September 24, 2009


In my last post on expertise and experts I indicated that an expert (one who has expertise) is broadly defined as someone who has acquired lots of knowledge in a particular domain.

So what is knowledge?

First a few preliminaries:

1.  Stephen Downes has a post addressing this issue from a different angle, so you might want to check that out to see where we agree and disagree.

2.  I addressed this same issue back in April so it will look familiar to some of you.

3. I've adapted this explanation from Martin Kozloff's Making Sense of What You Read and Hear, and Making Sense When You Teach.


Each form of knowledge represents a connection. To understand the knowledge is to understand the connection. To use the knowledge (to apply it to possible examples of it) is to apply the connection.

The forms of knowledge are:
  • verbal associations - facts and lists: (this one thing goes with that one thing);
  • concepts - sensory and higher-order: (all these things have some features in common);
  • rule relationships: (this set of things goes with that set of things); and
  • cognitive routines: (to read all of these words, or to solve all of these math problems, or to write these kinds of essays, do steps 1, 2, 3, 4, 5 and 6)
These forms of knowledge are defined by the logical structure of the knowledge itself. The logical structure is the connections inherent in the knowledge. Learning one of the forms of knowledge means learning the inherent connection.

Let's now look at each form of knowledge.  I'll provide some examples, a definition, and one way to teach the form.

1. Verbal Associations: Facts

Ex: “The U.S. Constitution was written in Philadelphia.”

For purposes of instruction a fact is a true and verifiable statement that connects one specific thing (Constitution) and another specific thing (Philadelphia).

Teach the connection.

2. Verbal Associations: Lists

Ex. 1: “The elements of sugar are carbon, hydrogen, and oxygen.”

Ex. 2: “Here is a list of facts about the U.S. Constitution. Written in Philadelphia between May and September, 1787; the draft was sent to the various states for ratification; the Constitution plus the Bill or Rights is a compromise between advocates of strong central government (Federalists) and advocates of strong state governments with a limited central government (anti-federalists); the Constitution was finally ratified in 1789.

Like with facts, these statements connect one specific thing (elements of sugar, Constitution) and a list (of other specific things).

Teach the connection(s).

3. Sensory concepts

Exs: blue, on.

The specific things (examples) of the concepts differ in many ways (size, shape), but they are connected by a common feature, such as color or position.

All of the defining features of the concept are in any example. Therefore, the concept can be shown by one example. However, a range of examples is needed for the learner to see what the common feature is and to cover the range of variations (e.g., from light to dark red).

Teach the range of examples needed for the learner to determine the common feature and the range of variations.

4. Higher-order concepts.

Exs: Democracy, society, mammal.

The specific things (examples) of the concepts are connected by a common feature or features; e.g., making societal decisions through elected representatives (representative democracy).

The defining features of higher-order concepts, however, are spread out. Therefore, you can’t simply show examples to teach a higher-order concept. You have to give a definition (that states the common, defining features) and then give examples and nonexamples to substantiate the definition.

Teach the definition of the common features and then substantiate the definition through suitable examples and non-examples.

5. Rule Relationships

These are statements that connect not specific things but whole groups of things (concepts or categories).

  • Categorical Propositions. Some rules or propositions state (assert, propose) how one kind of thing (concept or category) is part of or is not part of another kind of thing (concept of category). These are called categorical propositions. For example, all dogs (one kind of thing) are canines (another kind of thing). Or, No birds (one kind of thing) are reptiles (another kind of thing). or, Some bugs are delicious.

    Teach the rule or proposition.

  • Causal or hypothetical propositions. Other rules or propositions state, assert, or propose how one kind of thing (concept or category) changes with another kind of thing (concept or category). These are called causal or hypothetical propositions. You can tell that a statement asserts a causal or hypothetical proposition because it states (or suggests) the following signals: if, if and only if, whenever, the more, the less.  If one thing happens then another thing (happens, comes into being, changes, increases, happens more often, decreases).

    The “thing” (variable, condition, antecedent event) that is the alleged cause of something else can work (have an effect) in different ways. For example, the alleged cause might be considered a necessary condition for something else to happen or change. (“If X does not happen, then Y will not happen.” Or, “If and only if X happens will Y happen.”) Or, the alleged cause might be considered a sufficient condition for something else to happen. (“Whenever X happens, Y will happen.”)

