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December 2003, Volume 9, Issue 4

 FEATURES Surprise! Turn Routine Problems into Worthwhile TasksRichard Caulfield, Shelly Sheats Harkness and Robert RileyThis article describes what happened in the classroom when teachers "modified" a traditional textbook problem related to probability and turned it into meaningful mathematical investigations. The "modified" problem had multiple entry points and enough challenge so that students used their own prior knowledge of mathematics as they made conjectures, explored possible solutions, and engaged in rich discourse. Two tasks and an activity sheet are included. Improper Applications of Proportional ReasoningWim Van Dooren, Dirk De Bock, Lieven Verschaffel and Dirk JanssensA description of the improper proportional reasoning displayed by many students aged 12–16 when solving problems about the area of enlarged geometric figures and how persistent they are in this behavior. Geometric Conjectures: The Importance of CounterexamplesJeffery J. Boats, Nancy K. Dwyer, Sharon Laing and Mark P. FratellaAn exploration of the usefulness of geometric counterexamples in helping students develop deductive reasoning. Using Origami to Promote Geometric CommunicationRebecca R. Robichaux and Paulette R. RodrigueA middle school geometry lesson that uses origami to provide students with hands-on experiences related to such topics as angles, triangles, quadrilaterals, polygons, symmetry, congruence, similarity, and fractions. Mathematical communication is promoted throughout the lesson through the use of cooperative learning, peer teaching, and journal writing.a middle school geometry lesson that uses origami to provide students with hands-on experiences related to such topics as angles, triangles, quadrilaterals, polygons, symmetry, congruence, similarity, and fractions. Mathematical communication is promoted throughout the lesson through the use of cooperative learning, peer teaching, and journal writing. Lesson plan and activity sheets included. The Mathematics of Native American Star Quilts- FREE PREVIEW!Maureen D. NeumannThe author examines the mathematics involved in making star quilts and the cultural significance these quilts hold for the Lakota Sioux.

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