A solid understanding of fractions is the cornerstone for acquiring proficiency with rational numbers and paves the way for learning advanced mathematical concepts, such as algebra. Fraction difficulties limit not only students' educational and vocational opportunities but also their ability to solve everyday problems. Students who exit 6th grade…

This secondary analysis of data from a randomized control trial of an early mathematics intervention, ROOTS, explored whether patterns of intervention response were best categorized by the typical response/non-response binary or a more complex framework with additional response profiles. Participants included kindergarten students at risk for…

Many public and private initiatives have focused on improving prekindergarten (PK) through Grade 12 mathematics education, given that the mathematics content learned before college is foundational for later learning and college success across STEM subjects. Although decades of educational research have studied PK-12 mathematics interventions, the…

In basic regression discontinuity (RD) designs, causal inference is limited to the local area near a single cutoff. To strengthen the generality of the RD treatment estimate, a design with multiple cutoffs along the assignment variable continuum can be applied. The availability of multiple cutoffs allows estimation of a pooled average treatment…

In basic regression discontinuity (RD) designs, causal inference is limited to the local area near a single cutoff. To strengthen the generality of the RD treatment estimate, a design with multiple cutoffs along the assignment variable continuum can be applied. The availability of multiple cutoffs allows estimation of a pooled average treatment…

We report the results of a preregistered, cluster randomized controlled trial of a mathematics learning intervention known as interleaved practice. Whereas most mathematics assignments consist of a block of problems devoted to the same skill or concept, an interleaved assignment is arranged so that no 2 consecutive problems require the same…

The provision of high-quality early mathematics instruction and intervention is critical to ensure that all students are on track for academic success. Given this, identifying and utilizing assessments that can enable the detection of nonresponse to mathematics instruction is a critical aspect of early intervention. To this end, the current study…

We report the results of a pre-registered, cluster randomized controlled trial of a mathematics learning intervention known as interleaved practice. Whereas most mathematics assignments consist of a block of problems devoted to the same skill or concept, an interleaved assignment is arranged so that no two consecutive problems require the same…

Teacher professional development and in-class mentors were used to support structured inquiry with math manipulatives. Twenty-four primary schools (n = 6,628 students) were randomly assigned to treatment and control groups as an experimental field trial to examine the effectiveness of this instructional approach in a scaled-up application in…

Pathblazer is a supplemental, online intervention program that helps struggling learners in grades K-8 achieve grade-level proficiency in mathematics and reading. It offers students individualized learning progression paths with fun, motivating content that addresses skill and concept gaps. Using existing student data or results from a screener,…

The authors recently conducted a randomized controlled trial that showed a significant impact of teachers' lesson study, supported by mathematical resources, on both teachers' and students' understanding of fractions. The research and mathematical resources are described in the second part of this article. First the authors examine some of the…

We develop a theoretical and empirical basis for the design of teacher professional development studies. We build on previous work by (a) developing estimates of intraclass correlation coefficients for teacher outcomes using two- and three-level data structures, (b) developing estimates of the variance explained by covariates, and (c) modifying…

The current study employed a randomized controlled trial to evaluate the use of peer tutoring and fluency-based instruction to increase mathematics fluency with addition and subtraction computation skills. Forty-one elementary school students between the ages of eight and 12 years participated in the 8-week study using cross-age peer tutoring, Say…

To what degree can multilingual students profit from bilingual teaching approaches, even when they lack experience in the academic or technical register in their home languages? This study explores this research question in a mixed methods design for a German/Turkish bilingual intervention aimed at fostering conceptual understanding of fractions…

Background: Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. Aims: This study evaluated the effect of instruction on a math…