In his work leading professional development, Peter Klosterman found that teachers specifically asked for help teaching optimisation more effectively. To address challenges students often experience solving optimisation problems, he explains useful pedagogical strategies to support the teaching of optimisation and student learning in this topic.

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

Metacognition supports students in successfully working through struggle by equipping them with the tools to maintain an awareness of what they are doing and to change directions when needed to overcome obstacles. Thus, it is of little surprise that effective problem solvers spend a significant amount of time analyzing tasks relative to the amount…

Eddie Woo discusses the importance of problem solving in mathematics education. He points to the need for teachers to carefully consider the approaches they use to best support the growth of problem-solving abilities in students.

For over a decade, Which One Doesn't Belong? (WODB; Danielson, 2016) has been a beloved classroom routine that invites students to engage in mathematical decision-making and justification. In the WODB routine, four related figures are shown to students, and they are asked to decide which of them doesn't belong with the other three. The beauty of…

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…

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

The mathematical modeling process is also a powerful way to teach students the meaning of data. In mathematical modeling, students are collecting data to answer a question. Data collection is the means to an end and not the end in itself. The author was looking for an engaging way to introduce his third-grade mathematics class to the skill of…

Increasing the performance of secondary students with learning disabilities (LD) in mathematics on word problem-solving tasks involving ratios and proportions is challenging for secondary math teachers. Teachers must use evidence-based practices to enhance secondary students' problem-solving proficiency and math achievement. Schema-based…

This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts.…

'Mathematical sophistication' behaviours are often exercised by mathematicians in their work. In this article, the importance of mathematical sophistication will be discussed and three mathematics problems that activate mathematical sophistication behaviours will be presented.

This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students' horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the…

This article draws on the simple context of a two animal farm to create an engaging and mathematically meaningful problem solving task for students. It aims to encourage students to think systematically and to present their findings methodically. The task is structured sequentially, making it suitable for primary school students from Year 1 to…