In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

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…

Many ways exist to engage students without detracting from the mathematics. Certainly some are high-tech options, such as video games, online trivia sites, and PowerPoint® presentations that follow the same model as Jeopardy; but sometimes low-tech options can be just as powerful. One exciting way to connect with students is by incorporating…

Many middle school students approach math with caution, often trepidation, and generally less-than-complete confidence. Several factors contribute to their views of what math actually is (a system of rules to follow and formulas to apply) as well as who might be good at it (people who can see the path to an answer and calculate quickly). A few say…

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 will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

This intervention study compared the efficacy of small-group tutoring on the mathematics learning of third-grade students at risk for mathematics difficulty using either a school-provided standards-based curriculum (SBC) or a schema-based instruction (SBI) curriculum. The SBI curriculum placed particular emphasis on the underlying mathematical…

Teaching mathematics using graphic calculators has been an issue of didactic discussions for years. Finding ways in which graphic calculators can enrich the development process of creative activity in mathematically gifted students between the ages of 16-17 is the focus of this article. Research was conducted using graphic calculators with…

The main strand of the NRICH project is the NRICH website (http://nrich.maths.org), which was set up in 1996 to cater for secondary-aged pupils who were attending mathematics master-classes at the Royal Institution. By 1998, problems aimed at primary children were included and the site began to provide for students aged five to 18-plus. At this…

The authors answer conclusively the question of how certain regular polygons can be "fitted together" around a point in the plane. Proofs lead to the establishment of seventeen cases. (JP)

The author provides an example of obtaining the correct answer to a problem through a so-called nonsense solution. The conditions under which this incorrect method will yield a correct solution are examined. (JP)

Modular arithmetic is used to show that there is at least one Friday the 13th in every year. A case-by-case proof is outlined and a proof of the general case is given. (DT)

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12-15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). "Cabri-Geometry (software)," Universite de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct:…