Discussions about power have only recently begun to appear in the learning sciences literature. Most of this important work takes a critical perspective; the present work complements these efforts by examining power sharing as a catalyst for empowerment in teacher-researcher co-design. Even though teacher-researcher collaborations are discussed in…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

While symbolic number processing is an important correlate for typical and low mathematics achievement, it remains to be determined whether children with high mathematics achievement also have excellent symbolic number processing abilities. We investigated this question in 64 children (aged 8 to 10), i.e., 32 children with persistent high…

The present study tested the learning avoidance model by examining the degree to which learning avoidance in various afterschool settings mediated the negative association between math anxiety and math achievement. Participants consisted of 207 third to sixth graders. Using a path model, findings showed that students' math anxiety was negatively…

Students' understanding of the meaning of the equal sign develops slowly over the primary grades. In addition to updating their representations of equations to recognize that the equal sign represents an equivalence relation rather than signaling an operation, students need to move beyond full computation to efficiently solve equivalence problems.…

We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's "spontaneous" additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses…

This study presents the results of a series of design experiments that aimed to engage twelve fourth-grade students in mathematical activity exploring the volume of right prisms and cylinders as a dynamic sweep of a surface through a height, an approach that is referred to as Dynamic Measurement for Volume (DYME-V). This article describes this…

Proportional reasoning is a key topic both at school and in everyday life. However, students are often misled by their preconceptions regarding proportions. Our hypothesis is that these limitations can be mitigated by working on alternative ways of categorizing situations that enable more adequate inferences. Multiple categorization triggers…

Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…

Learning fractions poses a challenge for many elementary school students, including applying fraction knowledge in novel contexts. For instance, there are substantial individual differences in students' tendency of spontaneous focusing on quantitative relations (SFOR), which is related to the development of rational number knowledge. In this…

The statistical properties of data are not present in any individual value, but rather, emerge only by perceiving the set as a whole. Summarizing the statistical properties of sets (e.g., creating ensembles) is ubiquitous in cognition, yet one unanswered question is how this process changes over development. The properties of number sets (e.g.,…

The study of water as a K-12 science idea often divorces its properties from its deeply politicized history as a resource that has been limited, compromised, and intentionally withheld from nondominant communities. Although a robust body of scholarship has aptly critiqued decontextualized and depoliticized pedagogies and called for critical…

The present study had two aims. First, we set out to evaluate the structure of processing speed in children by comparing five alternative models: two conceptual models (a unitary model, a complexity model) and three methodological models (a stimulus material model, an output response model, and a timing modality model). Second, we then used the…

There is now wide consensus that the quality of family relationships is involved in the development of child executive functioning (EF), a set of cognitive skills that bear critical importance for social and academic adjustment at school. This body of research has, however, focused almost exclusively on dyadic parent-child interactions and failed…

Number lines and area models are both used pervasively in teaching fractions. Prior studies found that second and third graders demonstrated better magnitude knowledge of proper fractions after a 15-minute training using the number line as compared to using the area model. The current study aimed to extend these findings to improper fractions. We…