In Unit 2 of the online course, we highlighted a number of “contemporary obsessions” that have the potential to support effective learning but are easily sidetracked by features that have less to do with learning math.
In our discussion of the game Sleeping Queens, we highlighted opportunities for learners to practice making several significant mathematical distinctions (P-b*). But the game is not designed to prompt attention to those distinctions (P-a; i.e., to teach them). Without the teaching component, the game merely sorts learners into those with strong strategies (who only a few want to play against) and those with weak strategies (who quickly learn to hate the game).
In this post, we highlight how a game might be adapted so that it requires learners to make the particular distinction (P-b) we want them to make. We also highlight the importance of first presenting this distinction to them (P-a). Highlighting contrasts to prompt attention (P-a) and requiring learners to make relevant distinctions comprise the the change and choice of prompting.
In the original version of the game, learners attempt to hop their frog around a circle of lily pads as quickly as possible. In the center of the circle is a collection of “parent frogs,” each with two removable eyes.
On the base of one eye is an image of little green frog; the other is blank. A player can move their frog when they choose the blank frog eye.
A pair of dice with colored sides is used to identify which frog they have to choose the eye from: If you roll red with one die and purple with the other, you have to choose an eye from the red and purple frog.
In a nutshell: Roll the dice. Find the frog with those colors. Lift an eye. If it’s blank, move one forward. If it’s not, stay put. First frog back to the big lily pad wins.
If you like, you can watch this video to get a better sense of how the game works https://www.youtube.com/watch?v=jbA_tH9Jwhc
Where’s the Math?
In its original form, this is initially a game of luck. As the game progresses, it also becomes a memory test.
A small adaptation turns it into an opportunity to practice distinguishing right from left. When setting up the parent frogs, rather than randomly placing a blank and marked eye in each frog, always put the marked frog on the same side (right or left). Now finding the eye that lets them move requires distinguishing left from right. To an adult, this may seem obvious, but it isn’t to those who haven’t yet learned to make this distinction.
Again, it’s important to first prompt to the distinction (P-a) we want them to make (P-b). If all the frogs are facing the same direction, we might first identify a reference point in the room that indicates where the safe eye is.
Following this, we might say that the safe eye is on the frog’s right. For a player facing the same direction as the frogs, the safe eye will also be on their right. For a player facing the frogs, that means the safe eye is on their left. This must be prompted through contrast (P-a). To require all players to make the relevant distinction (as opposed to just memorizing which way is safe for the duration of a game), half the frogs could face one way and half the other. That way, every time they pull an eye, they have to make the relevant distinction (P-b).
Once they’ve mastered that version of the game, we might position the frogs facing outward in a square configuration…and then a circle…and then randomly scattered.
Prior to playing the full game, it is helpful to allow learners a chance to make and test their own predictions in order to get a stronger sense of how right and left work in each configuration. That way, they can directly focus on the necessary contrasts that allow them to make the relevant distinction rather than only those that the dice dictate.