You've just explored a problem through a variety of representations and considered the strengths and limitations of each representation. Now we'd like you to write about your own observations about representation. As you make your journal entries, keep in mind the material you've just seen and read as context.

• When cutting or drawing to model the problem, after a number of cuts you can't see the remaining pieces, so you can't continue. Discuss the significance of this fact and how it relates to the symbols and to the development of the concept of a limit.
• What pattern do you notice in the fractions that represent the sum? How is the sum depicted in the visual representation of paper? How would you build a connection to the numeric sum in both representations?
• How do your personal responses to the strengths and drawbacks of the various representations in this context relate to your teaching?
• Did you make any incorrect inferences from working with various representations? Were there things you didn't expect? How did you respond to this? How do think your students might respond? How could you help them learn from surprises like these?

• Use pen and paper.
• Use a word processor.
• Use the form below.

Your work will be displayed in a printer-friendly format to enable you to print.

Thanks for writing in your journal. Please keep your entries in whatever format you choose -- you will find them useful for reference later.

  Learn how the Standards define representation