Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as 'proficiencies' that are intended to be integrated with the content. There…

This article offers a description of how empirical experiences through the use of procedural knowledge can serve as the stage for the development of hypothetical concepts using the learning cycle, an inquiry teaching and learning method with a long history in science education. The learning cycle brings a unique epistemology by way of using…

The purpose of mathematics competitions, and in our case the South African Mathematics Olympiad (SAMO), is to promote problem solving skills and strategies, to generate interest and enthusiasm for mathematics and to identify the most talented mathematical minds. SAMO is organised in two divisions--a junior and a senior division--over three rounds.…

This article describes an investigation of Buffon's coin problem and related problems with the aid of an applet. The problems are accessible at a variety of grade levels and facilitate making connections between geometry and probability.

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. "Hands-on Activities for Teaching the Common Core Math…

To capture aspects of pedagogical content knowledge (PCK) not illuminated in an earlier written survey, an interview protocol was used with 40 middle school teachers. The scenarios were intended to elicit teachers' understanding of the big ideas, ability to anticipate students' answers, and intervention strategies for the classroom. This was…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Gaps between teaching practices and research recommendations have been well documented. One challenge for research is in understanding the processes and systems that promote a bridging of these gaps. A year-long study with four primary teachers documented ten support mechanisms, or connection levers, that the teachers raised as important for…

In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this debate by illustrating three learning opportunities that group discussions can create. In…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

This article presents two statistical tasks, one on comparing data sets, another on repeated sampling, both of which have powerful connections to proportional reasoning. Students' work and reasoning on these tasks are included, as well as suggestions for ways to use these tasks with middle school students to connect statistical thinking to…

New software tools for data analysis provide rich opportunities for representing and understanding data. However, little research has been done on how learners use these tools to think about data, nor how that affects teaching. This paper describes several ways that learners use new software tools to deal with variability in analyzing data,…

The most popular activities from APA's successful "Activities Handbooks for the Teaching of Psychology" are gathered together and updated in this book of teachers' favorites. The lesson plans, which encourage active learning and involve the whole class, have stood the test of time and proven themselves to be entertaining, effective, and easy to…

This document presents the proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of this conference is "Navigating Currents and Charting Directions." The theme reminds us that, although we are constantly pushed to account for the quality and impact of our research, we…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…