The importance of mathematical problem solving (MPS) has been widely recognized. While there has been significant progress in developing and studying interventions to support teaching and learning MPS for students with disabilities, the research on how to accurately and effectively assess the impact of those interventions has lagged, leaving a gap…

When children are aged around 2 years, many of the early foundations of mathematical skills are developing. Understanding this is important to shed light on theories of mathematical development. Nevertheless, little research has investigated 2-year-olds' early mathematical abilities, with most research focussing on either infants (aged 0-1 years)…

Adaptive tutoring systems often model student knowledge in ways that break away from a "one size fits all" approach to learning. Nonetheless, the strengths of these systems can often be limited, as knowledge representations are not easily interpreted by teachers, which make these systems difficult to integrate into pedagogical practices.…

Example-generation tasks have been suggested as an effective way to both promote students' learning of mathematics and assess students' understanding of concepts. E-assessment offers the potential to use example-generation tasks with large groups of students, but there has been little research on this approach so far. Across two studies, we…

Substantial research has explored the connection between children's spontaneous focusing on numerosity (SFON) and their current and later mathematical achievement. However, the findings have been inconsistent, and no comprehensive investigation has yet been conducted. This meta-analysis examines the relation between SFON and mathematics…

The School of Engineering of the Polytechnic of Porto (ISEP) has embraced the DrIVE-MATH project, since September 2017. Active-learning (AL) techniques were implemented in several Math courses, namely Linear Algebra and Analytic Geometry, Probability and Statistics, Statistical Models, Computational Mathematics, and Differential and Integral…

The development of a set of rubrics for teachers and curriculum designers interested in the quality of numeracy tasks emerged from our struggle with an attempt to clarify the distinction between numeracy and mathematics. Shifting our perspective from asking what numeracy and mathematics are to asking what they are about led to the…

Mathematical geometrical (MG) concept is often perceived as abstract and difficult to understand by students at the TVET College. Students are unable to perform well in Mathematic Assessments Tasks specifically on this concept. Drawing from this is the declining percentages of student enrolments in mathematics at National Qualification Framework…

The research aimed to analyze the students' abilities in solving realistic mathematics problems using "What-If"-Ethnomathematics Instruments with content focused on plane and space materials. The "What-If"-Ethnomathematics instruments are instruments that enable educators to analyze various errors and obstacles experienced by…

Arithmetic fluency is regarded as a foundational math skill, typically measured as a single construct with pencil-and-paper-based timed assessments. We introduce a tablet-based assessment of single-digit fluency that captures individual trial response times across several embedded experimental contrasts of interest. A large (n = 824) cohort of…

Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic…

Assessment is essential for teaching and learning mathematical concepts. Teachers' and learners' understanding of how assessment is to be conducted in mathematics classrooms will guide what is to be taught and learnt and how teaching and learning will be conducted. The researchers' assertion is that circle geometry lessons require thinking-based…

In order to identify the potential benefits and challenges of implementing student portfolios as quality mathematics assessment, a pilot study was conducted with teachers in various secondary school settings. The multi-case study consisted of five teacher participants from geographically and demographically differing contexts, four in the USA and…

This book provides an introduction to what it means to be numerate, and how numeracy can best be developed and nurtured in children and in adults. It also presents a cohesive coverage of numeracy development from early childhood to adulthood. This book draws on international research and practice to provide a comprehensive overview on the topic.…

We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…