Elida V. Laski

Learning from number board games: you learn what you encode.

We tested the hypothesis that encoding the numerical-spatial relations in a number board game is a key process in promoting learning from playing such games. Experiment 1 used a microgenetic design to examine the effects on learning of the type of counting procedure that children use. As predicted, having kindergartners count-on from their current number on the board while playing a 0-100 number board game facilitated their encoding of the numerical-spatial relations on the game board and improved their number line estimates, numeral identification, and count-on skill. Playing the same game using the standard count-from-1 procedure led to considerably less learning. Experiment 2 demonstrated that comparable improvement in number line estimation does not occur with practice encoding the numerals 1-100 outside of the context of a number board game. The general importance of aligning learning activities and physical materials with desired mental representations is discussed.

What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education

Manipulatives are ubiquitous in early childhood classrooms; yet, findings regarding their efficacy for learning mathematics concepts are inconsistent. In this article, we present four general principles that have emerged from cognitive science about ways to ensure that manipulatives promote learning when used with young children. We also describe how Montessori instruction offers a concrete example of the application of these principles in practice, which may, in turn, explain the high levels of mathematics achievement among children who attend Montessori programs during early childhood. The general principles and concrete examples presented in this article should help early childhood programs maximize the benefits of using manipulatives for developmentally appropriate mathematics instruction.

Computational fluency and strategy choice predict individual and cross-national differences in complex arithmetic.

The present study tested the hypothesis that childrens fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that differed in difficulty: single-, mixed-, and double-digit addition. Childrens strategy use varied as a function of problem difficulty, consistent with Sieglers theory of strategy choice. The use of decomposition strategy interacted with computational fluency in predicting the accuracy of double-digit addition. Further, the frequency of decomposition and computational fluency fully mediated cross-national differences in accuracy on these complex arithmetic problems. The results indicate the importance of both fluency with basic number facts and the decomposition strategy for later arithmetic performance.

Here, but not there: Cross-national variability of gender effects in arithmetic

The current study examined gender differences in arithmetic performance among first graders from the United States, Russia, and Taiwan. Children (N=250, Mage=7 years 2 months) solved simple (single-digit) and complex (mixed- and double-digit) addition problems and explained their strategies. On simple problems, there were gender differences in strategies that varied across countries but no differences in accuracy. On complex problems, there were gender differences among American and Russian students in strategy use that mediated differences in accuracy. In contrast, among Taiwanese students, there were no gender differences in strategies or accuracy. The pattern of results suggests that educational context may play a role in gender differences in mathematics.

Distinct Pathways From Parental Beliefs and Practices to Children’s Numeric Skills

ABSTRACT It is imperative to identify contextual factors contributing to the development of early math skills, considering their role in later academic achievement. To pursue this goal, the present study investigated the paths connecting parental beliefs and practices during the preschool years to children’s numeric skills at the end of kindergarten (N = 98). Results were consistent with theoretical predictions of specific relations between particular types of parental input and different aspects of number knowledge. Direct math learning activities mediated the relation between parental beliefs and children’s number identification skills. Daily activities involving quantitative components mediated the relation between parental beliefs and children’s numerical magnitude understanding. Both types of activities predicted arithmetic skills that integrate the basic aspects of symbolic number knowledge. These findings contribute to developmental theory by specifying how characteristics of children’s environments are related to particular aspects of their development, which is critical for informing intervention work to improve early math skills.

Not Sure Which Rubric to Use? Consider Cognitive Science Principles of Learning

Abstract The author describes two general principles of learning that have emerged from cognitive science and argues that analytic rubrics that capture these aspects may be particularly effective as instructional and assessment tools.

Development of children’s early understanding of numeric structure

Understanding of the base-10 structure of multi-digit numbers is one of the critical aspects in early mathematics learning. It has been documented that children from different countries vary in their use of base-10 representations. Questions concerning potential sources of this variability have been debated for decades. One commonly posited explanation is that some languages provide explicit cues about the structure of multi-digit numbers, facilitating the development of base-10 representations. In the present study, we tested this view against an alternative view, positing that variability in children’s learning of numeric structure may reflect differences in their experiences with numbers. The study examined kindergartners and first-graders from four countries: Taiwan, South Korea, the USA, and Russia. Results showed that the use of base-10 representations by American first-graders increased dramatically over the last decades, following changes in curricular guidelines. First-graders across the four countries showed some differences in performance (however, not consistent with the language account), whereas kindergartners performed comparably despite the differences in their languages. The results suggest that the nature of early math instruction may be critical for children’s developing understanding of numeric structure.

Arithmetic Accuracy in Children From High- and Low-Income Schools

This study investigated income group differences in kindergartners’ and first graders’ (N = 161) arithmetic by examining the link between accuracy and strategy use on simple and complex addition problems. Low-income children were substantially less accurate than high-income children, in terms of both percentage of correctly solved problems and the magnitude of errors, with low-income first graders being less accurate than high-income kindergartners. Higher-income children were more likely to use sophisticated mental strategies than their lower-income peers, who used predominantly inefficient counting or inappropriate strategies. Importantly, this difference in strategies mediated the relation between income group and addition. Examining underlying strategies has implications for understanding income group differences in arithmetic and potential means of remedying it via instruction.