W3 Learning Analysis
How learning works
As you saw in W2, there are two kinds of knowledge, which means there are two kinds of learning, declarative and procedural. For each kind of learning there are two different processes, what we'll call creation and strengthening. The distinction here is between getting an initial representation of some knowledge into your head, and strengthening that representation to the point where you use it reliably and quickly.
Creation of declarative knowledge. Whenever a production fires it creates propositions representing its results. These propositions are stored in declarative memory. This process is called encoding.
Strengthening of declarative knowledge. When a proposition is initially created and stored it is very weak, meaning that the probability that it will be retrieved when needed is low, and the time needed to retrieve it is long. Each time a proposition is successfully retrieved its strength is increased. This is part of the basis of the old saw, "practice makes perfect": effective learning crucially depends upon repeated use of knowledge. As propositions sit in declarative memory their strength decays. So to be effective, repeated use needs to start soon after the proposition is initially created.
Creation of procedural knowledge. While
propositions are created by productions out of nothing, new productions are
only produced from existing ones by processes of specialization and
combination. Both of these processes have the effect of replacing productions
that check for certain conditions by streamlined productions that don't do the
checks, but rather assume what the
results of the checks would be.
Here's an example of specialization. Take a production for multiplying digits:
PG: if the goal is
to multiply d1 and d2, and if the product of d1 and d2 is d3, then the answer
is d3
Suppose we successfully apply this production to multiply 2 and 3, along the way retrieving the number fact that the product of 2 and 3 is 6. This will create the specialized production
PS: if the goal is
to multiply 2 and 3 then the answer is 6
Implicitly this specialized production assumes that the check "if the product of 2 and 3 is d3" will always result in binding 6 to d3.
A similar specialization can occur to produce a production that combines the effect of more than one production. If we have two productions like
Pa: if P then Q
and
Pb: if Q then R
you can see that a production Pab: if P then R will do the same work.
Returning to PG and PS, notice that there is risk in the assumption that PS makes: maybe we don't know our number facts very well, and we actually retrieved the wrong answer. Then the specialized production would be wrong. To control this risk, newly-created, specialized productions are very weak. This means that they don't compete very effectively against other productions that can apply under the same conditions. In particular, PS initially won't compete very effectively against the general production PG.
Strengthening procedural knowledge. So how does PG ever get in the game? The answer is, if the same production is created repeatedly, your mental machinery detects that, and gives the fledgling production a boost. After a few re-creations, the new production is strong enough to compete with older productions.
Once a production is strong enough to compete, so that it is being applied, its strength is influenced by what happens when it is applied. Your mental machinery tracks the cost and benefit of productions, so that productions that rapidly succeed in processing goals get stronger. Since PS will be faster than PG, and processes the same goal, it will rapidly get stronger than PG.
More about the creation of specialized productions. In the two examples we've sketched, the assumptions implicit in the specialized productions are assumptions about our own knowledge. PS makes an assumption about our declarative knowledge: that we'll always retrieve the answer 6 if we ask our declarative memory for the product of 2 and 3. Pab implicitly assumes that Pb is always the production that we'd apply after Pa, and not some other production in our procedural knowledge, say Pc: if Q then S.
There would also be opportunities to create specialized productions based on assumptions about the outside world. For example, given
PGP: if the goal is to copy the word on the board, and if we see
that the word on the board is w, then write w
if we see the word "eggplant" on the board, we might be tempted to create the production
PSP: if the goal is
to copy the word on the board then write "eggplant"
But your mental machinery doesn't do this. Instead, it gets the same effect by a more roundabout, and perhaps safer, method. The first step is that the perception productions that are actually involved in seeing words on the board build propositions describing the results they obtain, and these are stored in declarative memory. Over time, if the word on the board does not change, this process results in a strong declarative representation of the word on the board. When this representation gets strong enough, PGP uses it rather than waiting for the perception productions to do their work. Since PGP is now using retrieval from declarative memory, rather than a perceptual check, the specialized production PSP is created just as in the PG example. As in that example, PSP starts out weak, but if it is repeatedly re-created it will eventually become strong enough to compete with PGP.
How learning can
occur in playing a game
We now have a kind of machine language view of the mechanisms of learning. How do these mechanisms work in the particular context of playing a game? We'll distinguish a number of phases, in which the mechanisms are applied to different kinds of knowledge. We'll use the board game Monopoly as the setting for this discussion. If you haven't played Monopoly, discuss this with a classmate who has.
