Class Structure

Each MATH 245 instructor implements their own style and philosophy of teaching. Below is an outline of what it will be like day-to-day in my sections of MATH 245 this semester. It looks complicated when written down, but I swear it’s not so bad!

// During class

  • Get back graded work from Section k-2:  The first 10 minutes of class will be spent deconstructing your writing and proofs using the overhead projector.
  • Turn in homework printouts for Section k-1:  All homework must be typed in LaTeX, available in Overleaf, and handed in as a printed copy, to get full credit.
  • Q&D (“Quiz and Discussion”) for Section k, including:
    • Effort Quiz: You will take a short quiz on which you will show your effort on a homework problem of my choosing. During the quiz you may use any worked problems or notes in your own handwriting. Generally, to get full credit you will be expected to write complete solutions for easy-to-medium problems, and show thought and preliminary work on harder problems.
    • Discussion:  The bulk of class will be spent discussing the more difficult points in the reading and the homework problems you have done for today’s section. You may be asked to answer questions and/or go to the board.
    • Choose problems for writing up: Based on what happens in the discussion, I will choose a subset of the day’s homework problems for your group to type up in LaTeX and hand in on the next class day.
  • Preview of Section k+1:  The last 15 minutes of class will be a short preview lecture of the material from the next section. It is up to you to carefully read this section and complete the bulk of the assigned homework for the next class day.

// After class

  • Do final group LaTeX writeups for Section k:   Work with your group to complete the today’s selected LaTeX assignment. Problems must be complete and well-written. Everyone in your group should participate on every problem; please do not split up work. During class I may call on individual group members to explain and clarify the group’s written work.
  • Do reading and initial homework for Section k+1:  Read the next section and complete as many homework problems as possible to prepare for the next class. You will be graded on your class participation, so don’t skip this part!

// But WHY

I strongly believe that students should understand the reasons for class structure choices like those above. Here’s my motivation for this course’s class structure:

  • First, note that the structure above means that coverage of any particular section stretches over four class days: I give a 15-minute preview lecture the first day, and you read the section and complete the homework after class; the next day we discuss the material as a class, and you have a chance to show your effort, present your work and ask questions on the material; then you type up a subset of the homework problems with your group members and hand it in; and finally, I return your written work and we review final writeups as a class.
  • In this “bridge course” it’s important that you start developing the skill of reading, understanding, and solving problems about a topic on your own, with less hands-on direction and help from an instructor than you may be used to. Most of the structure above is set up to force you to do this, but also to try to help you ease into it.
  • Specifically, the preview lecture helps you see the big picture before you read on your own; doing reading and homework on your own helps you grow your mathematical independence; but then in class you get to discuss and revise your work before having to hand in anything final. You also get credit for spending time on the reading and homework in advance, by showing what you’ve done on Effort Quizzes. Final writeups are done in groups to further bolster your communication skills and so that students can help each other with final understanding and communication of the material. And finally, in-class review of those writeups gives us a chance to fine-tune logical arguments and discuss best practices for communication.