December 13, 2007

Downes on Kirschner

Over at his Half and Hour blog, Stephen Downes has posted a speech he gave recently criticising Kirschner, Sweller, and Clark’s paper entitled, Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry based teaching.

Downes begins the speech by telling us that he believes in connectionism. He describes what it is and describes how one teaches in a connectionist manner. Oddly enough, I agreed with much of what Downes was saying and thought that much of it was complementary to the theories set forth in Kirschner, rather than opposed to Kirschner as Downes seems to think.

Basically, Downes believes that knowledge and learning can be explained by using network principles, specifically by understanding how connections are formed in the brain network. Knowledge means having a certain organization of neural connectivity such that you can recognize certain patterns in the environment.

This seems to be neither controversial or in apposition to Kirschner. Knowing something means being able to quickly recognize and retrieve it from your long term memory in response to some stimulus. And pattern recognition seems to play same role here.

Then Downes states that learning is not having things pushed into your head but growing and developing in a certain way such that you recognize certain patterns. If by this Downes means that teachers cannot induce learning, I would disagree. The literature is replete with experiments showing that learning can be accelerated by the use of good teaching. See for example, the famous chicken sexing experiment in which the patterns of recognizing the sex of newborn chickens was greatly accelerated by use of summary sheet prepared by an expert chicken sexer. In this case, knowledge was certainly pushed into the student's head quicker than having the student sit in an authentic environment at the foot of the expert learning by observation.

Perhaps, Downes mispoke or I am interpreting what he said incorrectly. I just don't think this statement follows from what he stated previously or what he states afterwards.

In any event, Downes next defines learning and teaching. According to Downes, to teach is to model and to demonstrate, to present experiences so people can form these connections in their mind. To learn is to form these connections by practice and repetition and by reflecting on that practice. I agree with this, even though I disagree with Downes next statement that learning is best done by participating in an authentic community of practice. It does not follow from Downes' definition of learning that an "authentic community of practice" is needed to form the desired neural connections. I might be able to learn physics the long and hard way by conducting thousands of experiments like the great discoverers did, but it's much quicker and easier to learn the same things by reading a physics textbook prepared by an expert in physics.

All of this occurs in the first seven minutes or so. Downes spends the remaining forty minutes of his speech criticizing the Kirschner paper. Downes seems to think that the connectionist theory conflicts with Kirschner and instructivist learning. And seems to favor constructionism, problem based learning, discovery learning, and the like.

In my opinion, much of this time is spent parsing Kirschner's language, erecting a few strawmen (which he curiously doesn't knoock down), and manufacturing a conflict with Kirschner when in fact his theory is complementary with Kirschner's. For example, Downes characterizes Kirschner's position as being that non-instructivist teaching results in no learning. This is a strawman. The standard position is that non-instructivist teaching often results in less efficient learning, the probability is increased that incorrect learning occurs, and it favors those with more background knowledge. These are the standard criticisms and Downes does nothing to refute them, choosing instead to attack a strawman.

Let's examine some of these issues using Downes' definition of teaching and learning.

Downes defines teaching and learning as modeling/demonstrating coupled with doing/practice so that proper connections can form in the student's brain. Downes leaves out the feedback loop, testing, which is needed so that the teacher can make sure the student has actually learned correctly from the demonstration/model presented. Let's add it back in. The full blown schematic goes something like this: model, (lead), do, test, practice, delayed test. The lead step is optional and depends on the amount of guidance needed by the student. The delayed test is for determining if the learning has made it to long term memory. Oddly enough, this is the procedure they use for Direct Instruction, a pedagogy I'm sure Downes is four-square opposed to, yet which oddly enough is fully in accord with his definition of teaching and learning.

Looked at this way, learning comprises a presentation of a demonstration/model, the student attempts to replicate the model/demonstrate with or without a teacher's leading, the teacher tests to see if the student can successfully perform and has understood the presentation, the student then practices the demonstration, after a period of time the teacher again tests the student to see if the student can perform what was taught.

