An impediment to conducting high-quality quantitative research studies in education is the paucity of valid measures of learning gains. Studies often seek to investigate students' deep, conceptual understanding yet many measures assess only surface, procedural understanding. One reason is that the development of validated measures of conceptual…

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…

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…

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…

In this article, the authors summarize results from 5 randomized controlled trials assessing the effects of intervention to improve the fraction performance of fourth-grade students at risk for difficulty in learning about fractions. The authors begin by explaining the importance of competence with fractions and why an instructional focus on…

Though research on effective instruction in math word problem solving is prominent at the middle and secondary levels, much less work has been done in elementary grades. In this article, we review the research on varied problem-solving instructional interventions at the third-grade level for students across ability levels. Third grade was chosen…

The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multicomponent fraction…

The Mathematics Mastery programme is a whole-school approach to teaching mathematics that aims to raise attainment for all pupils and close the attainment gap between pupils from low income families and their peers. The programme aims to deepen pupils' conceptual understanding of key mathematical concepts. This summary is based on two randomised…

The Mathematics Mastery programme is a whole-school approach to teaching mathematics that aims to raise attainment for all pupils and close the attainment gap between pupils from low income families and their peers. The programme aims to deepen pupils' understanding of key mathematical concepts. This evaluation assessed the impact of Mathematics…

The low level of mathematics performance of U.S. students in relation to national standards and in international comparisons has concerned educators and policy makers for many years. The authors' primary goals were to design a feasible and usable intervention and gather data on the promise of the intervention to foster students' conceptual…

The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…

The Mathematics Mastery programme is a whole-school approach to teaching mathematics that aims to raise attainment for all pupils and close the attainment gap between pupils from low income families and their peers. The programme aims to deepen pupils' conceptual understanding of key mathematical concepts. This clustered Randomised Controlled…

The authors are presently in the fourth year of a six-year, lottery-based randomized control trial (RCT) studying the effectiveness of nine Colorado charter schools that have implemented Core Knowledge®. Core Knowledge (CK) is a comprehensive K-8 curriculum for language arts, math, science, social studies, visual arts, and music that is intended…

Teaching students to use and interpret representations in science is critically important if they are to become scientifically literate and learn how to communicate their understandings and learning in science. This study involved 248 students (119 boys and 129 girls) from 26 grade 6 teachers' classes in nine primary schools in Brisbane,…