Children shouldn't memorize mathematical facts and procedures like parrots, but should learn to think mathematically. In this article, the authors stress that mathematics involves making sense. They provide some simple mathematical challenges for readers to make sense of and to try with their classes.

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12-15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). "Cabri-Geometry (software)," Universite de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct:…

Invites students to try magic-number tricks and discover how and why they work. (Author)

Discusses various tools to further understanding of measurement. (Author)

Argues that the way in which students solve a particular problem can be analyzed to gain insight into how students think about the mathematics involved. Discusses the use of knowledge gained from listening to student conversations about their strategies to orchestrate classroom discussions. (ASK)

Presents a common knowledge puzzle in which it becomes possible to reason about other people's responses to the puzzle. (ASK)

Mathematics truly is magical, especially for students with strong number sense and algebra skills. This paper describes a variety of mathematical surprises that will capture students' interest and motivate exploration of mathematical ideas. While the tricks themselves are fascinating, push students to think about the reasons why these stunning…

Presents activities providing a cultural journey through history that allow children to understand that many mathematicians have contributed mathematical thoughts and ideas. (KHR)

Presents responses to the Marbles problem, which explores the many ways to arrange a given number of square tiles. (Author/YDS)

Describes the work of one mathematics teacher as she uses literature to make factorials both interesting and comprehensible to middle school students. (Contains 10 references.) (YDS)

Uses a Calculator-Based Ranger and a graphing calculator in problem-solving mode to introduce an exploration of graphing-related concepts including intercepts, slopes, and rate of change. (YDS)

Describes the implementation of a real-world context focused on teaching proportional reasoning. (YDS)

Discusses problem solutions for questions originally posed in the column "Food for Thought from Jay's Diner." (YDS)

Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)

Examines activities and children's thinking in four main areas of the Geometry Standard in the National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics": (1) properties of shapes; (2) locations and spatial relationships; (3) transformations and symmetry; and (4) visualization. (Author)