Terence Mills introduces us to Keynsian probability and discusses its implications for teaching probability. The author considers it unlikely that Keynes's theory would replace how we teach probability, but argues that it may make us think more deeply about the use of terms such as chance and probability when used in our lessons.

To be successful in algebra, students need access to high-quality instruction that includes opportunities to develop their algebraic understanding. Yet research on algebra teaching suggests that instruction remains procedurally focused, indicating that teachers may need additional support to provide students such opportunities. One possible lever…

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.

There is a plethora of textbooks to choose from. While most textbooks contain the same content, teachers need to understand the textbook they have chosen to support their students' learning, as textbooks can significantly impact student learning and teacher instruction. When searching for a way to understand the various textbooks, my research…

In this article, we explore demands and tensions involved when schools implement ambitious mathematics teaching (AMT). Following a description of a framework that distinguishes between internal and external demands, we characterize the tension between these in terms of alignment, balance, and buffering, which collectively speak to coherence. We…

This study describes the experiences of secondary-level mathematics teachers from the Department of Education of Puerto Rico implementing the strategy of contextualized teaching. Qualitative research framed in phenomenology was conducted, collecting data through semi-structured interviews and a review of normative documents from the Department of…

Using mathematical modelling to solve problems appears in all year levels in the Australian Curriculum: Mathematics (v. 9), and is probably the most authentic way of teaching mathematics in context. However, the term mathematical modelling, even if familiar to teachers, may not be well understood or enacted confidently by teachers in their…

Students at the elementary level should have opportunities to critique the world through mathematics and to see themselves as capable doers of mathematics. The lesson described in this article prompted students to consider how to use mathematics to organize an emergency evacuation. In this article, the authors show how small changes to a task…

This article analyzes teachers' perceptions and experiences using an educative curriculum designed to promote high levels of mathematical discourse. After participating in 2 days of professional learning, grade 3 teachers implemented a predifferentiated and enriched mathematics unit in their classroom. The curriculum was designed to be educative,…

Our aim is to contribute to the body of research on learning trajectories (LTs) in mathematics by making visible a process for articulating a hypothetical learning trajectory implicit in a widely adopted, reform-based, middle-grades mathematics curriculum. In doing so, we highlight considerations, decisions, and challenges we faced as part of this…

In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…

The making of mathematical connections in the classroom plays a dual role. While many studies highlight the importance of connections for the learning of mathematics, others inform of students' difficulties associated with the making of connections. This study aims to characterise the mathematical connections that arise in habitual classroom…

This is the first of four columns by Tim Erikson which introduces us to the Common Online Data Analysis Platform (CODAP). CODAP is a free, web-based software tool that your students can use for many types of tasks. This first column shows how CODAP can be used for mathematical modelling and where it might fit with the "Australian Curriculum:…

This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing…

Recent research demonstrates that mathematics teachers rely on a variety of curriculum materials and must make meaning and synthesize these materials for use in a particular place with particular students. While there are multiple theories about the nature of this work and the factors which influence this work, the field continues to lack a…