So what have we done in this session?

• In Part A, you observed reasoning and proof, as a middle school classroom tackled the Building Rafts with Rods problem.
• In Part B, you explored your own problem-solving process with the Frosted Cube Cake activity.
• In Part C, you looked at a variety of methods that you can use with your students, as the Reasoning and Proof Standard was defined.
• In Part D, you applied what you had learned in the session so far by reviewing the Reasoning About Fractions activity, watching students use the fraction pieces to solve a problem, and thinking about how you would teach it in your classroom.
• In Part E, you wrote your own lesson plan as a way to evaluate what you had learned.

As students learn to justify their reasoning, they make the first steps toward formal proof. In many cases, students can begin to show formal reasoning by generalizing patterns to fit various situations. Remember, in the middle grades, we want students to be able to do the following:

• Reason about a problem
• Extend what they already know
• Make a conjecture
• Provide a convincing argument
• Refine their thinking
• Defend or modify their arguments

For many students, this will not be formal proof, but it will help them be better prepared to use proof in a more formal context in high school. More importantly, as students become more facile in explaining and justifying their thinking, the mathematics they are learning will make sense. And that's what mathematics should be for all students -- sensible! Reasonable!

We wrap up this session with another, you guessed it, journal. This final journal is different, however, and will mark your completion of the session.

  Completing your journal