Investigating symmetric dot patterns provides opportunities for foundational mathematical learning that is not restricted to multiplication alone. Students have opportunities to learn about the properties of symmetry, about the generalization of patterns, about writing and interpreting equations--all areas of study in grades 3-5. And symmetric dot…

The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

Arguing that mathematics is a form of communication that students need help in understanding, this article describes a set of seven simple interactive LogoWriter tools that can be used to help children explore the language of multiplication. Examples of the use of graphics in responding to children's commands are provided and several exercises are…

Calculators can be used in primary schools in a number of situations. They are most beneficial when working with large numbers, dealing with real data that leads to complex calculations, performing repetitive calculations, developing concepts, estimating and checking, problem solving, and looking for patterns and/or relationships. But what if the…

Design details, operation, and initial field test results are reported for DynaMath, a computer-based dynamic assessment system that provides individually tailored, instructionally useful assessment of students with disabilities. DynaMath organizes and outputs student performance data, graphically shows the "zone of proximal…