1. Prerequisite: MATHS 202 with a C- or better grade
2. Course Description: Investigation of selected topics in geometry and measurement, from both historical and contemporary perspectives, with applications in the elementary and middle school curriculum.
3. Course Objectives: The primary objective of this course is to help pre-service teachers recognize that geometry is a vibrant part of mathematics and a key to understanding the world in which we live. Through both informal and formal approaches, students will:
* Investigate properties and relationships of shape, size and symmetry in two- and three-dimensional space;
* Explore concepts of motion in two- and three- dimensional space through the investigation of rotations, reflections, and translations;
* Investigate the nature and purpose of proof (both formal and informal), present written and oral arguments to justify conjectures and generalizations based on explorations;
* Become familiar with the historical development of Euclidean and non-Euclidean geometries;
* Explore the relationship between geometry and measurement in two- and three-dimensional space.
4. Course Rationale: Topics of study in this course are guided by principles and recommendations of the National Council of Teachers of Mathematics (NCTM), the Mathematical Association of America (MAA), and the Indiana Professional Standards Board (IPSB). Mathematics teachers must learn to recognize patterns, make conjectures, and present heuristic arguments to support or explain their conjectures. Observations and deductions should be studied more formally as a mathematical system. Geometries should be considered with an emphasis on problem solving. The need for assumptions, for more formal arguments and for formulating testing and reformulating conjectures should become evident.
5. Course Content: The content of this course will emphasize a problem solving approach that includes generating hypotheses and proving or disproving conjectures. Possible topics of study are:
* The history of geometry, including study of parts of Euclid’s Elements.
* Both Euclidean and non-Euclidean geometries, including appropriate topics n transformational geometry, spherical geometry, analytic geometry, and geometric topology, approached informally and formally.
* Fractal geometry and chaos theory.
* Investigation of two- and three- dimensional physical models, drawings, and computer graphics (e.g. Logo, Geometer’s Sketchpad), emphasizing visualization.
* Investigation of concepts in measurement, including both non-standard and standard units (with emphasis on the metric system), as well as indirect measurement and its applications.
6. Course Format: Lecture, interactive discussion in large and small groups, computer labs.
7. Methods of Evaluating Student Performance: Attendance, in-class assignments and projects, homework assignments and projects, quizzes, exams.
8. Evaluation of the Course: Instruction in the course is evaluated by departmental student evaluations and peer evaluation. The course is reviewed and revised periodically by the Departmental Teacher Education Advisory Committee and the Undergraduate Programs Committee.
(Whitaker, Roebuck; 2/2001)