Learning is greatly dependent on the quality of the demonstration/model. The problem with most teacher presentations, as I pointed out here, is that they are usually fraught with ambiguities. Let's use the ambiguous glerm example. Some students will walk away from the demonstration thinking that glerm means rectangle or purple, instead of vertical, and may labor under that impression for quite some time. Using Downes connectionist theory we know that this student's brain is going to connect itself up so that the pattern for glerm is associated with purple or rectangle, all of which will have to be undone when the student finally learns that glerm means vertical. We also know that it takes many more repetitions to learn something that has been mistaught than it takes to learn something new.

Another problem is the misunderstanding of instructivist teaching as comprising mostly rote learning, learning devoid of understanding. Almost no one teaches anything by rote. The reason is that rote teaching is inefficient because rote learning doesn't generalize well. For example, one can teach addition by rote by asking the student to memorize all the addition facts, such as 1+ 1 = 2, 1+2 = 3, 1+3 = 4, ad infinitum. Using Downes' lingo, in order to learn these addition facts by rote, the student learns to recognize that the pattern 1+1 is 2 and that the pattern 1+ 2 is 3. This is inefficient because unless the student has been taught the pattern 1+3 he does not necessarily know that the pattern matches with 4. In contrast, it is more efficient to teach addition by teaching the general rule that to perform addition you need to start with the first number and count up by the second number. This is not rote learning and it is much more efficient. The student seeing the pattern 1+2 will connect it to the more general pattern number + number means perform the addition procedure. This is more efficient because the teacher does not have to teach every addition fact because the student has a basis for recognizing a pattern which leads to a generalized rule that works with all problems in the form number + number.

Constructivist pedagogy merely differs from the instructivist pedagogy in that the constructivists set up an environment in which it is hoped that the student discovers the general rule on his own with as little guidance by the teacher as needed. So, the teacher might show the student that 1+1 =2, 2+1=3, 3+1=4 in the hope that the student recognizes that adding one to a number means to count to the next higher number and eventually that adding any number to a number means starting from the first number and counting by the second number, which is the general rule. The theory is that the student, having discovered the rule for himself, will understand the rule better and be able to remember the rule better which means in Downes' terminology that he will be able to recognize the pattern better. There is some support in the literature for this effect. And, if all students always learned exactly what we wanted them the first time, this might be a more effective teaching technique.

But it's not. And the reason why it is not is because many students will not learn or discover the first time around as they try to discover the right pattern. What the students do is experiment by testing their known patterns to see if they fit. And, unfortunately, the students tend to learn these wrong solutions about as well as the right ones until the right solution acquires some dominance acquired through practice. And there's less time for practice what with all this discovery going on. Then there is the risk that the student hasn't learned the most efficient pattern, but one that happens to work with the environment at hand.

There is also the issue of the feedback loop, i.e., how does the teacher correct student errors when they fail to learn. This is also a pattern recognition problem; however, this time it is the teacher who needs to recognize the right pattern so the right remedy can be employed. This is difficult enough when the teacher has directly taught the rule to the student and there is some basis for knowing what the student has failed to grasp. But, imagine the difficulties for the teacher when the learning is occurring in a more information rich environment in which there are more variables to attend to.

I could go on, but this post is getting way too long. My point is that learning and teaching is a complex endeavor that isn't fully explained by Kirschner's or Downes' theories and that the theories are, my opinion, are more complementary than in conflict as Downes attempts to paint in his speech. For example, Downes ridicules Kirschner's brain model as being a flat store of data and procedures which gets searched sequentially. And offers, that the brain is more a neural network that searches for patterns, more of a relational database, if you will. More likely, the brain is more a network/schemata arranged according to patterns and containing lots of facts and procedures, and other knowledge that make up those patterns.

