A common exercise given to students early in a molecular biology course is the creation of a restriction map of a plasmid "digested" by two restriction enzymes (RE). Meanwhile, students have learned from an early age about the properties and analyses of circles in their mathematics courses. But it is rare for students to learn using…

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…

"Improvement Science in Education: A Primer," second edition, is the first and introductory volume in the Myers Education Press series, "Improvement Science in Education and Beyond." It provides a comprehensive overview of improvement science as a framework to guide continuous improvement and reconceptualizes improvement by…

The hanging rope problem is considered. The rope is subject to rotation with the rotation axis being parallel to the rope. Using a continuum model and the basic principles of dynamics, the differential equation governing the motion is derived. The dynamic equilibrium case without vibrational motion is assumed in deriving the equation. The equation…

Simplifying equations via assumptions is integral to the "engineering method." Algebraic scaling helps in teaching the engineering skill of making good assumptions. Algebraic scaling is more than a pedagogical tool. It can create a solution where one was not possible before scaling. Scaling helps in engineering proper design…

Polyiamonds are the 'and so on' when unit-squares are replaced with unit-equilateral triangles. Polyiamonds are used to play the satisfying Blokus variant, Blokus Trigon, where the playing grid is also hexagonal, and the playing pieces are all the polyiamonds from mono- to hex. This article discusses the use of polyiamonds in puzzles.

The growing use of programming in mathematics classrooms presents a challenge linked to implementation in general and task design in particular. This article presents design ideas for mathematical problems incorporating programming in which the focus remains mainly on learning mathematics and less on learning programming. The article starts by…

Many of today's educators learned math in elementary and secondary schools with approaches very different from those outlined in the current standards, and it is difficult to teach for proficiencies educators have not yet developed in themselves. How can teachers find time for this kind of professional learning with all the other responsibilities…

Various theories and models discuss how instructional designers can develop systems that allow learners to engage in problem-solving. To date, many of these theories and models that guide design often describe how learners engage in meaning-making within a situated context; however, they do not address strategies instructional designers can use to…

Examples play a variety of roles in proving and disproving. Buchbinder and Zaslavsky (2019) have produced an a priori mathematical framework for assessing students' understanding of the role of examples when proving and disproving universal and existential statements. In this paper, I highlight three important aspects that suggest an extension of…

This article highlights the primal concern of children at home and in school: knowing where safety lies in relationships of fairness. The article includes scenes where five-year-old children experience breaches in fairness and the framework commonly used to restore and maintain it. The work of Vivian Gussin Paley, the renowned early childhood…

A number of memorable tasks have been revealed through collegial exchanges with underlying philosophical, theoretical, and potentially nefarious motivations. Such was the origin of the probability problem, and the various differences of opinion, presented herein. This article recounts how, together, we explored and disputed the probabilities…

The advancement of large language model-based generative artificial intelligence (LLM-based GenAI) has sparked significant interest in its potential to address challenges in computational thinking (CT) education. CT, a critical problem-solving approach in the digital age, encompasses elements such as abstraction, iteration, and generalisation.…

Effective mathematics teaching practices include not only probing student thinking and selecting student strategies to share but also facilitating discourse and encouraging reflection about important mathematical ideas (National Council of Teachers of Mathematics [NCTM], 2014, pp. 36-37). Encouraging students to use precise academic vocabulary to…

This case study explores the complexity of leading adaptive change within a large RTLB (Resource Teacher: Learning and Behaviour) cluster in Aotearoa. Centred on the dilemma of how to adapt an internal case management tool (eRTLB) to strengthen best practices, the reflection draws on the principles of adaptive leadership and Robinson's (2022)…