    For instance, Whenever temperature increases (one kind of thing), pressure increases (another kind of thing). [This proposition suggests that a rise in temperature is a sufficient condition (by itself) to cause an increase in pressure.] Or, If and only if there is sufficient oxygen, fuel, and heat (one category of thing) will there be ignition (another category of thing. [This proposition suggests that sufficient oxygen, fuel, and heat are a necessary condition for ignition.]

    Note: When you have identified all of the necessary conditions, you now have a set of variables that are a sufficient condition. Think of a causal model of fire, a cold, and a revolution.

    Teach the rule or proposition.
6. Cognitive Routines

Routines are sequences of steps that usually must be done in a certain order. Solving math problems, sounding out words, and stating a theory or making a logical argument (each proposition in the theory or argument is like a step that leads to a conclusion).

Teach the routine.

Routines are often thought of as "skills."

: A routine is a connection of a number of events, such as steps in solving a problem or a listing of events leading up to a war. There are different arrangements of steps or events in routines. You want students to see what these arrangements are.

  • Sequence in one direction. A leads to B leads to C leads to D. Ex.: sounding out words, solving math problems.
  • Sequence with feedback loops. A leads to B and the change in B produces a (reciprocal) change in A which produces more change in B until some limit is reached. Exs.: Outbreak of war, onset of illness, falling in love, divorce, getting porky and out of shape.
  • Stages or phrases. A sequence of events or steps can be seen as a process divided into stages in a process.

    Ex1: Load rifle: steps a—b—c--d; Fire rifle: steps e—f—g; Clear rifle: steps h—i; Clean rifle: steps j—k, etc.

    Ex2: In history: If you examine enough (examples of) genocidal movements, you notice that one group has some features (e.g., property, social status) that produces envy in another group, or does something that threatens another group (e.g., resists power). This might be seen as the background (first) phase. Then (phase 2) the genocidal group demonizes the first group with racial slurs and propaganda. Then (phase 3) the genocidal group begins to mistreat the victim group; e.g., attacks, job loss, confiscating weapons, special (degrading) clothing. If (phase 4, escalation) the victim group fights back, this provokes worse treatment. If the victim group submits, it furthers the genocidal group’s perception of the victim as degraded. The genocidal group then (phase 5) creates an organization for killing or transporting. Then the killing begins (phase 6).

  • Logical argument. A text might be arranged as a logical argument. There are two sorts of logical arguments:

    a. Inductive. Facts are presented. Then the facts are shown to lead to a general idea, such as a conclusion. For example, examine five examples of genocide and induce (figure out) the common phases and the activities in each phase.

    b. Deductive. Or, text may be arranged so that it presents a deductive argument. It begins with a general idea, such as a rule--first premise.

    “If X happens, then Y must happen.”

    It then presents facts relevant to the first premise—evidence or second premise.

    “X happened.”

    It then draws a conclusion.

    “Therefore, Y must happen.”
So having knowledge means more than merely knowing lots of facts or having certain skills, 21st centurey ones or otherwise.  There is much more to it than that.

But, certainly, if you want students to have expertise in certain domains to gain the advantages that expertise conveys then these students will possess knowledge in these domains.  I don't think there's any way around that.  But, if you think there is, be sure to let me know.

Next we'll discuss Dinosaurs.


Stephen Downes said...

For those who want more on my approach to the subject of knowledge, you may want to read:

'An Introduction to Connective Knowledge'

'Learning Networks and Connective Knowledge'

'The New Nature of Knowledge'

These papers, in turn, contain numerous references to additional work on knowledge.

Stephen Downes said...

p.s. for those wanting a more orthodox treatment, I can't go wrong recommending this article in the Stanford Encyclopedia of Philosophy

which is achingly traditionalist but constains at the end an outstanding bibliography

The Wikipedia article is similar, a bit more wordy with a weaker bibliography, but links to numerous related wikipedia articles

KDeRosa said...

Thanks for the links, Stephen, the more info the better.

Parry Graham said...


I think I'm getting a little hung up on the "one way to teach" part. What exactly do you mean when you say "Teach the rule" or "Teach the connection"? Those are pretty open-ended statements.

