Originally intended as a replication study, this study discusses differences in problem solving performance among different domains caused by the same instructional intervention. The learning sciences acknowledges similarities in the learners' cognitive architecture that allow interventions to apply across domains, but it also argues that each…

This paper reports on an aspect of a research project that examined the use of apps in primary school mathematics programmes. It reports teacher and student perspectives on how they used a range of digital tools within the apps to solve problems. We consider the interplay between the affordances of the mobile technologies, including…

Open-ended questions, as discussed in this article, are questions that can be solved or explained in a variety of ways, that focus on conceptual aspects of mathematics, and that have the potential to expose students' understanding and misconceptions. When working with teachers who are using open-ended questions with their students for the…

This article presents a checklist of 10 evidence-based practices for educators to apply in mathematics instruction for students with learning disabilities. The checklist is "actionable," meaning the items on the checklist can be put into action immediately. It provides practical strategies teachers can adopt to fit their lessons…

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…

Generalizing--along with conjecturing, representing, justifying, and refuting--are forms of mathematical reasoning important in all branches of mathematics (Lannin, Ellis, and Elliott 2011). Increasingly, however, generalizing is recognized as the essence of thinking in algebra (Mason, Graham, and Johnston-Wilder 2010; Kaput, Carraher, and Blanton…

Mathematics is the study of structure but students think of math as solving problems according to rules. Students can learn procedures, but they often have trouble knowing when to apply learned procedures, especially to problems unlike those they trained with. In this study, the authors rely on the psychological mechanism of perceptual learning…

This paper aims to clarify how coherence of 'structured problem solving' mathematics lessons can be produced by comparing the lessons of three teachers from a narrative perspective. Results of our analysis showed three main coherence characteristics of lesson teaching sequences: (1) sequence scenes are recursively developed based on the previous…

Counting strategies initially used by young children to perform simple addition are often replaced by more efficient counting strategies, decomposition strategies and rule-based strategies until most answers are encoded in memory and can be directly retrieved. Practice is thought to be the key to developing fluent retrieval of addition facts. This…

Problem solving task design is not only the design of a non-routine problem to be solves by the students. Our task design also requires a supporting document, the practical worksheet, which would act as a cognitive scaffold for the students in the initial stages of the problem solving process before they can internalize the metacognitive…

This study aims to produce a learning trajectory using the mathematical modeling in helping students to understand the concept of algebraic operations. Therefore, the design research was chosen to meet the research aims and to give in formulating and developing local instructional theory in learning algebraic operations. Learning trajectory…

Characteristics of students who are diverse, such as different learning styles will also lead to the possibility of differences in students' ability to understand the learning material and every problem given, especially at the stage of understanding the problem given, because this stage is the most important step to determine the next problem…

In this design-based research project, we investigated how and to what extent participating in architectural building and problem solving via a simulation game-based learning platform (called E-Rebuild) would facilitate mathematical practices of middle-school students in the informal learning setting. This study encompasses 2 iterative design…

Spatial abilities--required in both academic and everyday information processing--are recommended as an important target for explicit instruction in the K-12 curriculum. However, most school curricula do not address this spatial issue, probably because spatial ability is a general rather than domain-specific skill and also due to debate regarding…

This article reports on a research project that examined the ways that 10-year-old students, who were using Scratch for coding, engaged with mathematical ideas. Interactive software is emerging that has cross-curricula implications and facilitates thinking in rich, problem-solving environments. Scratch, a free-to-use graphical programming…