# CHARLENE BECKMANN, KARA STAHL, AND TARA MAYNARD

The Tortoise and the Hare

*Teaching middle school mathematics is a challenge in itself The activities in this chapter met this challenge by immersing students in engaging activities that built their intuition about linear functions through conceptually developing their understanding of slope and* y-intercept *in the context of motion over time.*

*Charlene Beckmann, Kara Stahl, and Tara Maynard*

Dr. Charlene Beckmann (Char), a university mathematics and mathematics education professor, first met Tara, a secondary teacher, and Kara, an elementary teacher, while they were undergraduates enrolled in her mathematics and mathematics education courses. Both teachers struck Char as “perceptive and insightful” mathematics teachers. In these courses, Char provided students the opportunity to experiment with a motion detector and a calculator-based laboratory (CBL), attached to a graphing calculator. The unit described here was inspired by Kara’s response to a journal assignment after having experience with CBLs and motion detectors. Kara and Char expanded the activity and then asked Tara to join them in piloting it with middle-grade students. Char invited both teachers to join her in cowriting this and other articles. The teachers eagerly accepted, and a three-way school/university collaboration was born.

Aesop’s fable *The Tortoise and the Hare* provided the setting from which to develop students’ conceptual understanding of linear functions, particularly the concepts of slope and y-intercept. “How do I get students, no matter what their level, to understand the concept of slope?” This is a common question and one that Char, Kara, and Tara all asked during the creation and piloting of *The Tortoise and the Hare* activities. The idea of slope can be a complicated one for students to understand and for teachers to explain. It is one thing to teach students the mechanics of finding the slope, but it is entirely another to help students attach meaning to slope in the various contexts in which it arises.

The class with which the activities were implemented and whose students’ responses are described in this profile was Tara’s eighth-grade class. Char, Kara, and Tara used the Transition Mathematics program from the University of Chicago as their base. Students in this class were accustomed to having prospective teachers from Char’s university class in their classroom on a weekly basis. Thus, having a college professor join the class for a week seemed natural to the students.