Design­ing and test­ing the Con­struc­tion­ist approach to games for basic maths

Diana Lau­ril­lard, UCL
@thinksitthrough

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Diana Lau­ril­lard:
… And first of all, I want to thank Caul­dron very much for this invi­ta­tion and also for being such a great part­ner to work with to cre­ate games on the Goril­la plat­form. It’s been real­ly eight years, Joe. I can’t believe it. Okay. So this is about design­ing and test­ing the Con­struc­tion­ist approach to games for basic maths, as Joe mentioned.

Diana Lau­ril­lard:
So why do we need games for basic math? Well, spe­cial needs learn­ers with dyscal­cu­lia, that’s 6% of learn­ers of all ages, can learn to count. But they solve all prob­lems by count­ing. And to give you a sense of what this is like, what they will do is to say, which is the larg­er of two play­ing cards show­ing 5 and 8. They’ll count all the sym­bols on each card. And then to count down from 10 in ones, they’ll count 1 to 10, and then 1 to 9, and then 1 to 8. And so on. They can’t count back­wards one by one, as most of us find quite easy. So they have no sense of the inter­nal struc­ture of num­bers is what this means. The num­ber sequences for them is a lit­tle like the alpha­bet, it’s just a ran­dom sequence. And so of course that makes arith­metic very difficult.

Diana Lau­ril­lard:
So our ques­tion now is, can we design a game that would help dyscal­cu­lia and ear­ly learn­ers to under­stand the inter­nal struc­ture of numbers?

Diana Lau­ril­lard:
Why Con­struc­tion­ist? Well, Con­struc­tion­ist was defined orig­i­nal­ly by Sey­mour Pa pert at MIT. And it’s since been inter­pret­ed as the learn­ing sit­u­at­ed in a mean­ing­ful con­text. It must have a mean­ing­ful goal in view, mean­ing­ful to the learn­er, and achieved through learn­ers’ con­struc­tions of some­thing. The feed­back must show the result of their action in rela­tion to the intend­ed goal. The learn­er then uses that direct feed­back from the envi­ron­ment to improve their own con­struc­tions. And so the learn­er is able to work out how to improve their action with­out help either from the teacher or from the com­put­er advice.

Diana Lau­ril­lard:
Now, game mechan­ics and learn­ing goals. We know from research on game-based learn­ing that the game mechan­ics must be aligned with the learn­ing goals to be effec­tive. What does that mean exact­ly? How, for exam­ple, do we cre­ate the game mechan­ics that will help learn­ers get a sense of the inter­nal struc­ture of num­bers? What that means is that for each stage of the game, what we’re try­ing to ask as design­ers is what kind of cog­ni­tive pro­cess­ing do we want to try to elic­it here?

Diana Lau­ril­lard:
So one recent mod­el of game-based learn­ing is due to Lass, Homer and Kinder who pro­posed the rela­tions that we can prob­a­bly all agree on that almost any kind of game pro­vides a sequen­tial struc­ture of chal­lenge, response and feed­back. Repeat­ing for dif­fer­ent chal­lenges. But of course, it’s the learn­ing the­o­ry behind any edu­ca­tion­al game that real­ly informs the design of each of these things. I’m going to focus on what makes a con­struc­tion­ist game dif­fer­ent, name­ly the kind of cog­ni­tive pro­cess­ing it elicits.

Diana Lau­ril­lard:
So to help learn­ers under­stand the inter­nal struc­ture of num­bers, a con­struc­tion­ist approach would define the chal­lenge for this goal as being able to use giv­en sense to con­struct a tar­get set. And the response sec­tion would then be to be able to join or split giv­en sets. And then imme­di­ate feed­back is the result of that action. Either sets turn into oth­er sets which include the tar­get or the sets turn into oth­er sets which don’t include the tar­get. And that’s all. That has to be suf­fi­cient for the learn­er to work out what to do next, if they don’t make a tar­get. So the game design­er has to ask what kind of cog­ni­tive pro­cess­ing is being elicit­ed here? First of all, when the learn­er is pre­sent­ed with a chal­lenge and then when they received the feed­back and have to do some­thing with it. So let’s look at how those fea­tures work in the con­text of a spe­cif­ic con­struc­tion­ist game. And this one is called num­ber beads.

