The purpose of this study was to investigate the reasons behind fifth grade students' participation or non-participation in mathematical discussions, and determine whether this affected their understanding of the learning material. The researcher observed twenty-four students' participation or non-participation in mathematical discussions in a…

In 1999, Liping Ma published her book "Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in the United States and China," which probed the kinds of knowledge that elementary school teachers need to convey mathematical concepts and procedures effectively to their students. Later that year,…

When properly implemented, the vision of "Beyond Crossroads" will result in classrooms where students are actively engaged and responsible for their learning. They are able to share their thinking and the teacher, in turn, can use the emerging understanding as a foundation for learning. According to "Beyond Crossroads," students will be expected…

Our research in statistical cognition uses both qualitative and quantitative methods. A mixed method approach makes our research more comprehensive, and provides us with new directions, unexpected insights, and alternative explanations for previously established concepts. In this paper, we review four statistical cognition studies that used mixed…

The aim of this study is to analyse and discuss those strategies for learning that are essential for toddlers' development of an understanding of basic aspects of mathematics. Analysis focuses on authentic episodes where toddlers aged one to three are interacting with other people. The settings chosen for the qualitative analysis emanate from a…

This study investigated the effects of the concrete-representational-abstract (CRA) instructional sequence on the subtraction performance of students identified as at-risk for mathematics failure. Although the CRA sequence has been demonstrated as effective for teaching a variety of mathematical skills and processes its effects when used to teach…

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the "What If Not?" (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs'…

Technology is a means that makes work or tasks easy, efficient, and operative. A more encompassing definition refers to it "as the tools created by human knowledge of how to combine resources to produce desired products, to solve problems, fulfill needs, or satisfy wants" (Koehler and Mishra. 2008:5). It can either be contrivances of tradition or…

Infinity and infinitely small numbers pique the curiosity of middle school students. From a very young age, many students are intrigued, interested, and even fascinated by extremely large or extremely small numbers or quantities. This article describes an activity that takes this curiosity about infinity into the domain of adding the numbers of an…

The National Council of Teachers of Mathematics [NCTM] requires students in grades nine through 12 to be able to explain inequalities using mathematical relational symbols and be able to understand the meaning of inequalities and their solutions (NCTM, 2000). Studies have shown that not only middle and high school students have difficulties with…

Curriculum reform aimed at improving students' reasoning strategies for calculating was the focus of a research project in which the authors participated along with two school communities in regional Victoria. Another focus of the research was assisting teachers to gain insight into how their students approached calculations. This article explores…

The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics.…

The author provides an account of launching a new branch at the Institute of Education at Reading University, a joint branch with the Mathematics Association. In the inaugural meeting, teachers had gathered to explore the theme of creativity in learning mathematics. The workshop provides some indication of the creative spirit these teachers…