Playing board games and other math activities can provide young children with opportunities to develop their math skills. However, it is critical to understand for whom these activities may be most beneficial. In two studies, we examine the extent to which foundational cognitive skills moderate the effects of playing math games on math skills. In…

Understanding of the complement principle has been proposed as closely related to computational skills, but few studies have investigated their interrelations. The present longitudinal study attempted to clarify the picture by examining their potential cross-lagged relation. Fourth graders (n = 221) in Hong Kong received 3 cognitive assessments at…

Finger gnosia and fine motor skills (FMS) are assumed to play a key role in the development of arithmetic abilities, but their contribution to early numerical skills (i.e., enumeration skills and cardinality) has received little attention so far. The purpose of this study was to investigate the predictive value of finger gnosia and FMS to…

Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs. 3 of 4 apples), but have considerable difficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., "1/5" vs. "3/4"). Theoretically, reducing the gap between representations of implicit versus explicit proportions…

Prior research has revealed robust and consistent relations between spatial and mathematical skills. Yet, establishing a causal relation has been met with mixed effects. To better understand whether, to what extent, and under what conditions mathematics performance can be improved through spatial training, we conducted a systematic meta-analysis…

We investigated the effectiveness of a sustained and spiraled content literacy intervention that emphasizes building domain and topic knowledge schemas and vocabulary for elementary-grade students. The model of reading engagement intervention underscores thematic lessons that provide an intellectual structure for helping students connect new…

Plausible competing developmental models show similar or identical structural equation modeling model fit indices, despite making very different causal predictions. One way to help address this problem is incorporating outside information into selecting among models. This study attempted to select among developmental models of children's early…

Young children have informal knowledge of fractions before learning about fraction symbols in school. In the current study, we followed 103 children in the Mid-Atlantic United States from the fall to the spring of first grade to characterize the development of individual differences in early informal fraction knowledge, as well as its relation to…

Fractions are a challenging mathematics topic for many elementary and middle school students, and even for adults. However, a growing body of developmental research suggests that young children can reason about visually presented proportions, well before fraction instruction, providing insight into how fractions might be introduced to improve…

The aim of the present study was to examine the kinds of developmental profiles of arithmetic fluency skills that can be identified across Grades 1-9 (ages 7-16) in a large Finnish sample (n = 2,518). The study also examined whether membership in the developmental profiles could be predicted using a comprehensive set of kindergarten-age factors,…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use "partitioning": Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on…

Parents provide motivational and cognitive support within the same interaction, yet researchers have investigated these separately. We examined two key aspects of parental support, praise (motivational support) and spatial language (cognitive support), from fathers and mothers during three tasks with their first-grade children (6-7-year-olds; N =…

The sustaining environments hypothesis theorizes that the lasting effects of PreK programs are contingent on the quality of the subsequent learning environment in early elementary school. The current study tests this theory by leveraging data from students (N = 462) who did and did not enroll in the Boston Public Schools (BPS) prekindergarten…

Research has shown that two different, though related, ways of representing magnitude play foundational roles in the development of numerical and mathematical skills: a nonverbal approximate number system and an exact symbolic number system. While there have been numerous studies suggesting that the two systems are important predictors of math…

Early spatial skills predict the development of later spatial and mathematical skills. Yet, it is unclear how comprehension of the words that capture spatial relations, words like behind and under, might be associated with children's early spatial and mathematics skills. The current study addressed this question by conducting a moderated mediation…