Playing Linear Number Board Games Improves Children's Mathematical Knowledge
Author: Siegler, Robert S.
Date: 2009-00-00
Type: Reports - Research
Subjects: Feedback (Response),Disadvantaged Youth,Learning Strategies,Pretests Posttests,Child Care Centers,Arithmetic,Mathematics Instruction,Games,Teaching Methods,Mathematics Skills,Mathematical Concepts,Numbers,Recall (Psychology),Preschool Children,Computation,Comparative Analysis

The present study focused on two main goals. One was to test the "representational mapping hypothesis": The greater the transparency of the mapping between physical materials and desired internal representations, the greater the learning of the desired internal representation. The implication of the representational mapping hypothesis in the present context is that if the desired internal representation of numerical magnitudes is a linear number line, then playing the number game with a linear board should promote greater learning of numerical magnitudes than playing the identical game with a circular board. A second major goal of this study was to test the prediction that forming a linear representation of numerical magnitudes should improve young children's ability to learn answers to arithmetic problems. Linear representations of numerical magnitudes seem likely to help children learn arithmetic because such representations maintain equal subjective spacing throughout the entire range of numbers, thus facilitating discrimination among answers to different problems. Consistent with this perspective, linearity of number line estimates is positively correlated with arithmetic proficiency among first through fourth graders (Booth & Siegler, 2006; 2008). Thus, playing the linear number board game was expected to produce greater subsequent ability to recall the answers to arithmetic problems following instruction in them; it also was expected to produce errors on the arithmetic problems that were closer to the correct answer. The research was conducted at seven Head Start centers and two child care centers in Pittsburgh, Pennsylvania. Participants were 88 preschoolers (56% female), ranging in age from 4 years 0 months to 5 years 5 months (M = 4 years 8 months, SD = 0.47). The data were consistent with both hypotheses. On the number line estimation task, linearity, slope, and accuracy were all greater on the posttest for those who played the game with the linear board than for those who played it with the circular board. Mean percent variance accounted for by the best fitting linear function for each child increased significantly from 14% to 39% among children who played the linear board game; it increased non-significantly from 15% to 21% among those who played the circular game. Differences between groups were not significant on the pretest but were significant on the posttest. On the magnitude comparison task, percent absolute error improved from pretest to posttest among children who played the game with the linear board (29% to 21%) and also among those who played the game with the circular board (29% to 26%). The results did not differ on the pretest, but children who played the linear game were more accurate on the posttest. Even more striking was the learning to learn effect in arithmetic: Children who earlier had played the linear board game learned more from subsequent practice and feedback on addition problems than children who earlier had played the circular board game (45% versus 30% correct posttest responses). Their errors were also closer to the correct answer than were the errors of children in the circular board game condition.