Procedural flexibility is an important skill for algebra. Although prior work has focused on measuring students' procedural flexibility using arithmetic problems, word problems may also capture students' flexibility because of their open-ended nature. To date, no published study has examined the use of word problems as another measure of…

Mathematical skills significantly predict students' educational paths. Mathematical achievement varies depending on the student's socioeconomic status (SES). However, the extent of the SES gap for specific mathematical skills remains unclear. In this cross-sectional study, we examined age variations by SES in three mathematical skills, applied…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little evidence regarding a premise of a LT approach--that to be maximally meaningful, engaging, and effective, instruction is best presented 1 LT level beyond a child's present level of thinking. We evaluated this hypothesis using an empirically validated LT…

This study tested a novel approach to capitalizing on the benefits of play for informal math learning. Two experiments evaluated a platform called "Fraction Ball," that provides an embodied, playful, and physically active learning experience by modifying the lines on a basketball court to support rational number learning. In the Pilot…

The current study investigated the relation between spatial ability and children's math performance, as well as the potential mechanisms underlying this relation including numerical magnitude knowledge, understanding of arithmetic operations, and word-problem representation. A sample of 221 Asian sixth graders (age 11, 129 boys) completed a series…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…

Many primary school students have difficulties understanding mathematical equivalence with considerably poorer performance in some countries than in others. However, students' formal understanding of equivalence has significant and long-lasting effects, as it predicts arithmetic and algebra achievement throughout school years. Currently, little is…

This study investigated relations between the distribution of practice problems in textbooks and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal…

The study tested the hypothesis that there are sex differences in the pathways to mathematical development. Three-hundred and 42 adolescents (169 boys) were assessed in various mathematics areas from arithmetic fluency to algebra across 6th to 9th grade, inclusive, and completed a battery of working memory, spatial, and intelligence measures in…

Both mathematics anxiety and metacognitive monitoring have been identified as associated with or predictive of individual differences in arithmetic achievement in primary school children. Although there are various theoretical reasons for an association between mathematics anxiety and metacognitive monitoring, it is unclear at the empirical level…

We assessed a range of theoretically critical predictors (numerosity discrimination, number knowledge, counting, language, executive function and finger gnosis) of early arithmetic development in a large unselected sample of 569 children at school entry. Assessments were repeated 12 months later. Although all predictors (except finger gnosis) were…

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…

The strategy choice model (SCM) is a highly influential theory of human problem-solving. One strength of this theory is the allowance for both item and person variance to contribute to problem-solving outcomes, but this central tenet of the model has not been empirically tested. Explanatory item response theory (EIRT) provides an ideal approach to…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

Canadian students enrolled in either French-immersion or English-instruction programs were followed from Grades 2 to 3 (M[subscript age] = 7.8 years to 8.9 years; N = 244; 55% girls). In each grade, students completed two mathematical tasks that required oral language processing (i.e., word-problem solving and number transcoding from dictation)…