We've just observed a problem involving probabilities of taxicab rides with a focus on representation. Now we'd like you to write about the variety of forms of communication that are possible during similar lessons. Choose at least one of the questions below to answer. As you make your journal entries, keep the material you've just seen and read in mind as context.

• In the video, the students work with tree diagrams and matrices. How do these representations facilitate communication between students and with the teacher? How might you informally assess students' understanding of the matrix-based representation and related mathematical terms?
• How does the taxicab problem promote student understanding of the importance of representation in the solution and discussion of a problem? How do you promote such understanding in your classroom?
• How might the matrix solution method help students see the utility of basic skills such as matrix multiplication and at the same time expand their appreciation of mathematics as a subject with many interrelationships and applications?

• 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.

  Explore representation