Diana Lau­ril­lard:
Well, the learn­ing goal here is to give learn­ers, the ear­ly learn­ers or dyscal­cu­lia of any age, that all impor­tant sense of the inter­nal struc­ture of num­bers. They have a play area here with sets of beads with dif­fer­ent tuberosi­ties. And the goal is to try and make that tar­get set at the top, the twos. And they can do this by join­ing or split­ting. Here they’ve split off some num­bers and then put them togeth­er to make twos when they start get­ting clever and they real­ize they can do two sets at a time. And so they can com­plete the run faster and get their [inaudi­ble 00:05:03].

Diana Lau­ril­lard:
Then in the next stages, we can move on to look­ing at, for exam­ple, in this sec­ond for­mat. It’s slight­ly dif­fer­ent. In this case, each of the sets has a dig­it asso­ci­at­ed with it so they can begin to make that asso­ci­a­tion between tuberos­i­ty of the num­ber of beads and the dig­it. And you can make your six­es here now in a vari­ety of dif­fer­ent ways. So adding a 5 and a 1 and then 4 and a 2, and they’ve hap­pened to have made some is, and they can do that as well. And grad­u­al­ly the rewards of these stars are build­ing up here so they can begin to see how it’s going. And then as the mechan­ics, as the game pro­gress­es, we begin to fade some of those. We take away the col­ors, we take away the beads and they’re thrust in the final stages. They’re just left with the dig­its them­selves as in this par­tic­u­lar case.

Diana Lau­ril­lard:
So it’s a way of giv­ing you a sense of what the game mechan­ic is here is what I’m try­ing to do. Is that learn­ers are able to find out, they’re able to explore how to make num­bers out of oth­er num­bers, and then begin to have a sense of their inter­nal structures.

Diana Lau­ril­lard:
So, if we men­tion the game mechan­ics of chal­lenge, response and feed­back, what we’re try­ing to elic­it is think­ing about that rela­tion­ship between giv­en sets of beads, and how you can con­struct the tar­get by join­ing and split­ting them. And then when they see what hap­pens as a result, they’re com­par­ing the sets they’ve con­struct­ed with the tar­get set. If they’re dif­fer­ent, the chal­lenge is to decide on how to make one that is like the tar­get. If they’re the same, they’ve made the tar­get and they get a new challenge.

Diana Lau­ril­lard:
So they have to reflect on how their actions made that set and how they might have to change their actions to make the tar­get. So that’s a lot of think­ing going on. And sup­pose, instead, the learn­ing the­o­ry was using a mul­ti­ple choice ques­tion mechan­ic. Well, in this case, the learn­er just has to decide which of three pos­si­ble sets must be added to give a num­ber, to make the tar­get. So the only cog­ni­tive pro­cess­ing need­ed is to decide between options A, B and C. That is, should I add a 3 or a 5 or a 6, for exam­ple. And if it’s wrong, then they have to decide between the two choic­es now left and that’s all. Now of course they may think hard about it, but that kind of com­plex ana­lyt­i­cal think­ing is not elicit­ed by the game mechan­ics. And that’s real­ly what we’re try­ing to do in any kind of game design.

Diana Lau­ril­lard:
Well, what about the cog­ni­tive goal of how do frac­tions work? Well again, using the con­struc­tion­ist approach, we try to align the game mechan­ics with the learn­ing goal. And that means again, ask­ing what kind of think­ing we want to elic­it from each of the learn­ers’ actions.

Diana Lau­ril­lard:
Well, here we’re work­ing with dif­fer­ent objects. These are unit rods and the game mechan­ic now is com­bin­ing and split­ting frac­tions of that unit to con­struct a giv­en stair­case. So we’ve got to make these rods. I’m just going to move this all a lit­tle bit here. And you can see that the game mechan­ic here then is to try and split these rods. And this is a won­der­ful device invent­ed. We have to thank Nick [inaudi­ble 00:08:30] of Caul­dron here for invent­ing this split­ter, because it’s such a pow­er­ful embod­ied way of cre­at­ing frac­tions out of frac­tions. So they’re split­ting this [inaudi­ble 00:08:39] into 3. They’re mak­ing twelfths. Twelfths was too small, so they’re putting it back togeth­er again and hav­ing anoth­er go. Got twelfths again, put it back togeth­er, be very care­ful and get eighths on you if you’ve got your small­er frac­tion. And what’s so nice about that split­ter is that it’s show­ing you that the more frac­tions you’ve got, the small­er they are, even though the num­ber in the frac­tion is big­ger. I’m not going to try and move this on a bit.

