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.…

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…

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)

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)

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)

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)

Presented are several consequences of Ceva's theorem which deal with ratios of segments formed when a parallel to one of the sides is drawn through the point of concurrency. The proofs of these theorems are included and are of varying degrees of difficulty. (KR)