This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

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…

Students explore the Pythagorean theorem and an extension using jelly beans to measure areas. Deductive thinking and algebraic notation help establish connections. (Contains 8 figures.)

Diverse contexts such as "take away," comparison," and "completion" give rise to subtraction problems. The take-away interpretation of subtraction has been explored using two-colored chips to help students understand addition and subtraction of integers. This article illustrates how the difference and completion (or missing addend) interpretations…

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)

Discusses how important it is for teachers to be open to alternative procedures and strategies that students may use. Suggests that a method that is meaningful rather than one learned by rote will help students develop more confidence and understanding. (KHR)

Describes some differences in representations of mathematical concepts and procedures of recent immigrants. Discusses considerations for success of recent immigrants. (YDS)

Students can form beautiful curves through a kinesthetic experience by using a dynamic geometry program. The examples included are parabolas, pursuit curves, spirals, and more. (MM)