MAT 501 Foundations of Geometric Thinking

Instructor: Matt Jones email:

Website: You will find the syllabus and course assignments on the website.

Office: NSM A-120 phone: (310) 243-2410

Office Hours: Tu 11:30-2:15pm

Th 1-2pm

Tu 7-7:45pm

And by appointment

Text: 501 Course Reader, by Jones, et al.

Materials: As this is a geometry course, you will be expected to have a ruler, pencil, compass and protractor at all times.


MAT 543 or concurrent enrollment. Students must have graduate standing and must have completed one year of full time secondary mathematics teaching.

Course Description

This course is designed to bolster student understanding of geometry as well as introduce students to mathematics education research on geometric thinking. Students in this course will read and discuss research as well as do work on various topics in geometry, with a focus on developing both the notions of rigorous proof and of grade-appropriate explanation. The topics discussed within geometry will be informed by the topics of K-12 geometry, and are meant to enhance and deepen understanding of these topics.

Expected Outcomes

Students will

Demonstrate knowledge about some of the major research relating to K-12 student thinking in geometry and how students learn geometry. In particular, students will be able to use their knowledge of the research to inform pedagogical decisions

Explain the major concepts of geometry and geometric objects at both the formal level (proof) and at a level appropriate for explanation to middle school students, and understand the difference between proof and explanation

Use examples and non-examples to explain Geometric concepts


Students will demonstrate an understanding of the research and of the geometry through the following assessments (Category weights are given in parentheses):

Assignments (20%): There will be weekly homework assignments which will be collected and graded. Out of a possible 7 points, you will be given 6 points for attempting every problem assigned, and 7 points if all problems were attempted and, in addition, your solutions are correct. Five points or fewer will be given to incomplete work. If you will not be in class, you may have someone turn it in for you, or you may turn it in to my mailbox in the Math department, NSM A-124, by 6 pm on the day it is due.

Research Review (15%): Research papers to read will be assigned (see schedule below). A one page write up is required for each reading assignment and will be turned in the day it is due (see schedule). Use the following format for your write-up. List three things you have learned from the reading, your reaction to the reading, and a question you would like to discuss. This write-up needs to be typed, double-space, one-page long with one-inch borders in 12 point times or courier font.

Presentation (20%): Each student will be required to create a classroom lesson which integrates the research covered in this class, and which covers one of the topics in the class. You are encouraged to implement this lesson in your own classroom and collect student work. Then you will provide a summary oral report to the class as well as a written report. You will sign up for presentation dates on the first day of class. Written reports will be due 10th week.

Exam (20%): One exam will be given at the end of the 7th week of instruction. The exam will last one hour.

Final (25%): The final exam will be cumulative, and will be given as listed in the schedule of classes.


Students will be graded on the following scale: A 92-100%, A- 89-91%, B+ 87-89%, B 82-86%, B- 79-81%, C+ 77-79%, C 72-76%, C- 69-71%, D 64-68%, F below 64%.

Academic Integrity

Students are expected to follow university policy regarding cheating and plagiarism as indicated in the current University Catalogue. Cheating and plagiarism will not be tolerated in this class.

Make-Up Policy

Make-up work is not allowed. Exceptions may be made at the instructor’s discretion for missed exams for which the student has medical documentation.


Week 1 Introduction and reading research

Week 2 Triangles—angles and classification by angles or by sides, Polygon angle sum

Area—square units, triangles and quadrilaterals

Week 3 Area—finding areas of polygonal regions

Research assignment 1 due

Week 4 Polygons—area and angle sum

Week 5 Geometric probability

Week 6 Circles—pi, circumference and area

Research assignment 2 due

Week 7 Cubic units, volume and unit analysis

Exam 1

Week 8 Perimeter, surface area, and scaling factors in 1-, 2-, and 3 dimensions

Week 9 Constructions and patty paper geometry

Research assignment 3 due

Week 10 Line, angle, and triangle congruence, rigid and non-rigid motion

Written presentation reports due

Week 11 Pythagorean Theorem—concept, application, and proofs

Week 12 Applications of congruence to properties of polygons

Research assignment 4 due

Week 13 Coordinate geometry

Week 14 Cross-sections and perspectives of 3-dimensional objects

Week 15 4-dimensional geometry

Review and research wrap-up

Research assignment 5 due