Mathematical self-efficacy refers to an individual's belief in their ability to successfully perform tasks and solve problems in mathematics. This Snapshot examines gender differences in mathematical self-efficacy and the levels of confidence that students feel in doing a range of formal and applied mathematics tasks. It also examines the extent…

Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like…

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…

In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being…

While research on the opportunity to learn about mathematics concepts provided by textbooks at the secondary level is well documented, there is still a paucity of similar research at the undergraduate level. Contributing towards addressing this knowledge gap, the present study examined opportunities to engage in quantitative and covariational…

Research shows that though some students can easily find the correct solutions to the problem(s) at hand, the algorithms that these students create are not always ones that would, when implemented, produce the correct solution(s). Towards shedding light on this phenomenon, the present study explicates a mechanism--accounting for features of the…

Computational thinking (CT) has received much attention in mathematics education in recent years, and researchers have begun to experiment with the integration of CT into mathematics education to promote students' CT and mathematical thinking (MT) development. However, there is a lack of empirical evidence and new theoretical perspectives on the…

Although previous research has demonstrated that the acquisition of mathematical skills requires support from multiple cognitive abilities, the associations between cognitive precursors in different domains and mathematics at different hierarchical levels among primary school children are not well understood. This study explores the cognitive…

The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

Computation competence (CC) in simple addition and subtraction using non-counting (NC) strategies is an important learning objective in Grade 1 mathematics but many children, especially low achievers in mathematics, struggle to acquire these skills. To provide these students with the support they need, it is important to have valid and reliable…

As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

There is a strong need for fifth-grade students to become proficient in mathematical problem-solving using fractional computations because it will have a lasting impact on student achievement. Traditionally, mathematics is taught inside a brick-and-mortar classroom, grounded in rote memorization of facts, rules, and formulas. In recent years, more…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…

Individuals solve arithmetic problems in different ways and the strategies they choose are indicators of advanced competencies such as adaptivity and flexibility, and predict mathematical achievement. Understanding the factors that encourage or hinder the selection of different strategies is therefore important for helping individuals to succeed…