*Diana Laurillard, UCL**@thinksitthrough*

##### Full Transcript:

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.