This paper discusses an interesting, classic problem that provides a nice classroom investigation for dynamic geometry, and which can easily be explained (proved) with transformation geometry. The deductive explanation (proof) provides insight into why it is true, leading to an immediate generalization, thus illustrating the discovery function of…

Physics education research has a tradition of studying problem solving, exploring themes such as physical intuition and differences between expert and novice problem solvers. However, most of this work has focused on traditional, or well-structured, problems, similar to what might appear in a textbook. Less work has been done with open-ended, or…

Besides "thinking outside the box," the creativity needed to solve problems often involves thinking differently about the box, finding a new approach or off-beat way to use the materials, conditions, and even constraints that one has. Spencer discusses creative constraint--what happens when a problem solver runs into barriers that make…

Spreadsheets provide a rich setting for first-year algebra students to solve problems. Individual spreadsheet cells play the role of variables, and creating algebraic expressions for a spreadsheet to perform a task allows students to achieve a glimpse of how mathematics is used to program a computer and solve problems. Classic optimization…

In this writing, I report on how two 12-year old children used fraction strips to add 1/2 and 2/5. In their interaction with the tool, I look for the emergence of the tool-mediated Zone of Proximal Development to analyse the knowing that become available to the children. In thinking about this interaction, I ask what is the role of the more…

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and…

Collaborative problem solving (CPS) ranks among the top five most critical skills necessary for college graduates to meet workforce demands (Hart Research Associates, 2015). It is also deemed a critical skill for educational success (Beaver, 2013). It thus deserves more prominence in the suite of courses and subjects assessed in K-16. Such…

Consulting projects where students are tasked to propose solutions to a client issue are a common feature in many business courses. Whether scenario-based or dealing with real clients, students engaged in consulting tasks tend to focus on solution development without giving due consideration to the underlying process by which they derive their…

A multiweek laboratory experiment is described, which guides students to use data to make decisions through multiple steps, before reaching a final conclusion. The lab focuses on the comparisons of fluorescence and absorbance spectroscopies to determine the concentration of a desired substance in an unknown sample in consideration of a complex…

This professional practice paper is underpinned philosophically by the indisputable centrality of proof to the discipline of mathematics. Proof offers students the opportunity to deepen their own understanding of mathematical ideas, to construct and defend logical arguments, and to think critically about the veracity of mathematical statements.…

Breakout boxes are similar to the escape rooms that have popped up all over the country in the past few years. In an escape room, you and your friends are locked in a room and given a scenario and a time limit. You must work together to solve a number of puzzles to get out of the room before time runs out. Breakout boxes center around boxes, each…

The aim of this work is to examine pre-architects' use of metaphorical reasoning as a tool for design problem solving exercises in an unfamiliar environment. It is to improve their sense of place, which helps to identify and capture design concepts, as well as define goals and requirements. Regarding the three metaphorical reasoning operations of…

The paper aims to present application of Educational Data Mining and particularly Case-Based Reasoning (CBR) for students profiling and further to design a personalised intelligent learning system. The main aim here is to develop a recommender system which should help the learners to create learning units (scenarios) that are the most suitable for…

Founded on the need to help university students develop a greater academic metacognitive capacity, student-facing learning analytics are considered useful tools for making students overtly aware of their own learning processes, helping students to develop control over their learning, and subsequently supporting more effective learning. However,…

This paper develops the ideas of "The Pedagogical Power of Context: Iterative Calculus Methods and the Epidemiology of Eyam" (French "et al." 2018 "J. Phys. Educ."), where we considered the application of the Euler method to solve epidemiological problems. Our purpose was to convey some examples of school level work…