This study examined repeating and growing pattern knowledge and their associations with procedural and conceptual arithmetic knowledge in a sample of U.S. children (N = 185; M[subscript age] = 79.5 months; 55% female; 88% White) and adults (N = 93; M[subscript age] = 19.5 years; 62% female; 66% White) from 2019 to 2020. Three key findings emerged:…

Research distinguishes three types of arithmetic: exact arithmetic, computational estimation and approximate arithmetic. Little is, however, known about the interrelationship among these three arithmetic skills and the general cognitive and early numeracy skills that underlie these arithmetic skills. The current study investigates this…

Three rational number notations--fractions, decimals, and percentages--have existed in their modern forms for over 300 years, suggesting that each notation serves a distinct function. However, it is unclear what these functions are and how people choose which notation to use in a given situation. In the present article, we propose quantification…

Central elements of adaptive expertise in arithmetic problem solving are flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from…

We performed a meta-analysis of dual-task experiments to assess the robustness of the effects of conducting working memory secondary tasks on arithmetic performance. Four hundred effect sizes from 21 studies from 1,049 participants were analyzed across a variety of specifications. Results revealed that increases in working memory load resulted in…

People frequently encounter numeric information in medical and health contexts. In this paper, we investigated the math factors that are associated with decision-making accuracy in health and non-health contexts. This is an important endeavor given that there is relatively little cross-talk between math cognition researchers and those studying…

Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is students' tendency to apply the properties of natural numbers (inappropriately) when they are working with rational numbers (a phenomenon called "natural number bias"). Focusing on rational…

This study used a person-centered approach to examine mother-daughter dyad behaviors when jointly solving addition problems during a card game. The goal was to identify maternal and child profile behaviors during the interaction as predictors of children's autonomous addition accuracy and strategy use at the end of first grade. Videotaped…

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated…

While preschool-aged children display some skills with quantitative relations, later learning of related fraction concepts is difficult for many students. We present two studies that investigate young children's tendency of Spontaneous Focusing On quantitative Relations (SFOR), which may help explain individual differences in the development of…

Mathematical skills are becoming increasingly critical for achieving academic and professional success. Developmental dyscalculia (DD) is a childhood-onset disorder characterized by the presence of abnormalities in the acquisition of arithmetic skills affecting approximately 5% of school age children. Diagnosing students with possible dyscalculia…

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…

The authors used a multiple-probe, across-tasks design to evaluate the effects of a classwide, multicomponent intervention on first-grade students' addition-fact fluency. Intervention components included "cover, copy, and compare," a 2-min math sprint, and a weekly group reward. Results showed that classwide digits correct per minute averages…

Researchers debate whether one represents the magnitude of a fraction according to its real numerical value or just the discrete numerosity of its numerator or denominator. The present study examined three effects based on the notion that people possess a mental number line to explore how children represent fractions when they compare fractions…

Besides cognitive factors, children's learning at school may be influenced by more dynamic phenomena, such as motivation and achievement-related task-avoidant behavior. The present study examined the developmental dynamics of task-avoidant behavior and math performance from kindergarten to Grade 4. A total of 225 children were tested for their…