This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

Pattern blocks are inexpensive wooden, foam, or plastic manipulatives developed in the 1960s to help students build an understanding of shapes, proportions, equivalence, and fractions (EDC 1968). The colorful collection of basic shapes in classic pattern block kits affords opportunities for amazing puzzle-like problem-solving tasks and for…

The authors introduce an educational video game (application, or "app"), "CandyFactory Educational Game," designed to promote students' development of partitive understanding of fractions while demonstrating the critical need to promote that development. The app includes essential game features of immediate feedback,…

The present study aims to examine relations between number representations and various sources of individual differences within early stages of development of number representations. The mental number line has been found to develop from a logarithmic to a more linear representation. Sources under investigation are counting skills and executive…

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of…

This article analyzes the design decisions of a team developing diagnostic assessments for a learning trajectory focused on rational number reasoning. The analysis focuses on the design rationale for key decisions about how to develop the cognitive assessments and related validity arguments within a fluid state and national policy context. The…

Linguistic relativity, the idea that language affects the way that people think, and that people who speak different languages think differently, has implications for mathematics education because people use different languages to teach, learn and practice mathematics. This paper reviews research on linguistic relativity and number, looking at…

A list number recall test in English (L2) was administered to both Japanese (L1) students with beginning-level English proficiency who attended evening high school and Japanese college students with intermediate-level English proficiency. The major findings were that, only for the high school group, the small numbers 1 and 2 in middle positions of…

This study evaluated the effects of a mathematics software program, the Building Blocks software suite, on young children's mathematics performance. Participants included 247 Kindergartners from 37 classrooms in 9 schools located in low-income communities. Children within classrooms were randomly assigned to receive 21 weeks of computer-assisted…

This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…

The purpose of the present review was to evaluate the quality of the research and evidence base for representation of problems as a strategy to enhance the mathematical performance of students with learning disabilities and those at risk for mathematics difficulties. The authors evaluated 25 experimental and quasiexperimental studies according to…

A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…

Since 2011, the Department of Basic Education (DBE), has provided all Grade 1 to 6 learners in public schools with literacy/language, numeracy/mathematics and life skills workbooks. This study provides an assessment of the purpose to which the workbooks are best suited by analysing the Grade 3 Mathematics and Home Language English workbooks for…

The focus of the present synthesis reflects the research on programs, practices, and policies intended to improve mathematics outcomes funded through the Institute of Education Sciences' (IES's) National Center for Education Research (NCER) and National Center for Special Education Research (NCSER). The authors were asked to review those published…

The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the…