I'll give you two examples of what I mean, one from science and one from the humanities. I saw a video years ago in which a reporter stops a number of Harvard undergrads and asks them why we have seasons. Each of these students had been formally taught the rules underlying the seasons (the tilt of the earth) at some point, but many of them incorrectly stated that the seasons were caused by changes in the earth's distance from the sun. They were taught the rule, but they did not truly understand the rule at a conceptual level.

In my own teaching (I was a high school German teacher for six years), I taught my students many grammatical rules. Had I asked them to recite a rule back to me (for example, which prepositions always have their objects in the dative case, and the dative forms of indefinite articles), they could often correctly recite the rule and dative forms, but then they would fail to apply the rule correctly in actual written or spoken speech.

I guess this post strikes me as paying a lot of attention to the complex nature of knowledge, but in its brief statements about teaching seems to suggest that the actual acquisition of knowledge should be a relatively simple process: "Just teach the connection, darn it!"

Am I misreading your post?


KDeRosa said...

Parry, I wrote "one way to teach" in case someone wanted to argue that these forms could be learned other than direct teaching, which they can.

The statements are open-ended becasue there are many different specific ways to "teach the concept" but in the end the student must be able to discriminate things that are an example of the rule from things that are not examples of the rule. For example the student must know that for the concept red, something that is blue is not red but something that is dark red is an example of red.

I have another post back in April that discusses how students acquire knowledge. I also have an unposted post on the phases of mastery. To the extent they are relevant to this discussion I might use parts of those posts.

In your examples I think you are getting into the area of flexible and inflexible knowledge. Willingham has a good article on this. Engelman also alludes to this problem in the recent interview I posted where he indicates how the interviwer's child is struggling to read words in connected text and not the same words in word lists because of "ambiguity overwhelm."

Also, knowing a rule doesn't necessarily translate to being able to discriminate between examples and non-examples without a deeper understanding of the rule.

Parry Graham said...

10-4. Thanks for the explanation.


Dick Schutz said...

Seems to me your sequence of posts is deteriorating, Ken. The post on "expertise" was off to a good start. Regurgitating Kozloff seems a step backward. And gawd only knows what you will do with "dinosaurs." But your blog, your rules.

Knowledge is one aspect of expertise. But there are other aspects of expertise. And if you want to take on "knowledge," it can be addressed via epistemology a la the references that Stephen Downes provides. I don't find this route very productive pedagogically, but it's certainly legitimate inquiry.

A more direct address is via the cognitive science lit, a la the Cambridge Handbook of Expertise.

I seem to recall having commented on Kozloff's structure when you flagged it in April. It doesn't merit going around that block again.

Seems to me "this is getting us nowhere, slower."--which is where you started.

Tracy W said...

Regurgitating Kozloff seems a step backward.

Do you have any particular reason why this seems to be a step backward?

Knowledge is one aspect of expertise. But there are other aspects of expertise.

And what are these other aspects? And how are you defining knowledge?

Dick Schutz said...

As Ken says, he posted essentially the same lengthy quotes from Kozloff in April. Kozloff is noted for his application of behavioral analysis and is a DI proponent. Nothing wrong with that, but there are better treatments of "knowledge." Stephen Downes flagged the philosophical lit on epistemology and I flagged the cognitive science lit on expertise.

Kozloff treats what the lit refers to as "declarative knowledge." There is also "episodic knowledge" sometimes called procedural or functional knowledge, and there is tacit knowledge of a genetic/cultural nature. All of these aspects are involved in expertise They interact differently, depending on the domain of expertise at issue.

Few would recognize or accept Kozloff's six categories as THE forms of knowledge.

KDeRosa said...

Let me jump in here real quick.

The reason why I'm discussing knowledge in this series on experts and expertise is to get past the simplistic notion that knowledge is just a bunch of storage "facts." It is much more than that.More importantly, relative expertise the representation of knowledge is a distinguishing feature.

That's why I picked Kozloff's summary of knowldge because it is based on and classifies knowledge acording to how the inherent connections of the knowedge. I think those connections correspond at least in part to how knowledge is representated in the mind of an expert.

I'm sure there are other equally accurate and perhaps more accurate ways of understanding knowledge. However, for purposes of this discussion, understanding that we'll be focusing on K-12 education, I think Kozloff's categooies are sufficient.

