Spatial concepts are important to the development of many skills, including reasoning and problem solving. Here are guidelines for making geometry learning more effective for elementary-grade students. (Editor)

Three teaching ideas are presented: a way to solve problems based on the attitude to the hypotenuse in a right triangle, some interesting applications of percentages in determining pay raises, and a flowchart guide for reducing polynomials. (MP)

Describes an investigation of polygons and their properties in which students apply very basic understandings of geometric properties. (KHR)

Explores ways in which Information Communication Technology (ICT) can be used within the classroom environment to enhance pupils' learning and understanding of mathematics. Describes how to incorporate ICT into lessons investigating mathematical proof. (KHR)

Presents a teaching experience with high school students in geometry class using hand signals that reinforce meaning of geometric concepts. (KHR)

Describes ways of using existing popular songs, writing raps, or writing new words for existing tunes in the mathematics classroom to supply motivation and mnemonics. (KHR)

Presented is a script for a classroom presentation introducing weighted means and geometric means to students who are already familiar with arithmetic means. Frequent questioning is included to keep the students mentally active and involved in the development of this new idea. Typical student responses to these questions are provided. (CW)

Introduces four activities on forming rectangles according to specific directions. Critical reading, experimentation, logical reasoning, and validation of given directions are necessary for accuracy. Provides objectives, directions, extensions, answers, and a worksheet for each activity. (YP)

Argues that the derivation of the area of a circle using integral calculus is invalid. Describes the derivation of the area of a circle when the formula is not known by inscribing and circumscribing the circle with regular polygons whose areas converge to the same number. (MDH)

Contributes to the emerging picture of children's development of understanding in geometry and the kinds of teaching that can support it. Describes how teachers can use episode writing to capture student thinking and make instructional decisions. (ASK)

Introduces a technique for developing tasks suitable for group investigation where students work from sets of numerical examples toward making generalizations. (ASK)

Presents a study in which children in four grade 2 classrooms learned about transformational geometry and symmetry by designing quilts, while their four teachers participated in professional development focused on understanding children's thinking in arithmetic, and two of the teachers participated in additional workshops on students' thinking…

The expertise reversal effect occurs when a learning procedure that is effective for novices becomes ineffective for more knowledgeable learners. The authors consider how to match instructional presentations to levels of learner knowledge. Experiments 1-2 were designed to develop a schema-based rapid method of measuring learners' knowledge in a…

"The Simpsons" is an ideal source of fun ways to introduce important mathematical concepts, motivate students, and reduce math anxiety. We discuss examples from "The Simpsons" related to calculus, geometry, and number theory that we have incorporated into the classroom. We explore student reactions and educational benefits and difficulties…

Designing successful learning environments entails drawing on theoretical perspectives on learning while, at the same time, being cognisant of the affordances and constraints of the technology. This paper reports on the development of a software environment called "3DMath", a dynamic three-dimensional geometry microworld aimed at enabling learners…