Typically, vocabulary instruction is associated as part of reading instruction. However, vocabulary instruction is also a necessary component of mathematics instruction. In fact, state and national standards (e.g., Common Core State Standards) require elementary students to communicate about mathematics to provide clear explanations, construct…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology…

Ability of solving mathematical non-routine problems among Malaysian students remains at a low level, therefore there is a need to introduce a new and effective teaching strategy for the teaching and learning of mathematical problem solving. This study aims to determine the effectiveness of Mayer's problem solving Model with Visual Representation…

Epidemiological models have enhanced relevance because of the COVID-19 pandemic. In this note, we emphasize visual tools that can be part of a learning module geared to teaching the SIR epidemiological model, suitable for advanced undergraduates or beginning graduate students in disciplines where the level of prior mathematical knowledge of…

In the era of 21st century learning, many secondary students with learning disabilities continue to struggle with mathematics problem solving. Emerging evidence suggests self-regulated strategy development can be combined with existing evidence-based and promising practices during mathematics instruction. These practices include explicit…

Teachers do not directly implement new teaching materials, but rather adapt them. For changing teaching practice, research requires more insights into these adaptions. This study draws on the Theory of Instrumental Genesis to describe the ways teachers adopt the percentage bar model to create different learning opportunities. The results of the…

Learning rational number concepts is acknowledged as an important task but many learners find it difficult to make sense of them. This paper reports on a case study of the learning in a short (nine-lesson) learning programme for Grade 8 learners in a Namibian school, which sought to use visual models (circle area, bar area and number line) to…

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…

Developing multiplicative reasoning is an important milestone for elementary school students, which influences their learning of later mathematical concepts (Hackenberg and Tillema 2009). For children to conceptually understand multiplication, one should move beyond merely counting by ones to dealing with composites (twos, fives, etc.) and other…

This paper reports on a study of learners' use of immersive spatial diagrams to make arguments about three-dimensional geometric figures. Immersive spatial diagrams allow learners to use the movement of their bodies to control their point of view, while immersed in three-dimensional digital renderings. We present analysis of two pairs of…

Content area literacy has an important role in helping students understand content in specific disciplines, such as mathematics. Although the strategies are not unique to each individual content area, they are often adapted for use in a specific discipline. For example, mathematicians use mathematical language to make sense of new ideas and…

Using memorized rules and algorithms without coherence and understanding is a perennial problem for teachers and students especially in the teaching and learning of fraction operations. I present data in which prospective middle school teachers explain a commonly used rule for fraction division--keep-change-flip. I argue that using both strip…