Children's literature can provide useful contexts for teaching mathematics. In this article, the authors discuss the use of the children's book "Measuring Penny" (Leedy 1997) to support Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) related to length measurement. The authors first describe three types of misconceptions…

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…

In this article, the authors describe how their first-grade class used the book "Inch by Inch" (Lionni 1960)--the story of an inchworm that escapes from a hungry robin by proving he is useful for measuring--as inspiration for a lesson focused on exploring length measurement through examining the meaning of an inch. The authors designed a…

Many teachers experience the tension between using published curriculum materials and teaching in ways that are responsive to children. Teachers are often expected to use a particular mathematics curriculum series, but they still want to be able to build on and connect to children's multiple mathematical knowledge bases (MMKB).…

As partners in a professional development project, the authors jumped at the opportunity to use a real-life problem to engage elementary and middle school teachers in a one-day exploration of the concept of area. "Length times width"--a common response to the question, "What is area?"--is a rote formulaic expression that applies only to certain…

Several myths have grown up around problem solving as a result of the manner in which problem solving has traditionally been taught in schools. These myths are harmful to children, they affect curriculum decision of teachers, distort discussions about problem solving and undermine the mathematics reform movement in general.

Learning mathematics has traditionally been thought of as a sequential progression. Children learn to count to 10, then to 20, and then to 100. They learn to add without regrouping and then with regrouping. The authors teach addition before multiplication and the two-times table before the six-times table. They usually teach division as a separate…

The situations created by individual style of problem solving in mathematics by children are discussed. Children can solve their mathematical problem by correcting their misconceptions on their own with the use of open discussions with others.

When permitted, children frequently devise approaches to solving problems that are distinct from those typically used by adults. Presents examples of children's thinking from Project IMPACT which illustrate the crucial interplay between a teacher's instructional decisions and children's thinking while confronting mathematical misconceptions.…