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December 2011, Volume 105, Issue 5

FEATURES

A New Perspective on Three-Dimensional Geometry
Jennifer E. Circello and Scott R. Filkins
A geometric solids unit inspired by Plato’s Cave Allegory uses different forms of three-dimensional objects to give students a clearer understanding of the realities of these objects.

Teaching Geometry through Problem-Based Learning
Carmel Schettino
One secondary school’s mathematics department decides to change its geometry curriculum.
Second Look:
Problem-Based Learning

Analyzing Highway Speeding Data in the Statistics Classroom
Paul Laumakis
Students bring the real world into the classroom by studying speeding data collected on two Pennsylvania highways.

Adding Depth to Geometry through Flatland
Gail Marie Anderson
This classic novel introduces students to core geometry concepts, engages them in spatial visualization, and provides rich, cross-curricular learning opportunities.

more4u-MT-100x23 
Podcast from 2012 Annual Meeting in Philadelphia, Pennsylvania
The Making of Flatland 2: Sphereland
Presenters: Seth Caplan, Dano Johnson 

Customizable Activity Sheets for Adding Depth to Geometry through Flatland

Finding Possibility and Probability Lessons in Sports
Nutjira Busadee, Parames Laosinchai, and Bhinyo Panijpan
Tackling probability problems before being introduced to the formulas—especially when the problems involve sports—enhances students’ understanding of permutation and combination.

Second Look - Problem-Based Learning

Bugs, Planes, and Ferris Wheels: A Problem-Centered Curriculum
This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. Student examples and activities are demonstrated and discussed. The students discover mathematical concepts in the context of the problems and activities in the materials.

Transition to a Problem-Solving Curriculum
The author's experiences in attempting to transition students to a non-traditional problem-solving curriculum including examples of problems and pros and cons of the program.

Read how you can use this article as part of a Professional Development Experience.

Promoting Equity in Mathematics: One Teacher's Journey
The impact of using a problem-based curriculum in a heterogeneous classroom environment in a pilot program. The author finds tracking does not offer challenges to minority and struggling students. A problem based curriculum provides equity for all students.

Gathering Circles: An Experience in Creativity and Variety
Materials and methods that maintain students' interest and encourage them to think creatively, develop mathematical reasoning, and look at problems from different perspectives, all within an open-ended approach to problem solving. Questions for discussion are included.

Problem Solving Standard for Grades 9-12

Instructional programs from prekindergarten through grade 12 should enable all students to—

  • build new mathematical knowledge through problem solving;
  • solve problems that arise in mathematics and in other contexts;
  • apply and adapt a variety of appropriate strategies to solve problems;
  • monitor and reflect on the process of mathematical problem solving.