusiasm. For example, I saw a commenter (I'll spare the writer the citation, but I did notice that he worked at a university) write that Khan Academy was so incredible that he "shed a tear" and declared it "the logical conclusion in the evolution of education." That kind of reaction bothers me, and I wouldn't doubt that it bothers Sal Khan, too.

    And you're totally right to call me out on my "I don't know of an educational psychologist..." line. I wasn't quite comfortable with the words I had chosen there, and thanks for providing a comment that addressed the issue far better than I did.

  5. Heh, I didn't mean to "call you out", I just wanted to continue the discussion. :)

    As always, the question is, "what is mathematics?" The hook for the Wired article involves a fifth-grader who have gotten 649 inverse trig problems correct. So this student has certainly acquired some mathematical skill -- in fact, far more mathematical skill than many student who graduate from high school, and that is something to be commended. But is this mathematics?

    What we don't know is whether this student understands trigonometry in the multi-dimensional way described by Wiggins and McTighe. Of course, we might ask, is this "mathematics"?

    Or we might take Freduenthal's view that "Mathematics should be thought of as the human activity of mathematizing – not as a discipline of structures to be transmitted, discovered, or even constructed, but as schematizing, structuring, and modeling the world mathematically." (I think this is similar to what Keith Devlin would call "everyday math") In this cae, the student above is almost certainly not doing mathematics, as the Khan Academy offers very little (or perhaps no) opportunity to "schematize, structure, and model the world mathematically."

    For me, what is scary about the Khan Academy is that it propagates the common notion that math is just a bunch of skills. Those of us who believe that skills are just a tiny (but vital) piece of mathematics, (or, more precisely, that skills are (vital) tools that can enable mathematics), the Khan Academy can be a valuable resource. But too may people lack this nuanced view, and, scarily, these seem to be the people in positions of power.