Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

The theory of realistic mathematics education establishes that framing mathematics problems in realistic contexts can provide opportunities for guided reinvention. Using data from a study group, I examine geometry teachers' perspectives regarding realistic contexts during a lesson study cycle. I ask the following. (a) What are the participants'…

Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a…

Presents an activity suitable for rainy days in which students solve a story problem to determine how fast a person should run in the rain to get the least wet. (MDH)

This model is useful in identifying specific learning problems and in providing techniques for the teacher to motivate and teach students at all levels. What it is and how it can be used are discussed, illustrated by specific strategies for geometry and science. (MNS)

Two units are developed that provide the student with experience in constructing auxilary lines that are often needed in formulating geometric proofs. (MP)

Four problems are given and discussed involving reflection about a line or the reflection properties of conic sections. Solutions are given. (MP)

Some misconceptions about "squares" encountered among college students as they attempt to master appropriate subject matter in preparation for teaching elementary grades are presented. (MN)

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

The effect of testing format on achievement was investigated. Statistical analysis indicated no significant differences between any of the four formats used. (MK)

Presents the University of Chicago School Mathematics Project's (UCMSP) Every Day Mathematics Program as one current reform-based elementary curriculum incorporating geometry throughout the K-6 curriculum, with an emphasis on hands-on and problem-solving activities. Measures the longitudinal effects of such an approach. (Author/CCM)

Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

Presents a model that relates Polya's ideas on problem solving to teaching practices that help create a mathematics learning environment in which students are actively involved in doing mathematics. Illustrates the model utilizing a high school geometry problem that asks students to measure the width of a river. (MDH)

A list of potential writing ideas and general guidelines to be used in integrating writing into the mathematics classroom are provided. Ideas under the headings of narrative, descriptive, and expository writing are included. (KR)