Math for Teachers I                      Math 161 -- Fall 2005


Dave Kung


175 Schaefer Hall, x4433 (or 240-895-4433)


Classroom & Time

161 SH, noon-1:50 TR


Photocopied Materials from the University of Wisconsin ($20)

Office Hours:



and by appointment.






Overview:  Math 161 is a course primarily for students who are seeking teaching certification. Although more generally applicable, it will be geared toward those seeking K-8 certification. We will spend most of our class time doing group activities, working to develop mathematical reasoning and problem-solving skills.  Although the content will be similar to the mathematics covered in the elementary school curriculum, you will find difficult and interesting mathematical challenges unpacked within very familiar concepts.  The activities we work on will mostly be drawn from the course packet; at other times I will give out supplemental handouts. These problems are designed to be interesting and difficult - you should expect to spend some real time and effort (both in and out of class) struggling with them. However, by collaborating with your classmates, you will succeed at all of them!

As a teacher, you will find that your ability to communicate mathematical ideas will be much more important than your ability to just solve problems. Toward this end, you will be expected to discuss mathematics in class and to write out complete solutions to problems. The emphasis will always be on explaining your reasoning and reflecting on the process of mathematical reasoning in general.

Grading: Your grade in this course will be determined as follows

Class Participation:


Midterm Exam:


Class Visits:


Final Exam:


Written Work:


Class Participation: Learning in this class is considered to be everyone's shared responsibility. Part of that responsibility is attendance; when you are not here, not only do you miss important work, but the entire class misses out on your contribution. You may miss up to 3 days for reasons of health, religion, etc. without penalty. Arriving late or leaving early counts as half an absence. If something comes up which will cause you to miss class, please contact me ASAP (preferably by email). If you are a student-athlete or have special needs, please see me in the first two weeks of the semester.


Midterm Exam:  The midterm exam will be given on October 27th at 6pm. There is no time limit on the exam – I am more interested in knowing that you can solve mathematical problems, not how fast you can do it.  Please mark this on your calendars and inform me of any conflicts ASAP.  Both the midterm and the final will require significant amounts of writing, with the emphasis on your mathematical reasoning.

Final Exam: The final exam is scheduled for December 15th at 2pm.  There will also be no time limit on the final.

Class Visit: Once or twice during the semester, we will be visited by a class from a local school.  In preparation for their visit, you will choose activities appropriate for their ability levels and predict how students will approach them.  Afterwards, you will have the opportunity to reflect on the experience, critiquing both your interactions with the students and the materials you chose.  I am currently working on organizing these visits with local schools and will inform you of the dates as soon as possible.  It will be next to impossible to make up work if you miss a class visit.

Written work: There will be two types of written assignments in this course: problem write-ups and reflections.


Problem write-ups: You will be asked to write up some of the problems we do in class and to write reflections on some other related topics. Your problem write-ups should be clear and complete. They should include a clear statement of the problem, so that no reference to the text material is necessary. (In other words, if you hand your report to a friend who has never seen the problem, she should be able to understand the problem and your solution without you having to say anything.) They should describe the strategies you used to solve the problem, including those that didn't work so well and why they didn't work. In your description of your solution, you must explain why it is a solution as well as what the limitations of your solution are (Is it the only solution? Does it apply to all cases of the problem, or only to specific cases?). You should also include a conclusion that discusses what we can take away from the problem. In general, your write-ups should give a clear idea of the mathematical thinking that went into your work.

Reflections: About every two weeks, I will assign an essay which forces you to reflect on mathematics, learning, teaching, or some related topic. The more you've thought deeply about these topics, the better a teacher you'll be, and the goal of these assignments is to get you to think deeply.

I strongly encourage you to type your write-ups (adding pictures and mathematical notation if necessary). The reflections, which will be more like essays, must be typed. Your portion of the lesson plan critiques would also be typed. Accept for the very first assignment, you will have at least a week between when I give any assignment and when it is due.

Questions: Feel free to get in touch with me anytime during the semester with any questions or concerns you have. The more feedback you give me, the better I can adjust the course to your needs.

Philosophy and Practice: This is a course in mathematics, not math methods. Our focus will be on learning mathematics together by solving interesting problems, alone and in groups. Since all of us are in the process (which goes on forever) of becoming teachers, it will be appropriate to occasionally step back and reflect on pedagogy. I encourage you to do this in your written work whenever you feel so inclined, and to bring things up in class discussions when appropriate.