ALL THESE RAYS! What's the Point?

Every semester, the authors encounter students who are attracted to the visual and spatial aspects of geometry. They have other students who consider geometry to be challenging for the very same reasons. Students are confounded not only by the fact that geometry relies on visual interpretations but...

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Bibliographic Details
Published in:Mathematics teaching in the middle school 2011-03, Vol.16 (7), p.408-413
Main Authors: Roberts, Sally K., Tayeh, Carla
Format: Article
Language:English
Subjects:
Algebra
Curricula
Elementary school mathematics
Equations (Mathematics)
Geometric Concepts
Geometry
Mathematical Concepts
Mathematical problems
Mathematics education
Mathematics Instruction
Mathematics Skills
Mathematics Teachers
Middle school teachers
Middle Schools
Polygons
Preservice Teacher Education
Problem Solving
Secondary School Mathematics
Students
Teachers
Teaching methods
Vertices
Citations: Items that cite this one
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Summary:Every semester, the authors encounter students who are attracted to the visual and spatial aspects of geometry. They have other students who consider geometry to be challenging for the very same reasons. Students are confounded not only by the fact that geometry relies on visual interpretations but also because it has a language of its own and because the rules can change depending on underlying assumptions. Some students in their teacher-candidate classes testify that they are good at algebra but never did well in geometry. The "good at algebra" comment usually translates to being able to complete the symbol manipulation and to "plug and chug" numbers into an equation to return a correct answer. Deriving an equation or using algebra to generalize a solution to a problem is a very different story. Students repeatedly say, "Just give me the formula, and I can solve the problem," with apparent disregard for the fact that discovering the algebraic equation to solve the problem is the true demonstration of algebraic understanding and proficiency. To help their teacher candidates prepare to meet future classroom expectations, the authors begin their geometry courses by introducing a series of carefully sequenced investigations. Teacher candidates move beyond "Just give me a formula" to a deeper understanding by exploring the algebra found in geometric models. Integrating geometry and algebra helps students view mathematics as a connected whole, bringing meaning to algebra through geometry. (Contains 3 figures.)
ISSN:1072-0839
2328-5486
DOI:10.5951/MTMS.16.7.0408