Diana Lau­ril­lard:
If I can nar­row this to some­thing like this, which is a lat­er part of the game where they have to match now the frac­tions to these sym­bol­ic rep­re­sen­ta­tions of frac­tions. Here, they’ve tried to make an eighth and I’m just… Let me pause this. So they’re try­ing to make an 8 and they’re not sure if these are eighths, so they can check by using anoth­er type of device from Nick which is a sort of ruler. And you can count how many of these we’ve got in the unit rod. And there are eight of them. So there­fore it must be an eighth and indeed it is. Okay. So you can get a sense again, that this is exact­ly the same kind of approach of design­ing the actions that elic­it think­ing about what a frac­tion is and how to make it out of oth­er num­bers. Oth­er frac­tions in this case.

Diana Lau­ril­lard:
So to sum­ma­rize all that, a Con­struc­tion­ist game pro­vides the type of Chal­lenge, Response and Feed­back, which is need­ed to elic­it the cog­ni­tive pro­cess­ing to help the learn­er achieve the objec­tive. Now, from the game design­er’s point of view, that means you start with the learn­ing goal, decide what kind of think­ing it takes to achieve it, and what kinds of game mechan­ics elic­it that think­ing. Here are the links to the two games if you’d like to try them out. Please take a look. And final­ly, I just want to say a sin­cere thank you to Caul­dron for all that won­der­ful help with turn­ing our rub­bish ideas into some­thing that real­ly works. Thank you very much.

Speak­er 2:
You’re more than wel­come. Not at all your rub­bish ideas. Your absolute­ly won­der­ful ideas. I’m always blown away by the idea of design­ing games to elic­it the brain of the per­son play­ing them. The think­ing and thought process­es that are going to change how they think about the thing you want them to think about. It’s so neat and so clever. So if you were impressed by that, just type in the Chat that impressed or some­thing like that. So Diana know you were blown away by this idea of design­ing your task to change how some­body thinks about some­thing in the first place. Now, I have-

Diana Lau­ril­lard:
The point is, Joe, that you got it. You and Nick got the idea and it just isn’t that easy nec­es­sar­i­ly if you were to get it. And that’s what we appreciate.

Speak­er 2:
Well, I just want to say that the Chat is blow­ing up with feed­back from peo­ple who’ve been watch­ing, say­ing they’re very impressed. Wow! Total­ly impressed. They’re all very impressed as well. Now I have a ques­tion for you, to what… So I get it, with math games I real­ly see it because maths aren’t… That you’re sort of play­ing with objects in your head. Could you use the same approach to design­ing lan­guage games or some­thing dif­fer­ent? What could that look like?

Diana Lau­ril­lard:
So good, because I think the basic idea of Con­struc­tion­ist is that it cap­tures how we learn from the world around us. And when Pa pert intro­duced this idea, he talked about micro worlds. And essen­tial­ly what we’re doing is we’re cre­at­ing these lit­tle worlds that behave. And as long as you can have a kind of mod­el of that world and what you’re try­ing to learn with­in it, then yes.

Diana Lau­ril­lard:
And there’s aspects of lan­guage learn­ing which are quite rule gov­erned. And I could imag­ine that you could put into that. Again, where you’re con­struct­ing parts of lan­guage to make oth­er parts of lan­guage, for exam­ple. I mean, that sort of Con­struc­tion­ist approach is more or less what we do. And then sim­i­lar­ly, you could have it in all sorts of oth­er areas, like hav­ing it if you’ve got a good mod­el of infla­tion or cash flow in a busi­ness or cli­mate change and things like that. You’ve got to have an arti­fi­cial micro world that you then manip­u­late, but that would be very straight­for­ward. I don’t think it would be so easy with things like for philo­soph­i­cal dis­cus­sion and inter­pret­ing poet­ry exact­ly. But those kinds of ideas about how you under­stand the sys­tem. Now that’s what you can use it for.

 

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Design­ing and test­ing the Con­struc­tion­ist approach to games for basic maths