We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

Illustrates a way in which students can estimate the ratio of an area of a circle using the radius square. Discusses why the same value of pi appears in both the formulas for the circumference and the area of the circle. (YDS)

Geometrical representations can help students generalize arithmetic to algebra. Includes several examples including triangle numbers and models of cubes. (Author/MM)