MATH 5002/7002 Geometry and Problem Solving 3 hours

Oasis Title: GEOM & PROB SOLV.

Prerequisite: MATH 5001

A deep examination of topics in mathematics that are relevant for elementary school teaching. Geometric shapes and their properties. Measurement, especially length, area, and volume. Applications of elementary mathematics.

Course Objectives: To strengthen and deepen knowledge and understanding of measurement and basic geometry and how they are used to solve a wide variety of problems. In particular, to strengthen the understanding of and the ability to explain why various procedures and formulas in mathematics work. To strengthen the ability to communicate clearly about mathematics, both orally and in writing. To promote the exploration and explanation of mathematical phenomena. To show that many problems can be solved in a variety of ways.

Topical outline:

Visualization. Angles. Geometric shapes and their properties. Constructions with straightedge and compass. Transformation geometry: reflections, translations, rotations. Symmetry. Congruence. Similarity. Measurement, especially length, area, and volume. Converting measurements. Principles underlying calculations of areas and volumes. Why various area and volume formulas are valid. Area versus perimeter. The behavior of area and volume under scaling.

Computer technology will be used.

Text: Mathematics for Elementary Teachers volume II, preliminary edition, by Sybilla Beckmann, Addison-Wesley, 2003

Chapter 7 Geometry, Chapter 8 Geometry of Motion and Change, Chapter 9 Measurement and Geometry

Math 7002: for graduate credit, students must complete an additional course project. The project could consist of several essays, or a longer paper, in which the student discusses some aspect of the course material in depth, or in which the student relates the course material to their future teaching (e.g., with a collection of lesson plans or with a discussion of some lesson plans). However, other creative ideas could also be acceptable. For example, students might think of a creative way to tie their course project for math 7002 to something they will be doing for one of their other courses.