The reality is that textbooks and state standards have more content than can reasonably be covered for proficiency in most classrooms. In years past, this typically meant cutting the last unit or two or moving along regardless of who was keeping up, in many cases resulting in cutting statistics from the curriculum. This article provides five…

In today's fast paced early childhood classrooms, mathematics play activities in prekindergarten settings are not consistently supported. Administrators and educators have discussed with great intensity and passion about incorporating mathematics play in prekindergarten classrooms. Both groups discussed the benefits and reservations of…

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

Quadratic functions are explained in the three equivalent formats: Standard (or Expanded), Vertex and Factorised. However, cubic functions are represented only in the two equivalent formats: Standard (or Expanded) and Factorised. In this article, the author shows how cubic functions can be expressed in three equivalent formats like quadratic…

This article builds on the work of Professor Robyn Jorgensen and Associate Professor Peter Games and others on social justice and mathematics and links to the Ethical Understandings capability of the "Australian Curriculum." Presented in this paper is an argument for the importance of a social justice approach to teaching mathematics,…

This article is the second in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows how to determine the altitudes of a triangle, its area, and the lengths of its circumradius and inradius. [For the first activity in the series, see EJ1259412.]

The short activity presented in this article continues a discussion related to the value of golden ratio explorations in secondary mathematics, and acts as a companion to the earlier paper in this journal (Crawley, 2023). Exploring meaningful ways in which teachers can elicit students' interest and engagement in mathematics is vital, and…

A clear relationship exists between the consistent selection and implementation of cognitively demanding tasks and students' conceptual understanding of mathematics. However, mathematics teachers often struggle to maintain the cognitive demand of implemented tasks, with a number of factors identified as contributing to this decline. As many…

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.…

This article provides a task that can be used effectively for exploring arrays in middle and upper primary schools, and the notion of prime and composite numbers in particular. As students are engaging in these activities, teachers can encourage them to record their arrays both diagrammatically and as number sentences.

This is the third in a series of articles describing CODAP and where it might be used to address content in the "Australian Curriculum: Mathematics" v9.0 (ACARA, 2022). We've talked before about model-ling and about statistics; this time, we'll talk about exploring probability using CODAP. As before, we have also prepared online pages…

Relying on the students' cultural background to teach mathematics may be a strong incitement for the learning process. This background can include artistic creations, items from the news, among others. Because of the strong presence of space related news (in particular the almost simultaneous launching of three spacecrafts towards Mars), we…

Statistics has been a content domain in the mathematics curriculum for decades. However, statistics is a distinct discipline from mathematics and there are important differences in how one should teach the two disciplines. In this article, the authors consider how these differences can inform an adaptation to the 5 Practices for Orchestrating…

These educators share the "how" and "why" behind their use of open middle tasks in the classroom. In this article, the authors share a type of mathematics task, called Open Middle, that exhibits the characteristics outlined above. The authors frequently use Open Middle tasks in their classrooms because they teach students that…

How we should teach mathematics has long been debated by advocates of different instructional approaches. These debates can lead to tensions that are difficult to navigate for those who are new to (or even veterans of) the profession. Educators often propose a "balance" of different approaches as a solution. Charles Munter considers…