|Overview||Schedule of Assignments||Honor Code|
Dr. Pat Thompson (Pat.Thompson@Vanderbilt.edu)
|Office Hours||TBA and by appointment|
1. Quizlets (spontaneous quizzes, always unannounced)
2. Mini project
3. Two examinations.
5. Course project.
The course is about mathematics--teaching it, doing it, and thinking it. The only reason we will use computers is that--sometimes, if used properly--computer programs can be useful in all three.
We will be engaged in two qualitatively different kinds of activity over the semester. In the first kind of activity, content activities, you will be students of mathematics. In the second kind of activity, pedagogical activities, you will be teachers of mathematics. The programs you use as students will be the programs you use as teachers. The purpose for this structure is that to teach for understanding you must first have an image of what you want your students to understand. That image will be what guides you when selecting/designing course materials, preparing your instruction, and engaging your students during instruction. The content activities are intended to enrich your images of algebra, geometry, and calculus. The pedagogical activities are intended for you to learn to express those images in ways that are conducive for students to build powerful mathematical understandings.
One of the most important abilities you must develop to be a good mathematics teacher is the ability to conduct conceptual conversations, with yourself and with your students. A conceptual conversation is one that has a diminished emphasis on technique and procedure, and an increased emphasis on images, ideas, reasons, goals, and relationships. The one thing I hope you develop through this course, and which I will value and reward, is the orientation to look for big ideas--to realize that mathematics is not about getting answers to questions, but rather it is about developing insight into relationships and structures, and that solutions to a sophisticated or complex problems emerge from understanding them deeply instead of memorizing a procedure.
You will write a lot in this course. The reason for this is so you are forced to organize your ideas and understandings coherently. If you give incoherent explanations and analyses of a situation or an idea, then you don't understand it. Equivalently, if you understand an idea or a situation deeply, you should be able to speak about it coherently and conceptually. So, you can test your understanding of an idea by trying to explain it.
Written assignments will be of two types, one for individual assignments and one for groups of assignments. Assignment groups are indicated in the course syllabus by individual assignments being enclosed within a rectangle.
Individual assignments (those appearing in the syllabus and those I hand out in class) will contain questions and activities. Your write-up of an individual assignment will be to present your work on each question--logically, clearly, and neatly. Your work should not only respond to a task or question. It should respond in a way that would help one of your students come to understand essential ideas in the problem or task.
Feel free to write about insights you gained as you worked on the problem. Some people have found it useful to do their work in two columns--one for your scratch work and one for remarks to yourself about ideas that occur to you. Please include sketches, diagrams, etc., and write in complete, coherent, easy-to-read sentences. It sometimes help if you imagine that you are talking to a bright student who has not yet studied this material. Above all, do not imagine that you are talking to a professor of mathematics. If you do, you probably won't say what you should!
All assignments will be collected during the term. I will not accept late submissions of a write-up, except in the case of medical emergencies or excused absences. So, submit whatever you have on the day it is due. Due dates are posted on the course schedule of assignments. Assignments will be graded according to a highly sophisticated evaluation scheme.
It is easy to miss the forest by concentrating on the trees. In the case of this course, it is easy to miss the conceptual development of a set of assignments when focusing exclusively on individual assignments. To counter that tendency, you will write a summary of the assignments within each assignment group. An assignment group is indicated (on the course syllabus) by a heavy black border around the assignments composing the group.
Please use these major section headings to organize your assignment-group write-ups. You are free to use sub-headings of your own. I will not grade write-ups which do not use this organization.
Suggested questions to think about:
With what ideas did this assignment group start? With what ideas did it end? What are the connections among these ideas? How did the assignments build upon each other?
Suggested questions to think about:
What aspects of your activities with these assignments would have been less productive, or not possible, had you not been able to use a computer program, and what aspects of your activities might be productively taught without the aid of a computer?
In this section you are to reflect on the relationship between what you learned from this assignment and its implications for your teaching of mathematics. Examples of things people have written about in the past are:
- How using [this software] to explore [these ideas] made me--and will make my students--think about [the ideas] differently than trying to learn [these ideas] without [this software].
- Ideas that using this software makes accessible to students, but at the same time could set the bar for success higher than it is now.
- What I now realize is essential that students understand about [the ideas addressed in this assignment]
- Activities I might have students engage in to build up to [the ideas addressed in this assignment]
- How I might have taught [this idea] before this assignment, and how I realize the need to do things differently
- How my ideas of mathematics and teaching mathematics were affected (or not) by what I learned in [this assignment].
Please use a word processor (preferably MS Word) to prepare your group writeup. Use embedded, wrap-around graphics when including a screen from a program. (See me if you do not know how to capture a portion of a screen for pasting into a word processor.)
You will work with one student to determine what he or she knows about functions, teach one lesson using technology, and assess the students' learning. Click here for more details.
You will select a unit from a high school text and design instruction that builds upon what you've learned from this course so that the text is still a resource even though the instruction has a much more conceptual focus. Click here for more details.
Attendance: Class attendance is mandatory.