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Good Problems: Moving with Multiple Representations to Algebraic Reasoning
presented by Stephen Weimar & Steve Risberg

NCTM 2007 Annual Meeting and Exposition
Mathematics: Representing the Future

Session 436 in Atlanta, Georgia
Friday, March 23, from 8:30 am to 10:00 am
Omni Hotel at CNN Center - Grand Ballroom A

What is algebraic reasoning?
What are good problems for supporting the development of algebraic reasoning?
How do we move students toward developing algebraic reasoning through our questions, facilitation of groupwork and math talk, topic focus, and use of multiple representations?
Balloon Booths
Let's do math! Scale the size of a helium balloon so it will be small enough to fit through an opening but still large enough to pop when it hits the two nails on the other side.
Find a fraction that is greater than 3/2 and less than 5/3. Can you find more than one? Come up with a general strategy for finding fractions that lie between two other fractions.
What forms of algebraic reasoning can we apply to this problem? What role can technology play?
Summary discussion of the Balloon Booths problem: What do we notice about the nature of this problem, about the questions we posed, about our group discussions that supported or interfered with algebraic reasoning?
Congruent Rectangles
Let's do math! Work on the problem within your group. See if you can find at least two distinct solution paths.
Look at student solutions to this problem using an abbreviated form of our protocol for review of student work. What do you think that each student seems to understand and what do you wonder about the student's understanding?
How do we assess algebraic reasoning? How do our assesments affect our interventions and our suppport for algebraic reasoning?
Summary and Questions

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