The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded pre-algebraic reasoning instruction, improves word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or one of two variants of word-problem intervention.…

Using state-representative surveys of teachers and 94 interviews with state leaders and educators from 2016 to 2019, the authors examine perceptions of the policy environments for instructional content standards in Texas and Ohio and their association with teachers' practice. They find that Texas teacher perceive their policy environments for…

Many randomized controlled experiments in the classroom have found that mathematics learning is improved dramatically when practice problems of one kind are distributed across multiple assignments (spaced) and mixed with other kinds of problems (interleaved). In two studies, we investigated students' knowledge of spacing and interleaving. In Study…

This study investigates the associations of spontaneous "dynamic gesture" and "transformational speech" with the production of "deductive proofs" in participants' reasoning about geometric conjectures (N=77). Although statistical analysis showed no significant association, the result suggests that purposefully…

Findings synthesized across five empirical laboratory- and classroom-based studies of high school and college students engaged in geometric reasoning and proof production during single- and multi-session investigations (346 participants overall) are presented. The findings converge on several design principles for computer technologies to support…

This study looks at how students embody their ideas about geometry conjectures and how those ideas travel within and between student groups. In one classroom of a Title 1 high school, students participated in a three-part program in which they: (1) played "The Hidden Village," a motion-capture video game where they assess the veracity of…

We present an embodied theory of transfer as applied to mathematical ideas. Project-based learning (PBL) offers important sites for investigating transfer because students and teachers must track mathematical invariant relations that are embedded in complex settings where knowledge and information is distributed and extended across various…

Adoption of online resources to support instruction and student performance has amplified with technological advances and increased standards for mathematics education. Because teachers play a critical role in the adoption of technology, analysis of data pertaining to how and why teachers utilize online resources is needed to optimize the design…

The practice assignments in a mathematics textbook or course can be arranged so that most of the problems relating to any particular concept are massed together in a single assignment, or these related problems can be distributed across many assignments -- a format known as spaced practice. Here we report the results of two classroom experiments…

Some elementary students may exhibit challenging externalizing or internalizing behaviors in addition to difficulty with mathematics. In this study, we explored the behavioral patterns of 441 3rd-grade students with and without mathematics difficulty (MD). Compared to students without MD, students with MD demonstrated higher rates of externalizing…

Implementation of evidence-based practices (EBPs) is paramount to students' development of mathematics proficiency. This study investigated "practice-based evidence" (Green, 2008) of interventionists' actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data…

Historically, learning for young students has occurred in formal, in-person classroom environments. But in just a matter of weeks, children were mandated to transition to a completely new mode of learning, facing new learning challenges with heightened anxieties. To this end, we aim to better understand how our learning experience design (LXD)…

We examined whether students were accurate in predicting their test performance two testing contexts (low-stakes and high-stakes). The sample comprised U.S. high school students enrolled in an advanced placement (AP) statistics course during the 2017-2018 academic year (N=209; M[subscript age]=16.6 years). We found that even two months before…

A randomized controlled trial group design study funded by IES NCR Grant R305A090527 was conducted in which 16,307 3rd, 4th, and 5th grade students in 52 school grade-level clusters were randomly assigned to receive ST Math (program revision Gen3), a supplemental mathematics software instructional intervention, or to a business-as-usual…

Effective early mathematics instruction is critical to support long-term mathematics achievement. Given that student response to typical instruction varies, a range of mathematics interventions have been developed to support foundational mathematics development. However, not all students respond to these interventions. To better understand factors…