ALso, I don't think that Kozloff's categories are only relevant to descriptive of declarative knowledge. Most of them are, but that's because most of what gets taught in K-12 is declarative knowledge. But, Kozloff also includes concepts and procedures which I do not believe are declarative knowledge (I suppose in one sense they are, but that's not how Kozloff is defining those categories: when one learns a procedure, it is important to be able to perform the procedure not verbalize the steps. Same thng for concepts: one must be able to identify the concept of "red," not necessarily verbalize the definition of redness.)

I also think that you can pidgeonhole almpost everything that is typically learned (i.e., knowledge) into one of Kozloff's categories in a way that is accurate to it's relevance to expertise.

I could be wrong about all this (I am operating at the limits of my own knolwedge) and if I am let me know why and give some examples that demostrate your point. I don't want to go too far down this path is I am too far off base at the outset.

Dick Schutz said...

I'm not intending to be snarky. Kozloff presents his categories (per the link you provide) in a DI oriented paper. There is nothing wrong with that, but it's a restricted rather than a general perspective. Again, there's nothing wrong with that. That's all I'm trying to say.

"Each form of knowledge represents a connection. To understand the knowledge is to understand the connection. To use the knowledge (to apply it to possible examples of it) is to apply the connection."

That holds from a DI instructional perspective and it sets up Kozloff's categories. But only in the sense that "everything is related to everything else" does the first sentence hold.

Expertise in any area is not acquired by learning connections, and as I've tried to say, "knowledge" a la Kozloff's categories is only one aspect of expertise.

Try applying the categories to your current series of posts, that are aimed at clarifying/and extending our knowledge. I don't see that they apply. They are useful as background in prepping for the development of DI instruction, but they don't help (me) in "Making Sense of What You Read and Hear, and Making Sense of What You Teach."

But I may be missing something. I didn't, and still don't, see the connection between "Expertise," "Knowledge (per Kozloff)" and "Dinosaurs." Bring on the dinosaurs!

KDeRosa said...

Dick, I understand that Kozloff's categories are restricted or simplified. The question rather is are the categories so retricted or oversimplified to be in error?

I prefer simple unless the added complexity is an improvement. What I'm trying to say is that I don't think the general perspective adds anythingh to the discussion over Kozloff's simple categories. BTW, I'm happy to be proven wrong here.

But only in the sense that "everything is related to everything else" does the first sentence hold.

I don't think that everything is necessarily related to everything else. Knowledge can be inert, not all knowledge is going to connect to all other knowledge, and some connections can be missing, wrong, unclear, etc. But, is there a form of knowledge that doesn't represent some kind of connection to something else?

Expertise in any area is not acquired by learning connections, and as I've tried to say, "knowledge" a la Kozloff's categories is only one aspect of expertise.

I'd say that expertise is a function of knowledge. And that those with more expertise tend to have more well-structured knowledge. That's where the connections come in. The better the quality of the connections the more expertise. And, that's where the dinosaurs come in (which you'll have to wait patiently for).

Try applying the categories to your current series of posts, that are aimed at clarifying/and extending our knowledge.

Mostly what I've written so far falls into higher order concepts (at least I hop it's higher order)of "expertise" and "knowledge" as defined by two lists of higher order concepts. These two posts and future posts will (if all goes according to plan (which I'm not entirely sure of yet)) form the basis (i.e., premises)of a logical argument (or cognitive routine) which I haven't disclosed yet (because I'm entirely sure what that argument is). The real question is, as you watch the spins and twirls, is whether I can stick the landing.

Dick Schutz said...

I wouldn't say Kozloff's structure is "in error." I'd say it reflects a restricted perspective that supports a DI orientation to instruction.

"Mostly what I've written so far falls into higher order concepts (at least I hope it's higher order)of "expertise" and "knowledge" as defined by two lists of higher order concepts."

Well, if by "higher order concepts" you mean a structure of loosely coupled abstractions" I guess that's what you've written.

I'll wait for the dinosaurs. You're flying pretty high, but I wish you the best in nailing the landing--if you don't decide to parachute before that time.

KDeRosa said...

I wouldn't say Kozloff's structure is "in error." I'd say it reflects a restricted perspective that supports a DI orientation to instruction.

That's fair. I'm not going to argue that DI ia the only way to teach, learn, acquire knowledge, or gain expertise.

