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.

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…

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…

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…

Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…

Creative thinking in mathematics is an essential 21st Century skill that can be developed and encouraged through an exploration of mathematical concepts. In the context of the new "Australian Curriculum: Mathematics," this article explores the possibilities that are unlocked when students engage with tasks creatively in mathematics. By…

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…

Digital curricula can constrain teachers with ready-made instructional materials. The authors used Mathematics Teaching Practices (MTPs) to modify a digital curriculum to engage students in more thoughtful and meaningful lessons. In this article, the authors visit one of their third-grade classrooms, in which they used the prescriptive digital…

Mathematics is a core component of cognition. Unfortunately, most young children and teachers cannot access research-based early childhood mathematics resources. Building on a quarter-century of research, we are developing and evaluating an innovative, integrated, intelligent, and interactive system of technologies based on empirically validated…

According to the author, the "Australian Curriculum: Mathematics (AC:M) requires primary school students to measure the attributes of angle, time, temperature, length, area, capacity and mass. This article outlines some misconceptions held by primary school students which appear to stem from them not understanding terminology concerning the…

Many students who take a mathematics course as part of their post-secondary education are not enrolled in a mathematically-intensive degree program. This poses a challenge to mathematics departments that, for example, value and privilege more traditional mathematics curriculum: should students in such courses be taught differently than those in…

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

The use of technologies in mathematics education at all levels has been discussed extensively for a number of years. It is one of the few themes that was the object of two ICMI studies, the most recent being published in 2010. Two new approaches, emerging lately in the teaching and learning of Mathematics at all levels, will be discussed:…

Research shows that when students engage with mathematical inquiry their problem-solving skills are strengthened. Demands in the revised Australian curriculum raised problem-solving of new senior secondary mathematics assessment, specifically in Queensland Problem-solving and Modelling Tasks (PSMTs). The challenge for Queensland was to scale…