In recent years, science, technology, engineering and mathematics (STEM) approaches in education have received growing attention in the political arena and in educational research and practice. A concern consistently raised in the research literature regarding interdisciplinary STEM education is that the role played by mathematics is understated…

The production and use of explicit models of mathematics are important elements of research in Didactics of Mathematics. In this paper, we present and compare two different European approaches to didactical modelling. The first, centred around the notion of basic idea (Grundvorstellung), arose in German-speaking countries as a development within…

This paper presents a synthesis of the literature exploring the teaching and learning of geometry and the role that mathematical representations can play in enriching geometry experiences for our students. Geometry is the only content domain to be taught in all PK-12 grades, however, from historical trends in international assessment data, it…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

The concrete-representational-abstract (CRA) approach is an instructional framework for teaching math wherein students move from using concrete materials to solve problems to using visual representations of the materials, and finally abstract concepts. This study provides a literature synthesis and meta-analysis of the effectiveness of the CRA…

This article draws from Hiroko Kawaguchi Warshauer's conceptualisation of productive struggle, which capitalises on experiences that elicit struggle, that is, those that require students to 'expend intellectual effort' and that are productive, in the sense that they seek to 'advance thinking and deepen' understanding of mathematical concepts and…

Big Ideas can be seen as overarching concepts that occur in various mathematical topics and strands within a syllabus. Within our project on Big Ideas in School Mathematics, we developed instruments to measure two Big Ideas: Equivalence and Proportionality. The instruments we developed seek to assess students' ability to see these Big Ideas as…

Get a deeper understanding of teaching functions, 9-12 with our concise and comprehensive Go-To Guide. Based on "Developing Essential Understanding of Functions 9-12" and "Putting Essential Understanding of Functions into Practice 9-12," this summary distills the key concepts and ideas into a quick-reference guide that's…

The purpose of this resource is to help math teachers unpack, understand, and implement the current math content and practice standards. This resource describes the progressions of learning within each course and provides content support, which includes broad ideas about effective instruction as well as practical instructional strategies. Math…

Concept-based teaching is presumably more effective than popular procedure-based instruction in helping students develop conceptual understanding, an important conceptual base for mathematics teaching reforms in many countries. This study examined the extent to which this assumption is true by controlling the influences of student socioeconomic…

Research and theory indicate that the type and quality of instruction, not the delivery mechanism, are what impact learning. Previous reviews have not systematically explored variations in the instructional strategies, approaches, and designs of educational technology programs and also suffered from lax inclusion criteria, which has been known to…

Learning trajectories (LTs) can inform teaching by contributing a variety of pedagogical and content-related insights and strategies. They support sequencing topic introduction and development. Because ideas evolve gradually and often rely on a careful introduction of new representations, operations, cases of numbers, structures, and definitions,…

Typically, mathematics lessons are shaped around mathematical tasks. However, teachers frequently modify or enhance school- or district-adopted curriculum materials, often drawing on multiple sources to develop lessons. Research shows that teachers with a large percentage of students classified as English learners report modifying their materials…

Human-Computer Interaction (HCI) research aims to make systems versatile, easy to use, and accessible for most people. While computer technologies have successfully remodeled and improved the learning process, students with vision impairment (SVI) are at a disadvantage due to the lack of accessibility to their learning tools. This research aims to…

The Minnesota K-12 Academic Standards in Mathematics represent the work of the Mathematics Standards Review Committee who, during the 2021-22 school year, reviewed the 2007 Minnesota K-12 Academic Standards in Mathematics, other states' recently revised standards, current academic research, K-12 instructional best practices and public feedback.…