Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order…

The long-term negative consequences of learning difficulties have been acknowledged. Nonetheless, research is still scarce regarding the prediction of adolescent difficulties in reading and arithmetic skills. The present study examines at which age phase and with what kind of constellation of parent- and child-related factors can adolescent…

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,…

Processing speed is divided into general (including perceptual speed and decision speed) and specific processing speed (including reading fluency and arithmetic fluency). Despite several study findings reporting the association between processing speed and children's mathematical achievement, it is still unclear whether general or specific…

The Department of Basic Education in South Africa has identified factorisation as a problem area in Mathematics teaching. Learners in earlier grades are exposed to mathematical tasks, involving concepts, such as factors of integers, fractions, equivalent fractions and prime numbers, that are easier to solve when the divisibility rules are applied.…

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…

Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic…

We examined developmental and individual differences in 6th and 8th graders' fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross-sectional design. Results indicated that the…