Playing the game 0: interpreting the instructions
When you first played the game, you may have done so by working through step by step instructions that told you how to play, or a friend may have told you, step by step what to do (roll the dice, count off that number of spaces clockwise around the board, find out who owns that property, etc. etc.) What's happening here is that productions you have as a reader or speaker of English enables you to interpret verbal instructions in the same way, conceptually, as an interpreter for BASIC executes BASIC code. You don't start out with productions that can play Monopoly, but rather productions that can follow instructions in English.
Learning the game instructions I: building a declarative representation
Early in learning you may have to refer back to the printed instructions, or ask your friend to remind you what to do. But a side effect of the execution of your interpreter instructions is that they encode propositions, and over time these form a declarative representation in your head of how to play the game. As this develops, you no longer have to refer to the printed instructions or ask your friend. But you still don't have productions that can play Monopoly: you are still playing by interpreting the instructions, with your interpreter instructions running off information in your head rather than in the outside world.
Learning the game instructions II: building a procedural representation
Once your interpreter productions are feeding off data in your head, specialization starts working to create new productions, ones that really do embody knowledge specifically about Monopoly. These productions are very weak at first, but if you keep playing they will be re-created often enough to become strong enough to compete with your interpreter instructions. Once that happens, they will enable you to play more quickly: you won't be thinking "what do I do now" but rather just rolling the dice when it's your turn, and so on.
Learning game facts I: declarative
If you land on
Learning game facts II: procedural
Conceivably someone who plays a huge amount (a tournament player, if there are such people) would actually develop specialized productions that implicitly embed the price of St James, so that they would decide to buy St James or not based only on a check on their money supply, with no reference, even mentally, to the price.
Learning decision rules I: declarative
Playing Monopoly involves making decisions: Do I buy this? Do I mortgage that? Do I buy a house or hotel now? Initially you have to make these decisions by consulting whatever general decision policies your preexisting productions can find. For example, you might have something stashed in your head about the desirability of debt ("Neither a borrower or a lender be", say). Your productions might use that declarative knowledge as the basis for a decision not to buy St James, because you don't have enough money to buy it without mortgaging something. Note that a good deal of knowledge, declarative and presumably procedural, about money and how it works is brought into your thinking about decisions like this. For young children, who lack this background knowledge, Monopoly is presumably an occasion to develop knowledge about money and how to reason about it that they do not already have. For people like you who know about money, playing the game means building up declarative knowledge specifically about Monopoly ("the cheap properties aren't worth developing", or "the cheap properties are great because you can build them up early".) As the example indicates, it's not clear how much of this "knowledge" is really true, but you're going to build it up as best you can anyway.
Learning decision rules II: procedural
The aforementioned real or hypothetical tournament player
will eventually convert some of their declarative knowledge about Monopoly
decisions into specialized productions. They may buy
The educational value
of game learning
Now let's consider the value of these forms of learning. As we've just seen, if you have the goal of playing Monopoly fast, it's all valuable. All along the way, your mental machinery is replacing slow processes by faster ones: don't read the instructions, that's slow: just remember them; don't look at the deed, that's slow: just remember the price; don't think about rolling the dice: just do it when it's time; and eventually, don't think about whether or not to buy Connecticut Ave: just do it (or not). If you want to play Monopoly well, the theory has much less to say about that, and I think a little reflection will convince us that the theory is on target there. I think it happens often that people play something over and over again without actually becoming very good at it, meaning that our mental machinery, while we can rely on it to make us faster, offers no guarantee that we will get better. The machinery does favor productions that accomplish goals over those that don't, but the real problem often is that you don't have the right goals. I'd venture that there is a lot of declarative knowledge that some people build up, somewhat analogous to the knowledge that allows us to read and interpret instructions in English, that allows some people to do a better job of analyzing games and game situations than others. Presumably some of this even becomes proceduralized for people who play a lot of games.
So much for Monopoly, fast or slow, successful player or not. Educationally, we don't care! Playing Monopoly has no life value (well, except for those tournament players, if there are any.) More generally, for none of our games will we care whether players get good or not at the games themselves. Rather, we're hoping that some of what they learn will have value in some other setting. How can this happen?
Mostly, it won't.
We need to break this down and consider declarative and procedural knowledge separately, and here it's going to be simpler to consider procedural knowledge first.
