Schools in Florida used the multitiered system of support response to intervention framework to help students achieve the state and national standards but, in the national report card, 61% of the fourth-graders assessed in mathematics failed to achieve proficiency. Research indicated that the students lacked mathematical word problem-solving…

The topic of recurrence relations has recently been introduced in many discrete mathematics textbooks. Recurrence relations are efficient modelling and problem-solving techniques used in mathematics. Combinatorial problems are often used to introduce recurrence relations. However, many textbooks consider problems that can be reduced only to the…

The goal of this study is to characterize how pre-service teachers recognize students' reasoning, based in the unitizing process, when students solve ratio comparison problems and, how they consider the unitizing process as a Key Development Understanding to propose teaching decisions. Ninety-one pre-service primary teachers interpreted primary…

The questions in the practice assignments given to students in the form of worksheets or other formats are often grouped by chapter, topic, or concepts. There is a great emphasis on categorization. Most of the end-of-chapter problems in chemistry textbooks are organized by sections. Although this was done with the intention of helping students…

In this article, we address the limitations of sustainable development as an orienting educational horizon of hope and change, given that mainstream development presumes the possibility of perpetual growth and consumption on a finite planet. Facing these limitations requires us to consider the inherently violent and unsustainable nature of our…

This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they…

This study enquires into the embodied processes of children in solving multiplication tasks, considering how such processes can expand access to spatial reasoning skills and simultaneously develop students' understanding of multiplication. The analysis focused on four Year 2 students as they completed two embodied tasks. The aim was to understand…

We are surrounded by controversy--politics, religion, diets, and even science are all up for debate in our 24/7 world of social media and the internet. With this controversy comes a lot of misinformation and competition with what our students might otherwise be learning in our classrooms. I know this intimately, since I teach fitness and nutrition…

The literature describes different stances concerning the focus on how mathematics should be taught, with some preferring a conceptual knowledge approach and others a procedural knowledge approach. The current study investigated the relationship between students' conceptual and procedural knowledge in a calculus context. To better understand the…

Adaptive expertise represents the combination of both efficient problem-solving for clinical encounters with known solutions, as well as the ability to learn and innovate when faced with a novel challenge. Fostering adaptive expertise requires careful approaches to instructional design to emphasize deeper, more effortful learning. These teaching…

This study aims to determine the effect of the geographical inquiry learning model with the SETS approach on complex problem-solving abilities. The hypothesis in this study consists of H0 (There is no difference in the effect of the geographical inquiry learning model with the SETS approach on the students' CPS abilities) and H1 (There is a…

In this paper, we describe an experiment in using history to work on problem-solving and the relationship between arithmetic and algebra. The students involved attended the first year of the Italian upper secondary school (grade 9). The original sources we used are problems from Italian treatises on arithmetic and algebra that appeared in the…

A common task when problem solving in quantum mechanics, including in a spins-first curriculum, involves changing the basis of a given state. Our research in undergraduate quantum mechanics courses at three institutions explores student thinking about basis, basis expansion coefficients, and change of basis in the context of spin-½ systems. Our…

Positive creativity involves creative ideas and products that are beneficial to humanity. This paper discusses the importance of fostering positive and transformational creativity in PK-12 and college settings, and concrete classroom strategies for nurturing positive creativity through a service learning pedagogy. A brief history of service…