This study examined the effects of training involving spatial versus nonspatial representations of numerical magnitude for promoting arithmetic fluency. The key goal was to advance theoretical understanding of the relation between spatial and math learning, while simultaneously laying the groundwork for the development of future educational…

Effective classroom management is critical to supporting student learning and success in school. However, little research has focused specifically on the impact of classroom management on student mathematics achievement, especially in the early elementary grades or in a small group (i.e., Tier 2) context. To address this need we investigated the…

A concerning number of students enter kindergarten facing an intractable variation of mathematics difficulties (MD). This study investigated the impact of an explicit, core kindergarten mathematics program on the mathematical outcomes of kindergartners who demonstrated severe MD at kindergarten entry and examined whether these students improved…

Evidenced-based mathematics interventions are critical for supporting students with mathematics difficulties. In research and practice, collecting implementation fidelity is important for ensuring that all the core components of the intervention are implemented as designed. Historically, implementation fidelity has been defined as multi-faceted…

This observation study documents the amount and quality of mathematics instruction provided to students with intellectual and developmental disabilities in kindergarten through second grade in self-contained special education settings. We observed six special education teachers and their students (N = 12) during a total of 967 min allotted to…

Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children's…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

We tested whether mental rotation training improved math performance in 6- to 8-year-olds. Children were pretested on a range of number and math skills. Then one group received a single session of mental rotation training using an object completion task that had previously improved spatial ability in children this age (Ehrlich, Levine, &…

Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…

We investigated the relation between children's numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children's magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and…