The basic fact about procedural knowledge is that it is highly specific, meaning that it rarely transfers between different situations. "Transfer" is a technical term in the theory of learning: suppose you learn something A, and then you learn something else B, while somebody else just learns B. If it's easier for you to learn B than the other person (other things being equal) we say there is positive transfer from A to B. Sometimes you are actually worse off than the other person; then we say there is negative transfer from A to B. The robust finding about procedural knowledge is that it only transfers when it can be used without change: in terms of the theory, learning A helps you to learn B only when some of the productions needed for A are exactly the same as some of those needed for B. (You get negative transfer when your A productions apply when you're trying to do B, but they do the wrong things.)
It's not hard to imagine situations in which transfer of procedural knowledge can occur from a game to some real life situation. For example, in the Tic Tac Toe Products game, you have to factor small numbers. Factoring small numbers in the game is exactly the same as factoring small numbers in other situations, so you get transfer from the game to those other situations.
Considering Monopoly, it's plausible that playing it helps young children develop and strengthen some skills that do transfer to many other situations. Examples may include counting squares on the board, counting money, and making change.
But it's also easy to be misled, by false intuitions about the nature of knowledge, into imagining that transfer of procedural knowledge will occur from a game when in fact it will not. Many people suppose that it must be valuable, in some intellectual way, to play a game like Myst, that involves solving various puzzles, because the game must develop puzzle solving skill that will help in solving problems you encounter in the future. The evidence is that this does not happen, because the productions used in solving different puzzles are different. Another example: many people think chess players must be "smart", that the skills developed in playing chess are somehow valuable in other settings. The evidence is that this is just not so; being good at chess means being good at chess, period.
Happily, the transfer picture, and hence the value proposition, for declarative knowledge is very different than for procedural knowledge. Your declarative knowledge is not linked to any particular task setting: it's available wherever it's relevant.
As educational game designers, we still have to worry. The
question becomes, is the declarative
knowledge I obtain relevant to some other situation? Thinking about Monopoly,
for most of the declarative knowledge we discussed the answer is, obviously
not. Learning the price of
Is there any educational value in Monopoly? If there is, it lies in the declarative knowledge we may develop in the course of developing decision policies in the game. We may learn some consequences of borrowing, for example, in thinking about mortgage decisions in Monopoly. Another place these considerations may be reinforced is in connection with the price penalties associated with selling off houses to raise funds. I would assume that some players, at least, develop some declarative knowledge from Monopoly about keeping cash reserves.
Actually, here's another place where we really should put declarative "knowledge", in quotes. We have to ask, is what I learn about cash reserves in Monopoly really true, in the sense that it is applicable and valid in other situations? What do you think? This is a serious issue in using simulations in education!
There's one more issue we have to consider about declarative knowledge: level of generality. Do I learn, "Don't spend money if you can avoid it if you have less than $500," or do I learn, "Don't spend money if you can avoid it if it increases the likelihood that you'll need to borrow"? Presumably, the latter proposition is more valuable in other situations than the former, which can hardly make sense outside Monopoly.
As far as I know, it's not well understood what makes people frame declarative knowledge in more general or less general terms. As a rough theory, we can suggest that generalizations develop when (a) people are presented with comparable but differing situations, AND (b) they form the goal of forming a generalization from them. Both (a) and (b) have to be there: you need the raw material from which to form the generalization, AND you have to be trying to do it. Generalizations don't form spontaneously.
A challenge for us as game designers is, how can we induce generalization goals in players? One way, not very satisfying to me, but perhaps often the best we can do, is to rely on structure outside the game to do this. If a game is embedded in a school lesson, the school lesson can require students to think directly about the relationship between situations encountered in the game and situations somewhere "in real life". Notice that we have to follow this up with activities in which the new generalizations are repeatedly retrieved. Because they weren't formed in the game, they won't be practiced in the game. And it they aren't practiced, they won't be strengthened enough to be retrieved in the future. So you have to come up with some motivation, outside the game, for practicing with the generalization. Sounds just like work.
What can we do in a standalone game? Here's one approach; perhaps you can devise others. In the game, the player confronts a sequence of situations in which the same body of declarative knowledge is useful, PROVIDED that the knowledge is stated at the right level of generality. This brings the generalization goal into the game itself, not leaving it for an outside lesson. It's a bit labored, but one could illustrate the idea in a variant of Monopoly in which the price and income levels vary from round to round. You'd have to frame your policy about cash reserves in more general terms than "keep $500 on hand." The motivation for developing the generalization comes from the game, not from duty or coercion.
