Math 495:T1, Spring 2007

Course Title

640:495:T1 Topics in Mathematics

Connecting advanced mathematics to high school mathematics

Basic Information

LecturerProfessor Amy Cohen
Office530 Hill Center, Busch
Tentative Office Hours...Th 2:30-3:30pm and by appointment

Course Meetings... 4:30-7:30p.m. in Murray 115 on CAC

No textbook. Readings will be distributed

Registration requires a special permission number.

Students in the fifth year of the Five-Year Certification program will receive a special permission number by e-mail. Other students desiring to take this course should consult with Professor Cohen before attempting to pre-register for this course.

This course attempts to answer some very sensible questions: What can a future teacher get out of advanced math courses that makes a teacher more effective? How do the ideas, methods, and procedures of advanced math provide the kinds of insight into high school content that allows a teacher to answer questions, correct misunderstandings, motivate future work, etc? How does mathematical content knowledge strengthen pedagogical content knowledge?

Course overview

Completing advanced mathematics courses, including advanced calculus, abstract algebra, and college geometry, is an important component of students' preparation to become teachers of high school mathematics. In these advanced mathematics courses, students are exposed to the importance of mathematical precision and rigor as well as new modes of mathematical reasoning. By studying topics from high school mathematics from an advanced mathematical viewpoint, students' understanding of these concepts can be enriched so that they should be better able to teach these concepts in their classrooms. For a variety of reasons, these potential benefits are not always realized and future teachers frequently question the value of completing advanced mathematics courses.

The purpose of this course is to help you build connections between your experiences in your advanced mathematics courses and the high school mathematics that you will teach. The first nine weeks of this course will focus on mathematical content with frequent mention of pedagogical issues. The rest of the course will focus on mathematical pedagogy with frequent reference to mathematical issues. In some cases the content we discuss will overlap with that content you will teach. One example is the reason "spurious roots" arise in solving certain algebraic equations. In other cases the content will be an advanced concept that you will not teach, but which provides insight into material you will teach. An example here is the interactions among algebraic ideas like "group homomorphism", linear algebra topics like matrix multiplication, geometry topics like rigid motions, and high school topics like trigonometry.

Your responsibility will be to deepen your understanding of the mathematics and to develop insights into the ways that advanced mathematical issues can inform the way you teach and the way you react to your students' developing understandings and misunderstandings.

Goals of this course

Expectations of this course

Grading and assignments

Very Tentative Course Schedule
Week 1...Recall content from advanced math courses
Week 2... Groups and homomorphisms
Week 3... Rotations, equivalence relations, matrices
Week 4... Rotations, equivalence relations, matrices
Week 5... Modular arithmetic and divisibility
Week 6... Equations, inequalities, properties of number systems
Week 7... Solving equations, implicit implications
Week 8... Exponential functions, the number e
Week 9... Limits, real arithmetic
Week 10..Generating examples
Week 11.. Definitions
Week 12.. Didactic obstacles
Week 13.. Reading mathematics,turning exposition into dialog
Week 14.. Presentations

Textbooks and readings

There is no formal textbook. There will be assigned readings. Short readings will be distributed in class. Longer materials will be put on reserve in the library.

last modified 1 Nov 06