Many delegates at "conference" relish the opportunity, and the space, to "do some mathematics". Opportunity and space help to make the experience memorable, but how often is the quality of the starting point, or question acknowledged? Here is a set of starting points or problems that invite the reader to "do some mathematics". Deliberately, no…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

Art uses mathematics in many ways. The author's teaching and involvement with mathematics and art in the Bridges Conference connecting the two have convinced him more and more that concepts for understanding mathematics can be achieved by the use of art. The author states that one reason he believes in teaching mathematics through art is that it…

Making constructions with paper is called "origami" and is considered an art. The objective for many fans of origami is to design new figures never constructed before. From the point of view of mathematics education, origami is an interesting didactic activity. In this article, the authors propose to help High School students understand new…

This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…

Within the project "Engaging mathematics for all learners", led and funded by the QCA, the mathematics team at the Royal Institution of Great Britain (Ri) looked into how mathematical tasks usually reserved for the "gifted and talented" can be used in the mainstream classroom with a wide range of learners to address core…

Geometry certainly is in fashion, at the Henrietta Barnett School for girls in North London. Within the project "Engaging mathematics for all learners", led and funded by the Qualifications and Curriculum Authority (QCA), the Royal Institution of Great Britain (Ri) looked into how mathematical tasks usually reserved for the "gifted…

This article is about the students' investigation about the relationship between the diameter of the view tubes (x) of constant lengths and the viewable vertical distance (y) on the wall while keeping the perpendicular distance from the eyeball to the wall constant. The students collected data and used and represented it in tabular and graphical…

The problem of inscribing a square in a semicircle and related problems are discussed. Solutions to the problems are provided. (FL)

Includes discussions of right triangles having integral sides and integral circumradii, the role of axioms, tessellating hexagons, and descriptions of ideal teachers by 12 year olds. (RS)

Develops two-dimensional descriptions of degenerate transformations using elementary matrix algebra. (RS)