Early Career Outstanding Paper Award

Learning from number board games: You learn what you encode

This paper offers a concrete technique for improving young children's mathematical knowledge, within a theoretical framework, that can inform the design of instructional interventions. 

By Elida Laski

This article (Laski & Siegler, 2014), which was published in Developmental Psychology , serves as an exemplar of how developmental theory and knowledge can be applied to improve instruction and child outcomes. It integrates empirical findings across developmental psychology – from knowledge about analogical reasoning to the role of encoding in forming mental representations – to offer a theoretical framework for describing and predicting which experiences are most likely to promote learning.

The research reported in the article grew out of work conducted by Robert Siegler and Geetha Ramani that demonstrated that playing a linear number board game that included the numbers 1-10 led to substantial improvements in the numerical understanding of preschoolers from low-income, urban backgrounds. The game was pretty simple and the control groups in previous studies ruled out several plausible alternative interpretations, but they left unclear why the game was so effective. Laski and Siegler went a long way toward answering this question, as well as extending the research to somewhat older children and to a much larger range of numbers (0-100) than had been examined in previous research.

Informed by the Cognitive Alignment Framework she developed, Laski was able to predict and demonstrate the value of a simple manipulation for children's learning from number board games. She hypothesized that the effectiveness of number board games was due to the counting-on procedure, which was required in the game, promoting encoding of the numbers in the squares of the board that otherwise might not be encoded by such young children. The experimental manipulation was elegant. Children in the experimental condition counted on as in past number board game studies from whatever number their token occupied. For example, if their token was on 38, and they spun a 4 on the spinner, they needed to count, “39, 40, 41, 42.” If they were unable to do so, the experimenter counted for them and then had them repeat the counting. Children in the control condition played the identical game for identical time periods, but counted from 1. If they were on 38 and rolled a 4, they would count “1, 2, 3, 4.”

Laski found that relative to the control group, posttest performance of children who counted-on from the location of their token were superior in number line estimation, number identification, counting on, and encoding of the location of numbers on the board. Perhaps most important for the underlying theory, posttest encoding accuracy fully mediated the treatment effect. Given that the Cognitive Alignment Framework emphasized the importance of ensuring children encode key features in materials – in this case, encoding numbers in order to link numerical and spatial cues – this was a very important finding. The results of the study also indicated that the game was effective with a broader range of numbers than had been previously examined, 0-100 rather than 0-10, and with somewhat older children, 6-year-olds versus 4-year-olds.

A second experiment in the study demonstrated that simply counting-on with the same numbers outside of the board game context did not produce comparable gains. The experimental condition in this study involved children playing the board game as in the counting from one condition, and then separately counting the numbers from 0-100 from cards, with each card having from 1-5 numbers on it (“e.g., 39, 40, 41, 42.”) Mistakes that children made were corrected, and children required to count correctly, as in the counting-on condition of the prior experiment. As hypothesized, this condition led to improved numeral identification and counting-on skill, but did not lead to improved encoding or to improved understanding of numerical magnitudes. This further supported the underlying theory that the board game exercised its positive effects by counting-on leading to improved encoding of numbers and their spatial positions, which in turn led to improved knowledge of numerical magnitudes.

The paper offers a concrete technique for improving young children's mathematical knowledge, and does so within the context of a larger theoretical framework, that can inform the design of instructional interventions within and outside the field of developmental psychology. 

In fact, within just one year of being published the Cognitive Alignment Framework has already been used to successfully predict the kinds of instructional interactions that facilitate children's patterning performance (Collins & Laski, 2015; Fyfe, McNeil, Rittle-Johnson, 2015). Consequently, it was awarded the Early Career Outstanding Paper Award for its potential to broadly impact the field.

References

Collins, M. A., & Laski, E. V., (2015). Preschoolers' strategies for solving visual pattern tasks. Early Childhood Research Quarterly, 32, 204-214.

Fyfe, E., McNeil, N. M., & Rittle-Johnson, B. (2015). Easy as ABCABC: Abstract language facilitates performance on a concrete patterning task. Child Development, 86, 927-935.

Laski, E.V., & Siegler, R. S. (2014). Learning from number board games: You learn what you encode. Developmental Psychology, 50 (3), 853-864.