Educators usually mean different constructs when they speak of open tasks: some may refer to pure-mathematics investigative tasks while others may have authentic real-life tasks in mind; some may think of the answer being open while others may refer to an open method. On the other hand, some educators use different terms, e.g. open and open-ended,…

In large, introductory courses, instructors and teaching assistants often struggle to provide detailed feedback on student homework in a timely manner. Here we describe a peer-reviewed homework system that provides quick turnaround while offering flexibility in the construction of homework problems. Homework is administered through a cycle, which…

This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

Metacognition is vital for a student's academic success. Gifted learners are no exception. By enhancing metacognition, gifted learners can identify multiple strategies to use in a situation, evaluate those strategies, and determine the most effective given the scenario. Increased metacognitive ability can prove useful for gifted learners in the…

This paper investigates the difficulties that Moroccan pupils (18-19) of the second Baccalaureate year encountered in solving chemical equilibrium problems relating to ethanoate ions' reactivity with water and methanoic acid, and to copper-aluminum cells. The pupils were asked to provide answers to questions derived from two problems. The…

In this article, the authors first present the Hands Together! task. The mathematics in this problem concerns the relationship of hour and minute durations as reflected in the oft-overlooked proportional movements of the two hands of an analog clock. The authors go on to discuss the importance of problem solving in general. They then consider…

Learning the basic competencies of critical thinking are very important in the education of any young scientist, and teachers must be prepared to help students develop a valuable set of analytic tools. In my experience, this is best achieved by encouraging students to study areas with little scientific consensus, such as the control mechanisms of…

The design and fabrication of functional scientific instrumentation allows students to forge a link between commonly reported numbers and physical material properties. Here, a two-point and four-point probe station for measuring electrical properties of solid materials is fabricated via 3D printing utilizing an inexpensive benchtop…

This article describes the author's experience using SCAMPER, a creativity-building technique, in a creative problem-solving session that was conducted in an environmental conflict course to generate ideas for managing postconflict stability. SCAMPER relies on cues to help students connect ideas from different domains of knowledge, explore random…

From global hunger to the world's water crisis, middle school students at New Jersey's West Windsor-Plainsboro Regional School District spend the last few days of the school year problem solving about the planet's most dire issues. With the Global Challenge, the school district's administrators not only want to implement an interesting and dynamic…

How can the best of mathematical problem-based learning be applied toward literature classes? Daniel Sussman, an English teacher at Moorestown Friends School in New Jersey, discusses how he uses problem solving tactics to encourage close, critical reading of fiction texts in his Jewish literature and poetry classes. He explores the challenges of…

This paper is about the development of a task sequence to help overcome the fragmented understanding of the "function" concept that students often bring with them into the initial stage of upper secondary school level. Our aim is to make the students' use of functions more flexible in certain respects, for example when functions are…

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four…

Teaching introductory statistics using curricula focused on modeling and simulation is becoming increasingly common in introductory statistics courses and touted as a more beneficial approach for fostering students' statistical thinking. Yet, surprisingly little research has been conducted to study the impact of modeling and simulation curricula…