Reflective Journal for Math 421

For this project you will keep a journal which reflects on your experiences in the course and on ideas and questions that arise or occur to you as you participate in the class. You should type your entry as soon after each day's class as possible. Each day's entry should be close to a (typed) page for each class day. When entries get much shorter than this, they usually become somewhat superficial or perfunctory. Your writing should go beyond simple reports of what happened or what you did on any given day to include some reflection on what these events mean for you as a student and future teacher of mathematics.

Please do not take on this optional project unless you enjoy writing about your experiences and see some benefit in it for yourself. If your entries become perfunctory or too brief, I may ask you to discontinue it.

Journal entries will be submitted using at the course dropbox, M421 W11 Journals and Papers. You should write a separate entry for each class meeting, but may upload two entries for one week as a single document, no later than noon on Saturday.

Here are some topics you might reflect on. These are only suggestions. You should focus on whatever strikes you as significant in your role as a mathematics student in this class, especially those aspects that bear upon your intention to teach mathematics.

• Your experience learning mathematics. You might find yourself surprisingly stuck on a problem or surprisingly able to think about something because your surroundings, or the people you are working with, etc. You might notice how you see old calculus ideas in an entirely new light because of the nature of your activities here or because this is the first time you've been able to reflect on what you know about calculus. These and many other experiences could be the basis for reflections.
• Mathematical Ideas.You might reflect on particular mathematical ideas you have dealt with during the class. Are there some that strike you as particularly interesting, powerful, or unusual?
• Working in groups. Groupwork is highly promoted by some people as a good way to learn mathematics. Others have their (reasonable) doubts. What is your day-to-day experience of this learning environment? Think about particular moments in the day's experience. Were there moments in which it was helpful to be working with others? Are there "unique advantages" of working with others - benefits you derive from working in groups that you cannot get any other way? On the other hand, what are the drawbacks of working in groups? How have you tried to cope at moments in which working in a group was not helpful? What could an instructor do to minimize the effect of these drawbacks?
• Talking mathematics. Because of the nature of this class, you will undoubtedly spend an unusual amount of your time "talking mathematics," by which I mean, explaining your ideas in ordinary language, trying to understand the thinking of others, etc. You might comment on how you think this influences your mathematical experience and thinking. Does it shape how you think and understand things? If not, what is its effect on you?

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Most recently updated on January 3, 2011.