I had the pleasure this evening of attending a lecture on preschool math education by Dr. Robert Siegler, who is a visiting professor at my grad school alma mater, Teachers College, Columbia University.  Math is my favorite educational topic in children’s games, because I hated math so much as a student.  I can really identify with students’ frustration and confusion, and I think that makes me a better designer of math games.  I came to the lecture hoping to hear tips on ways math topics can be presented, so I could use them in designing games.  I was pleasantly surprised when he began to present research on board games similar to Chutes and Ladders and Candy Land.  I blogged about this research back in August, but I had forgotten Dr. Siegler’s name, and my invitation to the lecture didn’t say anything about games.

In the United States, there is a correlation between a child’s socio-economic status and his or her eighth grade math achievement scores.  This is not as true in Canada, Germany, Sweden or Japan.  In the US, differences increase with schooling.  In other words, preschoolers in poor communities test behind preschoolers in wealthier communities, and the gap only gets bigger as students progress through school.  What can we do to lessen this gap in the US, and at what grade level should this problem be addressed?

Siegler argues that we need to correct this problem in preschool.  Sample number line estimation taskStatistics show that if you start behind, you stay behind.  It is important to improve preschool students’ understanding of numerical magnitudes, or meanings.  A kid who can count from 1 to 10 may not know which is bigger, 6 or 4.  We need to help children create a linear representation of numerical magnitudes.  Students should be able to perform well on number line estimation tasks (see illustration).  These tasks allow assessment of relation between numbers and magnitude.  Chinese kindergartners are ahead of US kindergartners in number line estimation.

Playing numerical board games might play a crucial role in forming numerical magnitude understanding.  The greater number a game token reaches, the greater number of discrete movements the child has made, spoken, moved in distance, and time spent playing. Thus, playing the game provides visuospatial, kinesthetic, auditory, temporal cues to numerical magnitudes.  Students who played a number board game (similar to Chutes and Ladders) did far better on four math tasks than students who played a color board game (similar to Candy Land). 

What features of board games are critical to student learning?  Siegler & Ramani (2009) studied linear counting board games, and circular counting board games, both clockwise and counterclockwise.  They found that linear board games are much better for the improvement of numerical understanding, addition, and other math skills.  Perhaps most encouraging of all, children who started out testing the worst showed significant improvement in post-tests after playing linear counting board games.
Siegler & Ramani also discovered that it matters how you play the game.  Counting on from where the player was on the board (i.e., 32, 33, 34, 35) led to more improved skills than counting from one each roll.  Playing the game with students four times was enough to have significant effect on math skills.

Implications for game design: Siegler recommended exposing kids to numbers bigger than 20 in preschool.  Instead, we should go up to 100.  Video games, and adults playing board games with children, should count on when possible, rather than counting from one each time.  The child can count along from one with their fingers, if it helps the child to keep track of how many numbers they’ve counted off.

This article was also a featured post on gamasutra.com.

According to a recent article in Ed Week, research at Carnegie Mellon University and University of Maryland showed that preschoolers who played Chutes and Ladders showed significant improvement in math skills. Another experimental group in the study played a different board game, and a third group did non-game math activities. The children who had played Chutes and Ladders demonstrated greater understanding of numbers and numerical magnitude. The Ed Week article also says this group did best in the post-test of "learning to learn" new arithmetic tasks. The study was published in the Journal of Educational Psychology. I have not read it myself yet, but I look forward to doing so the next time I'm at my alma mater's library. I'm very curious to learn more about this measure of "learning to learn" new arithmetic tasks.

The article also mentions that previous research by the same team, Robert S. Siegler and Geetha B. Ramani, showed no such improvements among children who played Candy Land. How interesting!

I confess that although I did play both of these games as a child, I had to search for images on Flickr to jog my memory. The Chutes and Ladders board is a grid of 100 squares, which is a great visual representation of counting 10s, 20s, 30s, 40s, etc. You move by rolling a die, so the game play is accessible to any child who can count to six, and yet players are still exposed to the idea of higher numbers as they progress on the track.

Candy Land, on the other hand, has no numbers in it at all. The path on the board is made of different colored spaces. You do not roll a die to play. Instead, there is a deck of cards with different colors on them. On your turn, you draw a card and proceed to the next space on the path that matches the color you drew. The game does not encourage you to count at all, even as you move your piece from one spot to the next!

This is an excellent demonstration of how a simple design change can greatly influence the experience a player has.

Chutes and Ladders image courtesy of shawnblog.  Candy Land image courtesy of daveparker.