Increasing and decreasing functions can be combined into a quadratic to explore the competing demands of number of sales, price points and profit (or loss). An interesting application of taxation rates is also explored.

In this article, the authors present the use of digital tape diagrams--implemented using GeoGebra (2001) dynamic mathematics software--as a support to static diagrams to pose and solve proportional reasoning tasks. They show how dynamic sketches can allow students to explore standard tasks in proportional reasoning in ways that emphasise…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

With the advance of engineering education research and scholarship, there has been an increased focus on amending chemical engineering courses to increase student learning, engagement and enjoyment. These approaches are often incorporated in project-based courses such as capstone design courses and laboratory courses, providing opportunities to…

Arguably, constructive alignment has been the major challenge for assessment in the context of problem-based learning (PBL). PBL focuses on promoting abilities such as clinical reasoning, team skills and metacognition. PBL also aims to foster self-directed learning and deep learning as opposed to rote learning. This has incentivized researchers in…

Collaborations and partnerships across disciplines are becoming increasingly recognized as valuable endeavors toward solving emerging global challenges in our rapidly changing world. Thus, it is crucial to create STEM educational strategies that infuse diverse and interconnected perspectives among scientists, policymakers, and the general public.…

The teaching of Mathematics in the context of the Mathematical Olympiads in Brazil constitutes a context of research still little considered, with particular interest in the teaching and the learning phenomena. In Brazil, we identified a large number of teachers and students who do not participate in official math competitions, such as the…

Despite the requirement that teachers implement evidence-based instruction in their classrooms, a significant research-to-practice gap persists. Far too often, teachers resort to quick fixes found through online searches or rely on conventional wisdom to make instructional decisions. This is no surprise as identifying evidence-based interventions…

Project-/Problem-Based Learning (PBL) creates dynamic learning environments, incorporates various stimuli, allows learners to gain valuable experiences that extend to real-world applicability, and should be considered as a primary delivery method in STEM classes. The application and benefits of PBL in STEM classes are limitless. Students learn…

Because of the lack of tools available to assess problem-solving skills, teachers often revert to more traditional instructional approaches (e.g. lecture-based, memorization) that fail to prepare learners for the complexity of dynamic work environments. To overcome this challenge, technology solutions are needed that accurately and efficiently…

With the rapidly growing field of nanotechnology, there has been a pressing need to teach non-science undergraduate majors how to critically interpret science in popular media and news sources. The present work introduces students to chemistry concepts through the lens of relatable nanotechnology applications, including electronics, medicine,…

Students get a sense of realistic values for physical situations from texts, but more importantly from solving problems. Therefore, problems should use realistic values for quantities to provide needed practice. Unfortunately, some problems on tests and in textbooks do not use realistic values. Physical situations in electrostatics seem to be…

This article details a high school classroom activity in which algebra tiles are used to help students gain a conceptual understanding of completing the square. The activity utilises the eight elements of effective mathematics education suggested in the National Council of Teacher of Mathematics' (NCTM's) "Principles to action: Ensuring…

The article describes how one fifth-grade teacher helped her students to exercise their Rights of the Learner (e.g., to be confused; to claim a mistake; to speak, listen, and be heard; and to write, do, and represent what makes sense) as they learned to graph and interpret non-linear data.

Goal 2 of the "APA Goals for Undergraduate Major in Psychology," Scientific Inquiry and Critical Thinking, addresses the development of scientific reasoning and problem-solving, including effective research methods, in undergraduate psychology students. These skills serve as the foundation of not only introductory courses but also the…