Problems help students make sense of mathematics and development strategies. When we guide and watch students engaging in problem solving, we can assess both their procedural fluency and their conceptual grasp of mathematics.

We've just observed some problem-solving strategies used by ninth-grade students. Now we'd like you to write about your classroom practice. As you make your journal entries, keep in mind the material you've just seen and read as context.

• How can teachers create enthusiasm and interest in all students for problem solving?
• What are the criteria teachers can use to select problems for introducing new material?
• Problems should offer a rewarding challenge for students, being neither so obvious that they put no demands on them nor so difficult that they are clearly beyond their ability. How does the Staircase problem fill this role in Mr. Solomon's class? How do you make a determination about the appropriate level of difficulty in your own class?
• Different students solve problems at different speeds and with different approaches in this classroom, or in any classroom. Given this factor, what is the role of the teacher in fostering effective problem solving? Be specific.
• It is often straightforward to assess whether a student found the correct final answer. How do you assess whether the strategies and ability to apply them were sound? If a student has found a correct answer despite a faulty strategy, how do you respond?

• 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.

Thank you 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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