A core challenge for any organization is to create highly functioning teams that creatively and effectively find solutions to complex challenges. The authors propose the foundation of creating such teams is for the team to develop a shared understanding of the requisite knowledge of everyone on the team and then recombine that knowledge to find…

In this paper, we consider the issues involved in creating appropriate problems for a popular mathematics competition, and how such problems differ from problems typically encountered in a classroom. We discuss the differences and similarities in school curricula versus the generally agreed upon topics encountered in international competitions.…

For a century and a half, the scene of mathematics competitions underwent a remarkable transformation from isolated and geographically scattered events to a full-scale and a full-featured vibrant global ecosystem comprising an impressive variety of competitions, school students, university students, teachers, mentors, scientists, schools,…

In this paper, we consider mathematical competitions for pre-university students, such as the "International Mathematical Olympiad" (IMO) and many national and regional Olympiads following a similar model. The problems proposed in these contests must be solvable by 'elementary' methods (i.e., without using calculus) and belong…

In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and…

The World Federation of National Mathematics Competitions (WFNMC) was founded in 1984 as a professional organization that provides the possibility of international collaboration among mathematicians and mathematics educators working in the area of mathematics contests. Over the last decades the field, which has come to be called "competition…

This paper addresses a popular topic in science teaching and competitions for primary and secondary school students. Experiments with colliding coins are relatively easy to perform and therefore popular in science lessons. We used the idea in the science competition we organized for pupils aged 6 to 13 years.7 The science competition is based on a…

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

This paper is about an experimental problem on forced oscillations, which was given to 14-year-old primary school pupils at the Slovenian national (final) level of the physics competition in April 2019. At the time when the competition took place these pupils were approaching the end of the school year, when they encountered physics as a school…

As schools endeavor to provide all students with access to computational thinking and computer science, the hackathon emerges as a competitive and high-energy event that uses authentic problems to motivate learners to engage in the domain of computing. This article presents the design case of a hackathon for teenagers as enacted over five…

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

This case presents how the leadership team and faculty of a small, independent school used design thinking to respond to a competitive marketplace and desire for enrollment growth in the middle grades. The new middle school head came in with a mandate for substantial change and sought to engage all stakeholders in a process of redesign and program…

This practice report describes how escape rooms have been used by one Australian university to successfully engage with high-school students who reside in areas of relative socio-educational disadvantage. We discuss how the escape room approach aligns with Lizzio's "Five Senses of Success" and offer recommendations for further use and…

Ideas are offered to show how the science of density and displacement can be explored by students from year 5 through to year 7 (ages 9-12) through hands-on investigations to explore possibilities and solve problems. These demonstrate how the insights we gain by viewing a challenge through the multidisciplinary lenses of science, history,…

The International Mathematical Modeling Challenge takes place towards the end of Term 1 each year in Australia. Students use their research, mathematical and creative abilities to develop a mathematical model to address a real world problem. Ross Turner describes some aspects of the competition.