Course Title: Geometry and Measurement

Prerequisite: Numbers and Operations based on the Developing Mathematical Ideas Number & Operation materials

Course Credit: 3 graduate-hours mathematics credit

Catalog Description: Explorations of the foundations of informal measurement and geometry in one, two, and three dimensions. The van Hiele model for geometric learning is used as a framework for how children build their understanding of length, area, volume, angles, and geometric relationships. Visualization, spatial reasoning, and geometric modeling are stressed. As appropriate, transformational geometry, congruence, similarity, and geometric constructions will be discussed. A core course for preparation as a K-8 Mathematics Specialist.

Textbooks:

• “Developing Mathematical Ideas, Geometry. Examining Features of Shape; Casebook.” Schifter,D. Deborah, Bastable, V., and Russell, S., Dale Seymour Publications, Parsippany, N.J., 2000.
  
• “Developing Mathematical Ideas, Geometry. Examining Features of Shape; Facilitator’s Guide.” Schifter,D. Deborah, Bastable, V., and Russell, S., Dale Seymour Publications, Parsippany, N.J., 2000.
  
• “Developing Mathematical Ideas, Geometry. Measuring Space in One, Two and Three Dimensions; Casebook.” Schifter,D. Deborah, Bastable, V., and Russell, S., Dale Seymour Publications, Parsippany, N.J., 2002.
  
• “Developing Mathematical Ideas, Geometry. Measuring Space in One, Two and Three Dimensions; Facilitator’s Guide.” Schifter,D. Deborah, Bastable, V., and Russell, S., Dale Seymour Publications, Parsippany, N.J., 2002.
  
  

Conceptual Framework: The overall goal is to help prospective Mathematics Specialists develop a strong understanding of the geometrical ideas in the school curriculum that is tied both to the ways that children develop their geometric understanding and to the more formal process of definitions and proofs. Specialists should develop multiple ways of knowing why geometric facts are true.

Course Objectives: Develop a deep understanding of the topics in geometry and measurement that are taught in grades K-8 and of the way that children develop an understanding of these ideas.


Course Topical Outline:

• Foundations of Informal Measurement
  
• Van Hiele Model for Geometric Learning
  
• Area/volume/angles
  
• Visualization and Spatial Reasoning
  
• Geometric Modeling
  
• Geometric Constructions
  
  

Course format: The class is taught in a workshop/seminar format, with small group and whole group work and discussions. The class works well as a two week summer institute with 54 hours of class time and significant daily assignments. In a commuting two-week session, more hours are often scheduled with the last part of each day reserved for the participants to work on the team portion of their daily assignments. As a semester class 16 weekly sessions of three hours should work well. The advantage of the semester format is that the participating teachers can explore some of the material with their students.

Course Methods: The course includes mathematical activities, many of which are similar to those described in the case studies.

The course includes daily readings. Instruction is enquiry based and class time is spent on working problems and on large and small group discussions of the readings and problem sets.

Course Assignments:

• Tests and Quizzes - 40%
• Homework/written proofs - 15%
• Projects/papers/in class activities - 30%
• Journals/Exit Papers - 15%
  
  

Other Resources:

• Key Curriculum Resources
  Visit this site for additional mathematics resources for students and parents.
  http://www.keymath.com
  
  
• Serra, Michael, Discovering Geometry: An Investigative Approach
  (Berkley, CA: Key Curriculum Press, 2003)
  
  
• Bennett, Dan. Exploring Geometry with The Geometer’s Sketchpad
  (Berkley, CA: Key Curriculum Press, 2002)
  
  
• Sara, Michael, Patty Paper Geometry
  Berkley, CA: Key Curriculum Press, 1994)
  
  

Other Remarks: In this and other courses there is a difference between commuting and residential institutes in how to handle discussion of case studies and other reading assignments. When participants are doing their reading in a dormitory they are much more likely to discuss the readings before coming to class.