Activity 2: A Tool for Inquiry
Algebra with Manipulatives
Geoboard animation

The geoboard as a tool to support inquiry.

Lessons from Algebra: Themes, Tools, Concepts, by Anita Wah and Henri Picciotto.

What can I expect to get out of doing this activity?

 Algebra: Themes, Tools, Concepts (ATTC) shares with many of the new mathematics curricula an increased emphasis on functions, applications, and the use of technology. What distinguishes the ATTC approach is the pervasive use of thinking tools to support inquiry and enhance discourse. Hands-on tools include the Lab Gear (which will be featured in Content) and 11 by 11 geoboards, which will be explored in the remainder of this Topic.

In this activity you will carry out an initial exploration on the geoboard and read a bit about the philosophy behind ATTC in general.

how long will it take?

30 minutes for initial work with ATTC and the geoboard.

30 minutes for the reading.

Assignments:
Readings

A New Algebra: Tools, Themes, Concepts by Henri Picciotto and Anita Wah
(Journal of Mathematical Behavior, volume 12, #1, March 1993)

Read in the hard copy you received from your Site Coordinator, pp. 19-27 to the end of #8.

Hands-On
Activity 2
TO DO Checklist
__ Print this page!

Readings & Hands On
__ Complete the reading assignment.
__ Complete the hands on assignment.

Initial Thoughts
__ Post your initial comments on Activity 2 and read some of the module-based discussion in the Algebra Discussion area.

Local Study Group Meeting
__ Attend LSG meeting where colleagues share their new "tools" for inquiry. Doing your presentation this week? Here are the notes you'll need.

Further Reflection
__ Visit the Algebra Discussion area again to read more of the dialogue and share your insights and questions.

Algebra: Themes, Tools, Concepts: pp. 36-37 #1, 7-10, 12-17; p. 75 #13, 15, 17.

Algebra AnimationAs you work through these problems, put yourself in the place of a student who does not know the formula for the area of a triangle or who knows it and does not think of using it. Likewise, do not use the Pythagorean Theorem. This will give you a better sense of how students typically do this.

If you prefer working on dot paper to using rubber bands on the geoboard, print out this page.

The main purpose of the activity is for students to develop their own area techniques, to discuss them, and for you to bring their attention to which operations are used in their strategies. Those are addition, division by two, and most challenging, subtraction.