Lastly, even if we are to accep Downes' model, I still do not think that the model favors a constructivist/discovery learning paradigm as opposed to a instructivist paradigm. This confuses a theory of knowing for a theory of learning that I do not think is supported by the available evidence and ignores many real problems typically encounter in the learning process, some of which I've listed above.

Nonetheless, I think Downes's speech contributes to the discussion. I certainly learned something or at least it's lead to a better understanding. But, I'm not exactly an novice in this area.

4 comments:

Downes said...

Interesting and useful discussion. Some comments:

We need to be really careful about how we describe the contents of memory.

There is a tendency to think of mental contents as resembling objects. Things that look like sentences, say, and that can be stored and retrieved, like data in a database.

But when I say (to cite your summary) "Knowledge means having a certain organization of neural connectivity such that you can recognize certain patterns in the environment" it is important to see that the *organization* constitutes the knowledge, and there are no 'objects' that are stored or retrieved.

When we contrast that with Kirsher's view (again using your summary), "Knowing something means being able to quickly recognize and retrieve it from your long term memory in response to some stimulus," you can see that there is a significant contrast between the two positions.

This makes a significant difference in how one views instruction and learning.

Let me elaborate. You write:

"Then Downes states that learning is not having things pushed into your head but growing and developing in a certain way such that you recognize certain patterns. If by this Downes means that teachers cannot induce learning, I would disagree."

The choice of the phrase 'induce learning' is very precise and no doubt deliberate. It made me think at once of induction coils, which offers a useful analogy to illustrate my point.

For those unfamiliar with electricty, 'induction' is the generation of an electric current in a conductor by passing it through a magnetic field. Such a field can be produced by a coiled conductor. See the picture here: http://micro.magnet.fsu.edu/electromag/java/faraday/

Now the important thing here is that the electrons in the first coil never enter the second coil. The production of the current is entirely via the magnetic field. The first coil *induces* electrical current, but does not push electrons (or anything else) into the other wire.

Now there are obvious differences between human memory and magnetic induction, but you can see here that I can show how a teacher could 'induce' learning without actually 'pushing' facts into their memories. And, indeed, teaching is like induction.

What this illustrates is how you can't just 'produce' learning in a student, no more than you can induce conduction in a non-conductor. And learning in the student isn't something the student 'received' from the teacher, but rather, a new alignment into which the student shaped him or her self as a result of the teacher's influence.

This view is very different from what Kirshner appears to think about learning, based on his examples and phraseology. When Kirshner talks about 'search' and 'retrieval', he is very clearly employing a 'knowledge as object' perspective, one that is quite misleading.

What is also worth noting is that the 'induction' effect (to give it a hand name) is not unique to teaching. Thus, when you say "the literature is replete with experiments showing that learning can be accelerated by the use of good teaching" there is no reason to disagree - since it is obviously true - but to point out that the *explanation* of this phenomenon may be unclear.

Students learn through exposure to perceptual phenomena (there is, indeed, no other way), and teachers are but one source of perceptual phenomena. Students can learn from nature, other students, reading - a wide variety of phenomena. What is important, of course, is how the experience is shaped (much in the way the magnetic field is shaped) and what sort of influence it has - determined as much by the nature of the student. You cannot create a current in a non-conductor, for example.

So, to be precise: teachers do not implant knowledge in their students. They, a best, induce it. And this process of induction depends as much, if not more, on the nature of the student, as on the nature of the influence.

To turn to a different subject, you write, "It does not follow from Downes' definition of learning that an "authentic community of practice" is needed to form the desired neural connections."

Quite so. I would not say that an authentic learning community is necessary in all cases. Nor would I say that it is sufficient in all cases. The question is rather framed around the question of how best to create, shall we say, the most conducive (conductive?) environment.

A teacher is bt one element in an environment. Like it or not, a student's peers, his or her parents and pets, the walls of the buildings, local media including internet connections, and the rest, all form a part of that environment. If this environment is consistent and conduicive to a certain type of learning, then this type of learning is more like to occur (depending, as always, on the nature of the student).

