The author seeks to use the limited contact time they have with students to engage them not only in academic pursuits but also in a discussion of the divine mission of humans. Since this can be difficult to meaningfully do in a math class, the author is continually searching for meaningful, engaging points of contact between mathematics and…

External representations such as diagrams often appear in teachers' repertoire of pedagogical tools to support students' conceptual learning and problem-solving activities. The study of diagrams and diagrammatic representations has received growing interest from diverse disciplines. Diagrams remain a central feature of science, technology,…

"How Much Can You Bench?" appears in the "Mathematical Lens" section of "Mathematics Teacher." "Mathematical Lens" uses photographs as a springboard for mathematical inquiry and appears in every issue of "Mathematics Teacher." This month the mathematics behind the photograph includes finding areas…

Shared story reading is a practice that has been used successfully to promote literacy skills for all students. The benefits of shared story reading are not exclusive to literacy instruction and should carry into other disciplines such as mathematics. Using shared story reading to teach mathematics concepts can play an important role in…

This article uses photographs as a springboard for mathematical inquiry to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. Herein, two photographs are presented along with a discussion of the meaning of slopes and their relationship to gradient and pitch. (Contains 6…

This study investigates two sixth grade students' dilemmas regarding the parity of zero. Both students originally claimed that zero was neither even nor odd. Interviews revealed a conflict between students' formal definitions of even numbers and their concept images of even numbers, zero, and division. These images were supported by practically…

In 12 audio taped sessions, three kindergarten children engaged algebra in a teaching for understanding, thematic project. Toni, Asa, and Cornel had one-on-one lessons dealing with simple natural numbers, patterns, and relationships. Along the way, each child studied one of Toni Morrison's Who's got game books to explore repetition patterns in…

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be…

The authors discuss mass as one of the three fundamental measurements (the others being length and time), noting that estimation of mass is little taught and assessed in primary schools. This article briefly explores the reasons for this in terms of culture, practice, and the difficulty of assessing estimation of mass. An activity using the…