Chapter 21: A Story of Teacher Growth: Increasing Expectations: Increasing Expectations

During the spring of 1996 I was a student teacher at Traverse City East Junior High. At that time, Traverse City Area Public Schools was involved in a pilot with the Connected Mathematics Project (CMP) (Lappan, Fey, Fitzgerald, Friel, & Phillips, 1998, 2002, 2004, 2006). This was my first experience with a curriculum like CMP and I was amazed at how differently mathematics could be taught and learned. I remember wondering if this “new” approach to mathematics was a complete revolution or more of a baby-step toward what was yet to come.

During that semester of student teaching, I worked with a group of 8th-grade students. There was one experience with the unit Moving Straight Ahead (Lappan, Fey, Fitzgerald, Friel, & Phillips, 1998) that stands out in my memory. As an introduction to an investigation, students looked at graphs of linear relationships, one of which was of the equation y = 300 + 2x. With its graph on the overhead and pointing to the y-intercept, I asked the students, “What is this?” I expected students to identify the y-intercept. Instead students said, “That is the starting or initial amount.” I slowly thought to myself, “Yeah … yeah, that’s right!” That was exactly right. Until that minute I had never made the connection between the graphical representation of the y-intercept and the situation it represented. In my mathematical experience, I had been taught to look at tables, graphs and equations. “Story problems” were rarely assigned. Even when I was asked to look at all representations, I was not pushed to understand the connections between them. For me, algebra had been about following a set of rules. It was not about understanding patterns of change and how those were reflected in other representations. Geometry was something that was taught separately, not as something that was integrated and connected to algebra. Now here I was witnessing students making sense of mathematics, and making the connections I lacked. Students were teaching me how different representations of functions were related, and it was exciting.