We've just observed problems involving exponential functions, with a focus on connections to technology and representation. Now we'd like you to write about the variety of connections that are possible during similar lessons in your own classroom. Please reflect on the following questions and answer one in light of the students and content you teach. As you make your journal entry, use the material you've just seen and read as a context.

• In the assignment you just observed, students were asked to work in groups to make observations about y = 2^x - x - 3 and other equations and to write about the mathematics they notice within their observations. How did the nature of this assignment and approach encourage students to make connections as they worked? How might you further encourage awareness of mathematical connections during such an assignment?
• How did the use of technology serve as a forum for making connections to prior and future work with mathematics? Discuss how to encourage students to make and use connections as they work with technological tools, both to problem-solve and to view their work.
• How do your teaching practices compare to those in the video? For example, do you give open-ended assignments? If so, at what point during instruction on a topic would you give this type of assignment? Do your students make connections, such as those made by the students in the video? Describe an example of this kind of work in your own classroom.

• 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.

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