(By 'nature of the student' I am not referring to the student's innate properties, but rather, to the current constitution of the students - his or her health, thoughts, prior beliefs, and more).

You write, "I might be able to learn physics the long and hard way by conducting thousands of experiments like the great discovers did, but its much quicker and easier to learn the same things by reading a physics textbook prepared by an expert in physics."

Quite so. But could you learn to become a physicist without interacting with a community of physics?

Knowing 'physics' isn't just the accumulation of a set of facts. It is, again, to be shaped a certain way - 'knowledge', as instantiated by a series of connections, is not just the set of facts, but also the way of thinking, the way of acting, way of evaluating. It's very hard to do without relevant experience of people who think and act and value things in that way.

None of this says that someone *cannot* learn outside the community. You can get a sense by reading - much of my own background in the sciences comes from reading science fiction, and Kim Stanley Robinson's recent 'Forty Days' series illustrates the way the thought processes of the scientific mind. But, all things being equal, immersion and direct experience are more likely to induce the expected learning than reading or telling.

Finally, "All of this occurs in the first seven minutes or so."

Quite so. It is important to note that in this talk I offer only a short summary of connectivism.

Now, on to perceptions, "Downes seems to think that the connectionist theory conflicts with Kirschner and instructivist learning."

I need to be clear here, it is kirshner who is finding the conflict. Kirshner is very clear in his paper that his theory shows that all the other theories - disovery based learning. inquiry learning, constructiveism - fail (in fact, that's the *title* of his paper).

What is more important to me is showing that these theories do not fail than showing that they contradict Kirshner. But the route to this lies through kirshner, and specifically, the misundersatndings of both cognition and scientific method that his own papers presuppose.

I would point out, to change subjects, that my response to Kirshner is being mischaracterized in places. For example, yu write, "For example, Downes characterizes Kirschner's position as being that non-instructivist teaching results in no learning."

I do not say this, am in fact careful to use Kirshner's own phrasing when I make the relevant statements. Kirshner argues, very clearly, that non-instructivis methods result in no better learning than direct instruction, and sometimes in *less* learning, because of the 'cognitive overhead' required in self-directed methodologies.

Kirshner's argument on this point is not based on experimental data, but rather, on his theory of cognition. Specifically, he argues that short-term memory has a limited capacity, and that if some of this capacity is not available for new facts (because it is taken up 'selecting scientific principles') then the transfer of information to the student is reduced.

I respond to tis argument by showing how Kirshne's theory is false. We do not 'retrieve theories' into short term memory and then 'select' from them. That is not how thinking works; that is not ow scientific thinking works. And therefore, Kirshner's argument, on these grounds, against student-directed learning, fails.

(As an aside - I am very familiar with, and sympathetic with, Kirshner's line of reasoning. t is the sort of thing faced by students of mathematics or logic. Supposed, for example, you are posed with a statement, 'All S are P', and asked whether 'Some non-S are non-P' follows. Typical logic problems require that the student pick a theory - contraposition, obversion, etc - and work out the inference. Picking the correct theory is an annoyance. better just to see - suggests Kirshner - an instructor work through the example. The problem is, Kirshner is mischaracterizing the nature of scientific problems and how they are solved. You need to *recognize* the right sort of approach. I once created a 'categorical converter' which explicitly draws out the network structure of categorical inferences. This is what needs to be emulated - but the only way to get to it is to begin to think like a logician (or, like me, to be really persistent and to eventually draw it out for yourself)).

To continue, "The standard position is that non-instructivist teaching often results in less efficient learning, the probability is increased that incorrect learning occurs, it favors those with more background knowledge. These are the standard criticisms and Downes does nothing to refute them, choosing instead to attack a strawman."