Oddly enough, if you take a look at Downes' essay at his first link. It is very similar to Kozloff's with some added complexity, some pushing at the boundaries of categories, but ultimatel I don't see how the added complexity aids our undersatnding over and above Kozloff's more simple perspective. And, Downes is certainly not a DI or direct instruction proponent.

Dick Schutz said...

Personal view: I don't find Downes' presentation any more instructive than Kozloffs.

KDeRosa said...

Dick, since you have knowledge in this area, you might want to write-up a better categorization of knowledge that's more general than Kozloff's. It'd be interesting to contrast it with Kozloff has provided and it may make a differenc as to how I approach the rest of this discussion.

Just email me what you come up with and I'll post it up front.

Dick Schutz said...

That's a generous offer Ken. The thing is, I don't find ANY categories of "knowledge" useful. The effort goes back to at least Bn Bloom and Bob Gagne, and before that Thurstone's "Factors of the Mind."

I'd start from a system perspective with something like Herb Simon's "Science of the Artificial" In dealing with a matter like el-hi schooling, the methodology of engineering can be applied, but the hard part is structuring the artificial to make it operationally transparent.

More concretely, one of the "big things" in the corporate world these days is "Business Intelligence" with real-time indicators of how an enterprise is performing. There is as much bull shit (almost) in the corporate lit as there is in the ed lit. But the notions hinge on 5-9 Key Performance Indicators that mark the path from "First Contact" to "Sale." But the bottom line is "Sale" and el-hi has no obvious "bottom lines."

Key performance Indicators that mark the path to the operational accomplishment of any educational aspiration can be generated, but it takes concentrated background information and "mental fiddling."

Then it takes further background info and mental fiddling plus empirical tryout to go from "proof of concept" to reliable instructional product protocol.

Bereiter, Becker, Engelmann, Carnine, and colleagues worked out ONE workable architectural orientation and methodology for going about this, and Zig has "stayed the course."

As I've said the Kozloff categories are a good fit for this orientation.

[Part 2 to follow. It exceeed allowable 4,096 characters]

Dick Schutz said...

As I was saying...

Rather than trying to categorize "knowledge," I'd work from a different orientation with categories such as:

--What do you want to accomplish instructionally?

--How are you going to know it's been accomplished?

--How are you (roughly) going to go about getting the job done?

--How much additional marginal cost and calendar time will be required to generate "proof of concept'?

These categories are a good operational test of instructional knowledge and expertise.

Then in any new instructional initiative a different set of categories comes into play in dealing with any administrative unit larger than an individual teacher:

--Initiative preparation. The means for ensuring that all participants are "on the same page." At the school level, this involves all teachers, administrators, and parents. At the district level it involves school board, district administrators and local media. Interestingly, the larger the scale the easier this aspect because there are more personnel resources to bring to bear.

--Instructional product/protocol="program" This is the most visible part of the initiative. It's "core." But it's only one element.

--Instructional support. This element is analogous to "customer tech support" and replaces the traditional "training"/"Professional Development." Teachers are treated as "qualified." Their a priori "need to know" is only enough to get them started. Glitches WILL occur. But when they do, they can be handled as a trouble shooting matter. Either individually, or if the glitch is broader with the most functional and economical fix to keep the show on the road.

--Instructtional Accomplishment Information. The Program must include transparent feedback mechanisms to keep teachers, students, and parents continuously informed of individual student instructional status/performance. The 5-9 Key Instructional Status/Performance Indicators provide a mechanism for program accountability, aggregated by teacher, school, district, and by the usual bio-social categories of interest.

In short. the categories take the accountability monkey off the backs of kids and teachers and puts it on the purveyors of instructional products/protocols--the things people use, rather than on the people per se. These "things" can be manipulated and modified to obtain more reliable accomplishments, and to reduce time and cost.

This is the way every other sector operates. For historical reasons, el-hi dug itself--with help form friends and foes--into a hole. It's possible to get out of it, but not without "Change We Can Believe In."

It's a different orientation from Kozloff's. I think the alternative 2 sets of categories fit DI modus operandi, although DI is short in the Instructional Accomplishment Info element and takes a different view of Instructional Support.

Most other initiatives don't fit at all, but that's a whole nother story.