Middle school students need opportunities to craft informal mathematical arguments beyond justification of steps in an algorithm. Pentominoes provide an excellent vehicle for such activity. In this article, the authors describe an exploration with pentominoes that engaged a group of ninth-grade students in proportional reasoning, dilation, and…

This concluding commentary takes the perspective of research on practicing scientists and engineers to consider what open areas and future directions on relational thinking and learning should be considered beyond the impressive research presented in the special issue. Areas for more work include (a) a need to examine educational applications of…

Analogies have been widely used as tools for teaching difficult science concepts. The purposeful use of appropriate analogies can facilitate analogical thinking and help students develop the necessary transfer skills required for lifelong learning. Analogical thinking facilitates the development of higher order thinking skills among students. In…

Retrieving files from one's computer is done daily and is an essential part of completing most tasks at work, yet surprisingly little research has examined the ways that people structure and organize their files. Management of personal digital information is a challenging task that users approach idiosyncratically. Large individual differences…

How well are Wake County Public Schools (WCPSS) students prepared for problem-solving, scientific reasoning, and critical thinking? (1) WCPSS schools out-performed both the U.S., national, and international averages in each core subject of the Program for International Student Assessment (PISA): mathematics, reading, and science; and (2) overall,…

In this essay, I examine the extent to which mathematics education and education for quantitative literacy support students' present and future "flourishing", a concept that entails realizing objective goods in a life lived from the inside. This perspective requires disentangling philosophical assumptions about the aims of mathematics…

This pilot study explores the effectiveness of a strategy for overcoming post-primary students' misconceptions within the topic of algebra. Although central to the study of mathematics, algebra can be an area of difficulty for many students. A misconception is typically classified as flawed understanding of a concept causing repeated errors, and…

Applying knowledge from one context to another is a notoriously difficult problem, both for children and adults, but lies at the heart of educational endeavors. Analogical reasoning is a cognitive underpinning of the ability to notice and draw similarities across contexts. Reasoning by analogy is especially challenging for students, who must…

Conviction is a central construct in mathematics education research on justification and proof. In this paper, we claim that it is important to distinguish between absolute conviction and relative conviction. We argue that researchers in mathematics education frequently have not done so and this has lead to researchers making unwarranted claims…

Creating meaningful change in a state's education system from the capitol to the classroom is complex and challenging work. Over the past several decades, considerable research, policy, and funding have focused on the use of evidence-based programs (EBP) in schools. However, these practices only are effective when fully and effectively implemented…

The purpose of this study was to engage in a comparative analysis of Generation Z college students in the United States and Brazil regarding characteristics, motivations, interpersonal styles, learning styles, and learning methods. Quantitative data in both countries were collected and analyzed to formulate comparative findings. Themes that…

The purpose of this study was to investigate the contributions of general cognitive skills (working memory, inhibition, and reasoning) and metalinguistic awareness to young children's character reading. One hundred eighty-nine Chinese children, aged from 60 to 78 months, were administered with measures of character recognition, language,…

Reasoning about mechanism is central to disciplined inquiry in science and engineering and should thus be one of the foundations of a science, technology, engineering, and mathematics education. In addition, mechanistic reasoning is one of the core competencies listed in the Next Generation Science Standards (NGSS) Engineering Concepts and…

The current study was conducted in Taiwan to examine the effectiveness of using a self-monitoring strategy to increase the percentage of completion of classroom tasks for three high school seniors with moderate intellectual disability. We used a multiple-probe-across-subjects single-case design to evaluate the use of a self-monitoring tool to…

In this article we present the results of a study focused on engaging students in argumentation to support their growth as mathematical learners, which in turn strengthens their science learning experiences. We identify five argumentation categories that promote the learning of argumentation skills and enrich mathematical reasoning at the…