Again, I think if you go back and ook closely at my refutation of Kirshner, you will find I am ery careful to avoid that straw man.

Now let's turn next to a new issue. You write, "Downes leaves out the feedback loop, testing, which is needed so that the teacher can make sure the student has actually learned from the demonstration/model presented."

This is not qite correct. I identify four types of associative learning, one of which is 'back propagation'. Back propagation is a term from connectionism, a branch of computer science. It constitutes essentially a feedback mechanism for neural networks.

But 'feedback' is, of course, very different from testing, and the purpose of feedback is not "so that the teacher can make sure the student has actually learned." Feedback is a corrective mechanism, intended to send new informaton back into the network, causing it to alter the nature and strength of its connections.

The question of how learning is demonstrated is a very different question. It is not directly the subject of dispute between Kirshner and myself (I don't actually know his views on testing).

My own iew of testing, in brief, is that it is like using a hammer to find out if something is a nail. It sometimes works. But it can mislead, and it can produce harmful results.

The best mechanism for demonstrating knowledge is not likely the production of a certain set of facts on demand. Expertise in a discipline on the prt of a student is something that is typically *recognized*, not measured, by people who are already experts in the field.

But this is very much a side issue. testing is not a part of learning itself - indeed, the vast bulk of what we know is stuff we were never ever tested on. testing is an administrative process, intended to govern the allocation of resources and certification and credit.

To look at what you say is "the procedure they use for Direct Instruction," you state that the 'lead' step is optional, but in Kirshner's work, the 'lead' step is very much not optional, and is, according to him, the direct cause of the lessening of the learning.

le me also grab a snippet, to introduce yet another matter. You say, in part, "...Direct Instruction, a pedagogy I'm sure Downes is four-square opposed to, yet which oddly enough is fully in accord with his definition of teaching and learning."

The presumption, "I'm sure Downes is four-square opposed to," may be the result of jumping to conclusions. I have never expressed opposition to direct instruction (uncapitalized) in my work. I take prt in direct instruction myself, both in learning and in teaching. However, where I differ greatly from many others is that I believe that the process of direct instruction needs to be initiated by the student, and not imposed as a part of a required curriculum or instructional method.

As I said before, the ability to learn depends on the nature of the student. When the student is motivated to learn, when the student is in a specific frame of mind, when the student has the requisite background to know what (and what kind) of knowledge is needed, then direct instruction is very effective.

Simply putting a bunch of students in a room and 'direct instructing' them on mathematics will produce some results (generally, some improvement in mathematics), but is a wasteful and disempowering way to approach learning, particularly when compared to how much they could be learning in a wide range of subjects (not just mathematics) in the same time.

You state, "Learning is greatly dependent on the quality of the demonstration/model."

Yes, but in what does this quality inhere? There has ben a lot of discussion about what constitutes 'quality' in teaching, but I would think that it's a mistake to look for quality only in the teacher.

The models and demonstrations in fact come from a wide variety of sources - teachers, co-students, parents, media, more. The best example in the world, the best teacher in the word, can be effectively undercut by other elements in the environment.

This isn't the place for a lengthy discussion of how best to provide 'quality' in the environment as a whole. I think it will do for now to suggest that there is such a discussion that could be had, and that 'quality' constitutes more than just 'quality performance by a teacher'.

With this in mind, let me address directly "The problem with most teacher presentations, as I pointed out here, is that they are usually fraught with ambiguities. Let's use the ambiguous glerm example. Some students will walk away from the demonstration thinking that glerm means rectangle or purple, instead of vertical, and may labor under that impression for quite some time."

It is interesting that you use this example. It seems to be drawn either from Quine's 'gavagi' (on the indeterminacy of translation) or Goodnam's 'grue' (on the indeterminacy of projection). The two are fundamentally the same.

This is one of the reasons *why* I say that knowledge is constituted of connections, rather than sentences or propositions. The 'gavagi' and 'grue' poblems are inherent in the nature of language and inference; they are the rule, not the exception.

