Math problem solving frequently involves choices among alternative strategies. Strategy choices, and effects of problem features on strategy choices, both vary among individuals. We propose that individual differences in strategy choices can be well characterized in terms of parametric variation in three types of influence: global bias, relevant…

Motivated by a curriculum privileging number-based strategies but national tests highlighting students' reliance on standard algorithms, this study analyses 2,216 Danish Grade 3, 6 and 8 students' solutions to various multidigit arithmetic tasks, each designed to elicit shortcut strategies, against background variables including sex, ethnicity and…

We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as…

Self-regulatory efficacy (SRE) among elementary school children is of interest because pupils' self-regulation capacities and SRE influence in managing learning situations. This study investigated variations in the four sources of SRE and how these variations were related to SRE, reading skills and arithmetic skills. The participants were 1284…

Language skills play an important role in mathematics development. Students (7 to 10 years of age) learning school mathematics either in the same language used at home (first-language learners; n = 103) or in a different language (second-language learners; n = 57) participated in the study. Relations among cognitive skills (i.e., receptive…

We examined the contribution of a major predictor of basic literacy ability--phoneme awareness--to individual differences in two arithmetic computation tasks: a speeded task consisting of simple computation problems (arithmetic fluency) and an untimed, more complex computation task involving multi-digit operands (numerical operations). The…

This 13-month longitudinal study investigated whether different phonological processing components independently predicted individual differences in Chinese word reading and arithmetic. Three phonological processing skills [phonological awareness, phonological memory, and rapid automatized naming (RAN)], word reading, and arithmetic were assessed…

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…

Digit comparison is strongly related to individual differences in children's arithmetic ability. Why this is the case, however, remains unclear to date. Therefore, we investigated the relative contribution of three possible cognitive mechanisms in first and second graders' digit comparison performance: digit identification, digit--number word…

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children's individual differences in mathematics achievement. However, research into the predictors of children's individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We…

The present study tested the hypothesis that children's 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…

In the present study we examined whether children with Developmental Dyscalculia (DD) exhibit a deficit in the so-called "Approximate Number System" (ANS). To do so, we examined a group of elementary school children who demonstrated persistent low math achievement over 4 years and compared them to typically developing (TD), aged-matched…

The purpose of the study was to determine whether individual differences in at-risk 4th graders' language comprehension, nonverbal reasoning, concept formation, working memory, and use of decimal labels (i.e., place value, point, incorrect place value, incorrect fraction, or whole number) are related to their decimal magnitude understanding.…

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…

In this paper we investigated the contribution of a dynamic testing procedure, including multiple graduated prompts protocols, in identifying differences in need for instruction of second grade children (N = 120) with arithmetic difficulties. The training was adaptive and prompts were provided according to one of six protocols, each focusing on a…