Teachers have long struggled with the tension between ensuring a rigorous education for all their students and the reality that students arrive at the start of a school year with vastly different skills and conceptual understandings. The tension can be even more acute in math, which relies heavily on students mastering foundational concepts in…

Making connections within and between different aspects of mathematics is recognised as fundamental to learning mathematics with understanding. However, exactly what these connections are and how they serve the goal of learning mathematics is rarely made explicit in curriculum documents with the result that mathematics tends to be presented as a…

The virtual-representational-abstract (VRA) instructional sequence presents as a viable mathematics intervention for students with disabilities, including students with autism spectrum disorder (ASD). Yet, to date, all research has been conducted face-to-face with students. However, virtual manipulatives provide an opportunity for educators to…

As a multifaceted concept, the learning of angle concepts takes years to achieve and is beset with challenges. This paper explores how the processes of constructing and validating a learning progression in geometric reasoning can be used to generate targeted teaching advice to support the learning of angle concept. Data from 1090 Year 4 to Year 10…

Although lesson study has been shown to improve the teaching and learning of mathematics, little research has focused on reasons for engaging in it from a teacher's perspective, particularly after sustained engagement with lesson study. This qualitative study reports on thirty-three teachers from the United States who were involved in twelve…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

The International Association for the Evaluation of Educational Achievement (IEA) Research for Education series represents a further effort by IEA to capitalize on it's unique datasets, so as to provide powerful information for policymakers and researchers. Each report focuses on a specific topic and is produced by a dedicated team of leading…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

This report examines which instructional components (e.g., visual representations, use of number lines, teaching and using of mathematical language) and study features (e.g., group size, interventionist training) may have contributed to the effectiveness of intervention. In choosing to focus on instructional components and study features, the…

Visualisation is an important part of the cognitive process in mathematics. Pedagogical-psychological theoretical frameworks concerning cognitive processes consider perception and visualisation as basic conditions for the creation of correct mental imagery. This study examined visualisation as a key factor in the development of geometric concepts…

The paper presents results from the evaluation of the Teach for Bulgaria (TFB) program, which is part of the Teach for All global network. TFB activities have relevance for a variety of fast-track pathways to the teaching profession. The evaluation is based on a quasi-experimental assessment of teacher performance through student value-added…

We study an early effort amid the COVID-19 pandemic to develop new approaches to virtually serving students, supporting teachers, and promoting equity. This five-week, largely synchronous, summer program served 11,769 rising 4th-9th graders. "Mentor teachers" provided PD and videos of themselves teaching daily lessons to "partner…

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…

Mathematics related affect turn from positive to negative during comprehensive school years worldwide. There is a clear need to find solutions to the problem. However, some gaps and problems appear in the methodologies and the common approaches used in the field. This article discusses five studies addressing affective development, challenges some…

Interest has long been regarded as an important motivational construct in the learning of mathematics. It has been contended that the development of interest is directed by two control systems: an emotional and a cognitive. Under the former, students are attracted to activities that are enjoyable, whereas under the latter they consciously engage…