True, insufficiently imprecise teachers are a problem - people in general are very sloppy with their language - but the problem is not simply the quality of the teacher. In the right context, there would be no issue whether the teacher meant rectangle or purple (if the child was taught, or read at home, that this is what the word means, for example). In other cases, the teacher must move slowly, with clarity and precision.

But, again, imprecision is not the sole issue. The same sort of imprecision that causes no problem at all on the playground or in the bar with your friends cannot be blamed for the failure of learning to occur.

That said this, then, creates what is in fact one of the most common arguments against associationist theories in general: "Using Downes connectionist theory we know that this student's brain is going to connect itself up so that the pattern for glerm is associated with purple or rectangle, all of which will have to be undone when the student finally learns the right meaning of glerm."

Quite so.

But my response, here (just as it is against Chomsky's prety of the stimulus argument) is that the precision presumed in the objection never existed in the first place.

This, obviously, is a discussion that could continue at some length.

But we really have to be careful.

Take this statement: "We also know that it takes many more repetitions to learn something that has been mistaught than it takes to learn something new."

Well, no. We need to say, "it takes many more repetitions to learn something that has been misLEARNED." Because there isn't a direct (deductive, simple-causal) connection between what is taught and what is learned. Something can be taught correctly and learned incorrectly; somthing can be taught incorrectly and learned correctly (that's how I learned grammar!).

Another matter, "the misunderstanding of instructivist teaching as comprising mostly rote learning," does not form part of my argument (nor Kirshner's) and so is a bit of a distraction from what I actually say.

The example provided of mathemaical learning bears very little resemblance to what I would actually say. We could look at this in more detail, if you like. But, again, it's a common argument (based in the work of people like Chomsky, Fodor and Pylyshyn) that we must use rules to manage any rule-based domain, such as mathematics or language. My response, as before, is that the nature of a 'rule' in a network-based system is different than the nature of a 'rule' in a formal system (a difference Kripke tries to mask in his treatment of Wittgenstein on rules and private language.

As a result I think that your conclusion, "Constructivist pedagogy merely differs from the instructivist pedagogy in that the constructivists set up an environment in which it is hoped that the student discovers the general rule on his own with as little guidance by the teacher as needed," is incorrect.

As I state above, doing something like mathematics or science simply isn't a mater of 'finding' a rule.

It doesn't involve 'general rules' (properly so-called) at all.

The 'rule' that the scientist or the mathematician follows is an epiphenomenon. To take that epiphenomenon and use it to *direct* a ocess of reasoning is to misrepresent the manner in which the process of reasoning happened in the first place.

Think about adding two plus two. You got four, right? Did you follow a rule? Or did you just 'know'? Was it an experience more like following a map? Or more like recognizing your mother's house?

I've tried to writ about this at length elsewhere, but I'll just say for now, any account that depends on 'a student learning a rule' or the sort given in this post is missing the point of my own approach to learning (missing Wittgenstein's, too, but I digress).

Anyhow, like I said, a worthwhile discussion. I hope my comments have added to an understanding of how I think a network theory of learning differs from more traditional theories.

Anonymous said...

Downes is not an expert on learning. He tends to speak as if he is an expert.

The Internet is such that those who have more resources can have a louder voice. Because he has a tool such as OLDaily he has managed to create the perception that he is an expert. Having an audience does not make someone an expert.

Such is the power of Internet marketing. It is not always the best or most useful products that are available.

Beware of internet made experts.

Downes said...

> Because he has a tool such as OLDaily he has managed to create the perception that he is an expert.

I built my website - including OLDaily - from scratch by myself. I 'have' the tool because I created the tool.

As for the rest, my qualifications are what they are, and I invite readers to judge for themselves:
http://www.downes.ca/me/index.htm

KDeRosa said...

Anon, then you should have no problem refuting Downes' arguments on their merits.