Manipulatives are concrete or virtual objects (e.g., blocks and chips) often used in elementary grades to illustrate abstract mathematical concepts. We conducted a systematic review to examine the effects of interventions delivered with manipulatives on the learning of children with mathematics learning disabilities (MLD). The outcomes observed in the sample (N = 38) were learning, maintenance, and transfer in a variety of mathematical domains. Interventions using manipulatives were reported to be effective for a range of learning objectives (e.g., conceptual understanding and computational fluency), but several methodological weaknesses were observed. Analyses also highlighted considerable heterogeneity in the studies reviewed in terms of participant characteristics, intervention approaches, and methodology. We discuss overall effects of interventions with manipulatives in the MLD population, the methodological quality across the sample, and implications for practice.

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In Grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In Grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in Grade 3, whereas addition fluency did not. In Grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

In the current study, we used a multi-method approach to understand the quality of math homework-helping interactions between parents and their children and how parents’ and children’s own math achievement and math anxiety relate to the quality of the interaction. Forty Canadian parents and their children (ages 10–12 years; grades 5 to 7) completed self-report measures of math and general anxiety. Parents and children completed standardized assessments of math achievement and were then recorded as they engaged in a simulated math homework interaction. Coders assessed parent–child interaction quality during the interaction. Parent–child dyads generally performed well on the simulated math homework task. Nevertheless, task performance was correlated with the quality of the interaction, with high-quality interactions associated with high accuracy on the math task. Furthermore, the variability in the quality of the interaction was associated with parents’ and children’s math achievement and with the math anxiety of the children, but not the parents. Identifying the elements that influence parent–child interactions in math-related situations is essential to developing effective interventions to scaffold children’s math learning and attitudes.

Children’s emotional abilities have been shown to be related to academic performance, peer acceptance, and in-school adjustment. The main objective of this study was to evaluate the effect of innovative emotion training designed to promote the emotional abilities of 316 preschool/kindergarten children aged from 3 to 6 years old enrolled in public schools in the first three levels (L1, L2, and L3). Another objective was to examine the transfer effects on language comprehension and mathematics abilities. The emotion training (eight sessions) focused on the identification, comprehension, and expression of emotions and were co-constructed with teachers. Children were tested before and after the training on emotion, language, and mathematics skills. Results showed an improvement in emotional abilities in young children of L1 (3–4 years) and L2 (4–5 years) in the intervention group compared to those in the non-intervention group. Also, although children’s emotion basic abilities were correlated with their language comprehension and mathematics abilities, the nature of this link was not demonstrated to be causal. Findings are discussed in regard to the influence of the level and in regard to links with academic variables.