Math 162 Math for Teachers II Spring 2006
Professor: Dave Kung
Office: 175 Schaefer Hall, x4433 or 240-895-4433
Text: Mathematics for Elementary School Teachers by Tom Bassarear
Office Hours: Monday 10:30-11:30
Overview: Math 162 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. The activities will be drawn from the two texts, from handouts, and from other sources. These problems and the related readings 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 be able to complete every math problem asked of you this semester!
As a teacher, your ability to communicate mathematical ideas will be much more important than your ability to just solve problems. Furthermore, every day you will have to listen to students’ explanations and try to discern what they mean. To help develop these skills, you will be expected to discuss mathematics in class, listen and respond to your classmates’ ideas, examine multiple solutions to problems, and write out complete solutions as homework. The emphasis will always be on explaining your reasoning and reflecting on the process of mathematical reasoning.
In the classroom, we will put a significant emphasis on modeling the many facets of mathematical thinking. Thus we will all work to make clear, precise definitions, formulate conjectures, be critical and skeptical of others’ work (but not of other people themselves), and prove or disprove those conjectures.
We will also have the opportunity to practice two important skills this semester: choosing classroom activities and anticipating student reactions. One day this semester we will host a local class. For this class visit, you will get to find activities appropriate for their ability levels and hypothesize what difficulties they will have with your problems. Afterwards, you will have the opportunity to reflect on the experience, critiquing both your own work and the materials you chose.
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.
Topics: After working on general problem solving skills during the first week, we will dive into geometry, covering chapters 8, 9 and 10 over the course of 6 or 7 weeks. From there we will go back to chapter 7, covering probability and statistics over 3 or 4 weeks. If there is time, we will spend a week or two covering algebra, and how the concepts of algebra can be introduced early in the K-6 curriculum.
Grading: Your grade in this course will be determined as follows.
Class Participation: 10%
Midterm Exam: 20%
Class Visit: 10%
Written Work: 20%
Running Class Discussion: 10%
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. 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 March 9th at 6pm. I don’t believe in timed tests; you may take as much time as you’d like on this exam. Please mark this on your calendars and inform me of any conflicts.
Class Visit: Once this semester, we will be visited by a St. Mary’s elementary school class. In preparation for this, you will be planning a mathematical activity for them. Written reflections before and after the visit will be required.
Written work: Written work will come in two flavors, solutions to mathematical problems and written reflections on mathematical topics. In general, you will have a week to complete each written assignment (though I reserve the right to give a quicker deadline for smaller writing assignments).
Running Class Discussion: Many scholars have researched the teaching and learning of elementary mathematics. In consultation with Dave, you will identify an article for the class to read. After doing additional background reading, you will run a class discussion on the reading. Possible topics include the NCTM Standards and their implementation, the Van Heile levels of geometrical understanding, and Ma’s Profound Understanding of Fundamental Mathematics.
Final Exam: The final exam is scheduled for Saturday, May 6th at 2pm. Again, you may take as much time as you need.