December 14, 2007

Downes responds

Stephen Downes left the following comment to my last post. It's a good comment so I'm going to pull it up front so it'll be easier to read. It's unedited, except for a quick spell check (I know the perils of the blogger comment system):

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 electricity, '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 but 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 conducive 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 - discovery based learning. inquiry learning, constructivism - 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 misunderstandings 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, you 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-instructivist 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 this argument by showing how Kirshner'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 look closely at my refutation of Kirshner, you will find I am very 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 quite 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 information 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 view 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 part 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.

Let 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 part 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 been 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; something 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 mathematical 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 process 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.

6 comments:

rightwingprof said...

I've been a connectionist (more properly, Parallel Distributed Processing) since Rumelhart and McClelland published their two volume research compendium with the PDP Research Group. However, there is absolutely nothing about PDP that would relate to, much less support, constructivism. And nobody would argue that at some level, in some way, patterns are construed as discrete symbols. After all, if they weren't, we would never have developed symbolic systems in the first place. And the processing of patterns is a low-level, neurological process that has nothing to do with the classroom. Any input, no matter how it is presented, will be processed in the same way, and ultimately, will be comprehended symbolically by the learner. PDP is wholly internal. The model is the model. The input is the input. And the model has nothing to say about the type of input. Neural nets tend to produce very much the same output no matter the input. That was one of the (then) amazingly controversial things about the theory.

Constructivism is yet another symbol manipulation paradigm. The difference is that you're letting students manipulating the symbols and giving them minimal feedback. But symbol manipulation is symbol manipulation. There is nothing about PDP that makes constructivism more attractive. There is nothing about PD that makes any pedagogical theory more attractive, although PDP requires feedback, and therefore would contraindicate pedagogy with minimal feedback.

Note that PDP models are very good at processing certain kinds of input, like language, but very poor at others, like math. Draw what conclusions you will.

If you're interested, start with both volumes of Rumelhart and McClelland's Parallel Distributed Processing: Explorations in the Microstructure of Cognition, then go from there.

rightwingprof said...

"And nobody would argue that at some level, in some way, patterns are construed as discrete symbols."

That should be are not, obviously.

Tracy said...

When Kirshner talks about 'search' and 'retrieval', he is very clearly employing a 'knowledge as object' perspective, one that is quite misleading.

How is this perspective misleading?

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.

How do you measure the relative dependence of the various factors on the process of induction? For example, is there any evidence that would convince you that the process of induction was more important than the nature of the student?

A teacher is but 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 conducive 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).

Is there anything special about your theory that this means this is more true for your theory than for any other theory of learning?

Or in other words, is there anyway in which you are not just stating the obvious?

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.

Is there anything special about your theory that means this is more true for your theory than for any other theory of learning?

Or in other words, is there anyway in which you are not just stating the obvious?

But, all things being equal, immersion and direct experience are more likely to induce the expected learning than reading or telling.

Is there any evidence that could convince you otherwise?

My own view of testing, in brief, is that it is like using a hammer to find out if something is a nail.

Huh? Interesting view. My view of testing is that it is essential for any progress to be made. Is there any evidence that could convince you that testing is not like using a hammer to find out if something is a nail?

Do you distinguish between brain-dead testing, and testing that is carefully designed for the task in hand?

The best mechanism for demonstrating knowledge is not likely the production of a certain set of facts on demand.

Well, it depends on what knowledge you want to demonstrate. For example, the best mechanism for demonstrating driving skills is driving on demand, and undergoing a series of maneovourers (ranging from doing a 3-point turn in a wide space as a basic skill, to weaving in and out of cones at high speeds for an advanced driving course).

In other areas, it is unethical or impossible or just too expensive to demonstrate knowledge practically. For example, first aid skills are not tested by blocking a person's airways and seeing if the first aider can get the person breathing again. Instead they are tested by a combination of quesion-asking and tests on a dummy.

Expertise in a discipline on the part of a student is something that is typically *recognized*, not measured, by people who are already experts in the field.

So, let us say that the people who are already experts in the field recognise that a student is not an expert. Where does the teacher go from there? How is the teacher to know why the student is not an expert, and what skills the teacher should teach to improve the student's skills? There is no point in wasting time teaching a student what they already know. Testing is necessary for effective teaching.

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.

Really? Then how do you know that you know it? I know I can walk - I've tested that every day of my life since I first learnt. I know I can drive, I've tested that less frequently but frequently enough.

Feedback is an essential part of learning. If you've never tested your knowledge, or had it tested for you, how you do you it's true?

Why do you believe your theory about connections if it's never been tested?

Tracy said...

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.

Kids may indeed be able to learn far more in an hour than they can under Direct Instruction. But, can we achieve such learning? Let's see your experimental evidence. How much have you shown that kids can learn, hour-for-hour in a wide range of subjects, as opposed to spending the same number of hours using best-practice Direct Instruction in mathematics?

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.

This analogy is wrong. Conductor vs non-conductor is a matter of degree of conductivity. At a high enough voltage, a "non-conductor" will start conducting. This is how lightening works and why it is dangerous to get too close to a high voltage line even if you don't touch it. The air is a good conductor at low potential differences but it conducts well enough at high potential differences. (Sorry about the switch in language from voltage to potential differences, voltage is a relative measure).

If you doubt me, how about you climb a transmission tower up to some live lines? Make sure not to touch them.

Cal said...

"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."

A statement crying out for parody, except it *is* parody.

Really, can't people stop romanticizing students? If stidemts are sitting in a classroom to learn math, TEACH THEM MATH. Don't pretend that more than 5% of them want, much less are capable of handling, "empowerment".

Joanne Jacobs said...

I've tagged you with the "seven random things" meme here.