Instructor: Jennifer Christian Smith
Office: SZB 340E
Phone: 232-9682
Email: jenn.smith@mail.utexas.edu
Office Hours: Wednesdays 4:00-5:00, Thursdays 3:00-4:00, and
by appointment
AIM: drjennsmith
Course Description:
What do upper division courses such as abstract algebra, number theory, topology, and analysis have to do with the mathematics taught in middle and high school? What are the connections between university level and secondary school mathematics? Why is it important for future high school mathematics teachers to take such courses that seem on the surface to have little in common with secondary math?
In this course, we will address these questions by carefully examining important concepts in the secondary mathematics curriculum, such as real and complex numbers, functions, polynomials, solving equations, congruence, distance, similarity, area, volume, and trigonometry. We will solve and extend problems, discuss the history and applications of these topics, analyze problems from high school mathematics from an advanced perspective, and explicitly make connections between the concepts taught in high school and their more abstract analogues encountered in undergraduate mathematics courses. We will utilize appropriate technology whenever possible. The structure of the course will be problem- and discussion-based.
Course Information:
• Meets Wednesdays, 5:00-8:00, in SZB 344
• Prerequisite: At least one of M328K, M343K, M341, M361K
Required Materials:
• Usiskin, Z., Perssini, A., Marchisotto, E., & Stanley, D. (2003).
Mathematics for High School Teachers: An Advanced Perspective. New
Jersey: Pearson Education, Inc. (Available at the Co-op bookstore.)
• A graphing calculator, such as a TI-83 plus, or a TI-89.
Course Evaluation:
(A) Participation: 40%. This includes attendance, regular presentation of problems,
preparation for class (reading and working problems in advance), and degree
of participation in small group and whole class discussions. (See rubric below.)
(B) Written assignments: 40%. You will be required to turn in written explanations
for 2-3 problems each week. These problems will be chosen at the end of each
class meeting and will be due at the beginning of class the following week.
(C) Final project: 20%. Projects will be chosen from the book. You may work
alone, but I prefer that you work with a partner. You will present the results
of your project in class and turn in a paper. (See Project information below.)
Course Policies:
1. Attendance is critical in a course that meets weekly! Because of the structure
of this course, it is virtually impossible for a student to make up a missed
class. More than one absence will lower your participation grade by a letter.
2. This course will be problem-based, and so it is critical that you have read
the chapters and worked through the problems prior to class. Your participation
(and hence your grade) will be hindered if you are not prepared for class!
3. I will utilize BlackBoard for course announcements and assignments. It is
your responsibility to check the course page regularly.
4. Homework is due at the beginning of class. Late work will receive a grade
that has been reduced by one "letter". That is, late work that would
have received a B will be given a grade of C.
Class Structure:
We will typically follow this format:
5:00-5:30 Warm-up problem and discussion of the day's topic, questions about
the text reading
5:30-6:00 Small group discussion of problems completed in preparation for class.
Groups will work on extending problems and will choose problems they want to
examine more closely.
6:00-8:00 Presentation and large group discussion of selected problems
There will be a 15 minute break at an appropriate time.
Goals of the course
• Examine the structure of secondary mathematics from an advanced perspective.
• Make connections between topics taught in high school math and topics
studied in undergraduate mathematics courses.
• Deepen ability to analyze and generalize problems and their solutions.
• Deepen understanding of previously learned concepts.
The vehicle by which we accomplish these goals is the discussion of problems we’ve solved. It is thus very important that you have worked all the problems before class. The problems are, for the most part, examples of what you would expect your advanced high school students to be able to solve; you should be able to solve most of them without a lot of review of the material. In class, we will discuss these problems and extend the solutions, examine the mathematical foundations of them, and use them as a vehicle for deepening our understanding of secondary mathematics. We will make attempts to tie the underlying ideas to undergraduate mathematics topics whenever possible.
In your small groups, you will begin the process of extending and generalizing solutions of problems you solved before class. One student will then lead a class discussion of the problem, guiding the analysis, extensions, and connections. Each student will be required to lead six of these discussions during the semester.
NOT Goals of the Course
• To find and present answers to as many problems as possible.
• To learn specific content; i.e., to “cover” the text.
• To learn new mathematics topics. (Though this may well happen.)
When examining a solution presented by a classmate, consider the following:
• Is the solution correct?
• Do you understand the solution?
• Do you understand the problem?
• Why is this a correct solution to the problem?
• Can the solution be generalized?
• Can the solution method be generalized or applied in other problem situations?
• What mathematical concepts or theorems can be applied to this problem?
• Is the problem an example of a particularly important concept?
• Does the problem highlight a common misconception students have?
• Are there connections we can make between different areas of mathematics
based on this solution?
• What alternate solutions methods (geometric, algebraic, estimation,
numerical reasoning, modeling, etc.) could be used? What insight would we gain
about the problem from using them?
Study Groups:
I strongly encourage you to meet with your classmates outside of class to discuss
the readings and work on problems. Start building those collegial relationships
now!
Participation Grade Rubric
| Grade | Attendance | Preparedness | Participation | Presentations |
A |
No absences, or one absence due to an emergency or medical situation. Always prompt. | Has clearly read the text prior to class and reflected upon them. Has worked through all assigned problems and is prepared to discuss them. | In small and large group discussions, participates frequently and appropriately. Comments are insightful and contribute positively to the discussion. Respects and listens to the perspectives and ideas of classmates. | At least six individual problem presentations during the semester (approximately one every two weeks). Presented solutions are well thought-out, generally correct, and presenter engages in the whole group discussion. |
B |
One or two excused absences. Occasionally late to class. | Has clearly read the text prior to class, though has not always reflected on them. Has worked through most assigned problems and is prepared to discuss them. | In small and large group discussions, sometimes participates, and participation is generally appropriate. Comments are sometimes insightful and often contribute positively to the discussion. Generally, though not always, respects and listens to the perspectives and ideas of classmates. | Less than six individual presentations, though all of high quality. Presented solutions are well thought-out, generally correct, and presenter engages in the whole group discussion. |
C |
More than two absences, or frequently very late to class. | Has skimmed the text. Has worked through some problems, but is clearly unprepared to discuss them. | Does not participate in class discussions, or participation is frequently inappropriate. Comments are off-topic or otherwise do not contribute positively to class discussion. | Less than six individual presentations, and not of good quality. Presented solutions are not correct or are those of another student. |
If your participation does not meet the standards for a C above, you will receive a participation grade of D. This is bad.