## Math 444 and 487 Autumn 1998

This is a brief collection of information about Math 444 and Math 487. It will be expanded as the quarter progresses.

### Contents

#### Purpose of 444

While everyone is welcome in the course, the primary purpose of the course is to prepare students for teaching geometry in middle and high school.

Thus on the one hand, the course aims to instill a broad understanding and appreciation for geometry and on the other hand it aims to help students to acquire the competence in geometry they need to be mathematics professionals.

In addition, it is important that students experience a variety of ways of learning geometry so that they can make informed choices for methods of instruction when they become teachers. Thus the course provides experiences in working in groups, problem solving, mathematical writing, making and experimenting with physical models and manipulatives.

Plus, the required Math 487 Computer Lab provides an extensive experience using technology, mostly The Geometer's Sketchpad.

#### Content of 444

This is a rough outline of the topics in Math 444.

##### Elementary and Plane Euclidean Geometry.
This will include a quick review of high school geometry and then quickly move to important ideas such as the idea of a locus and how loci are used to solve problems.
##### Intermediate Geometry of Triangles.
The approach will be synthetic (no coordinates) at the beginning, but will later include coordinates and algebraic tools.
##### Vector and Coordinate Geometry.
The approach will be synthetic (no coordinates) at the beginning, but will later include coordinates and algebraic tools.
##### Beginning Polyhedra.
The Platonic solids and derived polyhedra will be studied using physical models.
##### Plane Transformations and Symmetry.
An important tool for thinking about geometry is the concept of a transformation. We will begin with the nature of transformations, their classification, how they combine, and how they can be used for geometric problem solving. Then the theory of transformations will be applied to study symmetry in the plane and plane tessellations.

#### Structure of 444

The course is organized fairly conventionally in some respects, with regular homework assignments, a midterm, some quizzes, and a final exam.

In addition, because of the preservice teaching role of the course, there will be a number of assigned activities that involve presentation and evaluation of mathematics.

One unusual feature of the grading is that we will attempt to measure and count a very high level of mastery of the more elementary topics (i.e., "high school geometry") as well as a more conventional approach to more advanced topics.

There is some homework in Math 444 which is based on what has been learned in the required computer lab, Math 487.

#### Math 487

This is a computer lab required of all 444 students. The two-hour labs will generally consist an exploratory geometry investigation with software such as The Geometer's Sketchpad. There may be a small amount of additional work outside the lab to finish the 487 assignment for the week.

However, the 487 work may segue into a homework activity in Math 444. It is probably most useful to think of 444 and 487 as two parts of a single course. It is misleading to think of every computer-based assignment as part of 487 just because it uses computers.

#### Textbooks

1. ```Author: Bix
Title: Topics in Geometry
ISBN:   0-12-102740-6.
(required for 444)```
2. ```Author:  Birkhoff, G. D., and Beatley, R.
Title:  Basic Geometry
Publisher:  Chelsea
(required for 444)```
3. ```Author: James King
Title: Geometry Through the Circle with The Geometer's Sketchpad
Publisher: Key Curriculum Press
ISBN:  1-55953-047-2
(required for 444 and 487)```

Students in Math 444 will need the following materials in class each day:

• Ruler
• Protractor
• Compass
• Scissors
• Graph Paper

In addition, for certain class sessions (announced in advance) and homework, students will need the following geometry tools or "manipulatives". These will be available at Math 'n' Stuff.

• Mira or Reflectview
• Hinged mirrors

Finally, students who have home computers may find it convenient to purchase a copy of the Student Version of The Geometer's Sketchpad for \$45 from the Math Sciences Computing Center or to download a Free Demo Version .

#### Prerequisites

The prerequisites are listed in the catalog, but the most frequently asked questions or concerns are these.

• I haven't had geometry for 5, 10, 10 years. Will this be a problem?
• How much linear algebra or calculus do I need to know?

Not much specific knowledge from high school geometry is required, but a lot more "mathematical maturity" is expected than from a high school geometry student. For example, students in 444 are expected to have a good understanding of functions, of algebra, of coordinates and some experience with mathematical reasoning.

From linear algebra, a student should understand linear equations in 2 and 3 variables and to have some knowledge of vectors and matrices.

In addition, some facility is expected with visualizing shapes in two and three dimensions, as done in Math 126 multivariable calculus.