Children's understanding of fractions, including their symbols, concepts, and arithmetic procedures, is an important facet of both developmental research on mathematics cognition and mathematics education. Research on infants', children's, and adults' fraction and ratio reasoning allows us to test a range of proposals about the development of…

The idea of good governance is central to democratic consolidation; and there can be no good governance without a vibrant democratic order that is participatory. Citizenship education is a tool for enhancing participation of the citizenry in the affairs of governance and all that pertains to the socio-economic and political life of the people as…

Student teachers in their final year of college preparation enter a profession that is facing a severe shortage and an alarming rate of attrition. Novice teachers, those with five or fewer years of experience, are faced with myriad challenges that makes retention a problem for the colleges preparing them, the school districts that hire them, and…

This paper describes a task that was used, in a broader study on mathematical giftedness and mindsets, as part of a process to identify mathematical giftedness in primary school students (see Parish, 2019). A discussion of the task, together with an analysis of student responses, offers insights that could be used by classroom teachers for both…

This working group continues to develop a research program on the practice of launching mathematical tasks and its resulting impact on learners. Our research agenda contains two strands of inquiry exploring (1) theory and framework building concerning effective launches and (2) empirical examination of the link between launching and opportunities…

The implementation of high-stakes testing has radically altered mathematics instruction in elementary classrooms. A curriculum that is heavily focused on developing successful test takers has fostered a weakness in our students' ability to solve complex problems. The purpose of this record of study was to examine the impact of a problem-solving…

The purpose of this mixed methods study was to determine how teachers use questioning techniques in their mathematics classrooms and if teacher questioning techniques correlate with student achievement in mathematics. As pacing and rigor increase and students learning styles vary, schools are challenged with finding new ways to make connections…

The goal of this paper is to isolate the preparatory effects of problem-generation from solution generation in problem-posing contexts, and their underlying mechanisms on learning from instruction. Using a randomized-controlled design, students were assigned to one of two conditions: (a) problem-posing with solution generation, where they…

Visual problem solving is essential to highly visual and knowledge-intensive professional domains such as clinical pathology, which trainees learn by participating in relevant tasks at the workplace (apprenticeship). Proper guidance of the visual problem solving of apprentices by the master is necessary. Interaction and adaptation to the expertise…

The solution of problems and the provision of proofs have always played a crucial part in mathematics. In fact, they are the heart and soul of this discipline. Moreover, the use of different techniques and methods of proof in the same mathematical field, or by combining fields, for the same specific problem, can show the interrelations between the…

Since the first descriptions of design research (DR), there have been calls to better define it to increase its rigour. Yet five uncertainties remain: (1) the processes for conducting DR, (2) how DR differs from other forms of research, (3) how DR differs from design, (4) the products of DR, and (5) why DR can answer certain research questions…

One way to ease the solution of physics problems is to visualize the situation. However, by visualization we do not mean the pictorial representation of the problem. Instead, we mean a sketch for the solution of the problem. In this paper a new approach to solving physics problems, based on decomposing the problem into with and without gravity, is…

A new visual representation for insight problems permits 22 new quantitative measures; which leads to a detailed diagnosis of a person's (or team's) creative weaknesses; which then leads to prescribing targeted, effective counter-techniques for each weakness. Currently, only two measures are consistently used for insight problem solving: the…

Integrating different perspectives is a sophisticated strategy for developing constructive interactions in collaborative problem solving. However, cognitive aspects such as individuals' knowledge and bias often obscure group consensus and produce conflict. This study investigated collaborative problem solving, focusing on a group member…

This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…