One last point about declarative
knowledge. One of our knocks on Monopoly as an educational game was that
there's no value in knowing the price of
Analyzing a game
Let's pull this discussion together in a framework that we can apply to analyzing (and eventually designing) a games. Fill in the blanks:
Procedural knowledge: Playing this game involves the skill of _____________________, which is a real-world skill. Playing the game provides extensive practice with the skill (yes or no.) You have to already have this skill in rudimentary form to play (yes or no). The game includes resources, such as instructions or demonstrations, from which a declarative representation of the skill can be formed (yes or no). These resources are_____________________________.
Specific declarative knowledge: Playing this game involves knowing these important real-world facts:________________________. You already have to have a rudimentary knowledge of these facts (yes or no). Playing the game requires repeatedly retrieving these facts (yes or no). Within the game, access to these facts is provided by ________________.
General declarative knowledge: Playing this game involves knowing these important generalizations:_________________________________________. Forming these generalizations is supported in the game by presentation of the comparable but contrasting situations or entities, in this way_________________________________
Efficiency: Processing the above knowledge represents a (choose one) negligible, minor, major, dominant proportion of the time players spend on the game. (We haven't discussed this, but obviously using Monopoly as a way of giving students practice calculating percentages is dumb. Playing Parcheesi as a way of giving kids practice counting is not so dumb: there's not much time going into anything else in that game.)
Assignment
[Problem W3-0]. Remember that you are encouraged to work together on these assignments, as long as you do that in the spirit of "working together" and not "divvying up the work".
[Problem W3-1].
Electric Field Hockey (EFH) is an educational simulation game about electric
charges. Read the description of EFH in Miller et al, pp 308-309. [Miller, Lehman, and Koedinger,
Goals and learning in microworlds, COGNITIVE
SCIENCE Vol 23 (3) 1999, pp. 305±336. Access this via
Chinook... look for Cognitive Science as Periodical Title, then go for online
access, select the right volume and number. Access is free if you do it from
CU's network, either by being on campus or using the VPN that you can get from
ITS.]
Miller et al use the term "microworld" here and elsewhere in the paper, meaning a simulation that allows players to explore the effects of various manipulations of the elements of the simulation, in this case by placing charges in different locations. One could say that Monopoly is a kind of real estate microworld; many games can be seen as microworld based.
DO NOT read other parts of Miller at al yet.
You can experiment with a version of the game at http://www.colorado.edu/physics/phet/simulations/electrichockey/webstart.jnlp
BUT NOTE that this is not quite identical to what Miller et al describe. Turn on the trace to make it more similar. In the analysis you'll do, below, stick to the Miller et al description where it differs from the online version.
Fill in our framework (above) as well as you can, for three different versions of EFH:
SG standard goal: This is the version described in what you have read. There are some obstacles in place, and you have to make the puck go in the net.
NG no goal: Here there are no obstacles or net, and the player isn't given a specific task, other than to experiment with the system. They are told that there could be obstacles and a net. I guess this isn't really a game, but try to work out what the player might do and learn.
SP specific path: This is like the standard goal version, but there's a trajectory sketched in that the puck has to follow.
In your analysis, assume that players already know the following:
* A fixed particle with the same charge as
the puck gives an initial push along the line
that connects the charges, but in the opposite
direction.
* The path of the free-floating charge will
be deflected by like charges.
* Closer charges have more effect.
Pay special attention to whether you think players are likely to learn the following in playing the different versions:
*the relationship between force and
acceleration,
*the relationship between an electrical
charge’s distance and its effective force (inverse square relationship)
*the relationship between the locations of multiple charges and
their net effect (superposition).
[Problem W3-2]. Miller et did an actual comparison of these
three versions of the game, and tested what players learned. See the sentence
beginning "The no-goal
condition... " in
the next-to-last paragraph on p 322 to get the gist of their results... just
use the percentages they present in that sentence to compare the versions.
Write a few sentences comparing their results with the results of your analysis
in (1).
[Problem W3-3]. Read the section "Implications for Instruction" in Miller et al, starting on p327. Distill this discussion as well as you can into a slogan for educational game designers that contains as few words as possible; we'll select the best of these slogans and award a worthless prize to its creator(s).
[Problem
W3-4]. IF you have more time, feel free to read the rest of Miller
et al. Their work includes a simulation model that learns to play EFH, using
another popular cognitive theory, different in some respects from the