The Compulsory Education Course Standards for Mathematics 2022 have highlighted the educational objectives of junior secondary mathematics by emphasizing the development of mathematical competence and practical learning. Model consciousness, as one of the fundamental mathematical competencies to be developed at the junior secondary level, can…

Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.

In this article I explore some of the underlying mathematics of Poke´mon battles and describe ways that teachers at the secondary level could explore concepts of mathematical game theory in this context. I discuss various ways of representing and analyzing a Poke´mon battle using game theory and conclude with an example of applying concepts of…

Smartphones used as tools provide opportunities for the teaching of the concepts of accuracy and precision and the mathematical concept of arctan. The accuracy and precision of a trigonometric experiment using entirely mechanical tools is compared to one using electronic tools, such as a smartphone clinometer application and a laser pointer. This…

This article describes "modeling" as the act of creating an "idealized version of a real-life situation" that has been "translated into mathematical terms." By exploring an open-ended investigation involving proportional reasoning, sixth grade students were able to walk through both problem solving and modelling. The…

The purpose of our modeling effort is to predict future outcomes. We assume the data collected are both accurate and relatively precise. For our oscillating data, we examined several mathematical modeling forms for predictions. We also examined both ignoring the oscillations as an important feature and including the oscillations as an important…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…

With teachers and students in Government and Catholic schools in three geographical clusters in Victoria, the Task Type and Mathematics Learning (TTML) project is investigating the best ways to use different types of mathematics tasks, particularly in Grades 5 to 8. This article describes Type 1 tasks and discusses how they contribute to…

We report on a small scale study with six experienced teachers of mathematics in which we have applied a general theoretical model of expert practice (developed by the second author) to explore the nature of the knowledge base that enables teachers to operate effectively in the complexity of a class of 30 pupils. This model uses the notion of…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

In this article we examine students' perspectives on the customary, public work of proving in American high school geometry classes. We analyze transcripts from 29 interviews in which 16 students commented on various problems and the likelihood that their teachers would use those problems to engage students in proving. We use their responses to…

This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse.

Provides mathematical activities in reproducible formats appropriate for students in grades 7-12. The objective is to practice using area models in analyzing compound situations and calculating the expected value or long-term average. (PK)

Presents suggestions for making statistical topics interesting and relevant in the classroom. For each of the topics, a general discussion is followed by a suggested teaching sequence with specific activities and examples. (PK)

Attempts to raise some of the issues involved in incorporating mathematical modelling with classroom teaching, as well as providing some background for those unfamiliar with the area. (PK)