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.…

It is widely acknowledged that communicating mathematical thinking is complex, difficult, and often messy. In this article, the authors explore how mathematical thinking is communicated, providing examples of strategies for teachers and students to use in the mathematics classroom.

This paper argues for effective sequencing of mathematics content to aid transition from junior (Year 7 to Year 10) to senior mathematics (Year 11 to Year 12) curriculum in Queensland, Australia and provides a tool for sequencing the mathematics content. Planning templates and samples are available to schools; however, it is imperative for…

Over a sixteen-week term, the study dove into how chess could enhance math skills for eleventh graders at three public schools in Cartagena, Colombia. It assumed that chess would sharpen their minds and problem-solving prowess. Seventy-one pupils took part, trying out a chess-centric way of learning. Researchers used multiple statistical…

In third grade the focus on math word problems becomes prominent. In the limited third grade research, teacher-mediated explicit instruction with multiple exemplars, teaching students to use visual representations, and the incorporation of self-strategies, have proven effective. For these practices to reach their full potential though, their…

The learning sequence described in this article was developed to provide students with a demonstration of the development of box plots from authentic data as an illustration of the advantages gained from using multiple forms of data representation. The sequence follows an authentic process that starts with a problem to which data representations…

Numeracy in schools is becoming an increasingly important part of mathematics learning and teaching. This is because educators want students to engage with mathematical concepts more deeply, use mathematics to make sense of their environment and make decisions that are based on the analysis of mathematical information. In order to be numerate,…

Although research on the effectiveness of differentiated and enriched instruction in improving the achievement of diverse students is still emerging, some studies suggest that students in academically diverse classrooms benefited academically from differentiated learning experiences. The primary research question explored in this study was…

When taking mathematics courses, students will sometimes ask their recurring question, "When will I ever use this in real life?" Educators are often unable to provide a direct connection between what they are teaching in the classroom and a real-life application. However, when such an opportunity does arise, they should seize it and…

This paper presents an investigation by pre-service secondary school teachers in a geometry class of the relationship between the perpendicular distance from the eyeball to the wall (x) and the viewable vertical distance on the wall (y) using a view tube of constant length and diameter. In undertaking the investigation, students used tabular and…

Now that most states have adopted the new Common Core State Standards, the next major challenge is to simplify and implement them by 2014. That is why it is important to begin this work now. Joe Crawford, Milken Award-winning educator and author of "Using Power Standards to Build an Aligned Curriculum", shares his proven process for…

This article provides an overview of vertex-edge graphs as an essential topic in the high school mathematics curriculum, including rationale, recommendations, and sample applications. A classroom-ready activity with full teacher notes is also included. (Contains 1 table and 9 figures.)

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater…

The fortunes of chance and data have fluctuated in the mathematics curriculum in Australia since their emergence in the National Statement in the early 1990s. Their appearance in Australia followed closely on similar moves in the United States. In both countries the topics, taken together, were given a section status equal to other areas of the…

With regard to transfer, is it better to provide pupils with ready-made representations or is it more effective to scaffold pupils' thinking in the process of generating their own representations with the help of peers and under the guidance of a teacher in a process of guided co-construction? The sample comprises 10 classes and 239 Grade 5…