Teaching Math and Science

Abstract

Local Systemic Change projects, funded by the National Science Foundation, were designed to help teachers of mathematics and science deepen their content knowledge and improve their instructional practices. Ms. Weiss and Ms. Pasley describe how these aims were accomplished through combination of intensive professional development and follow-up support when the teachers took their new knowledge and skills back to the classroom. ********** IN THE FALL of 2001, University of Delaware Professor Jon Manon observed mathematics lesson about factoring in an eighth-grade classroom of an urban middle school, a school which is home to what is often reputed to be one of the most challenging student populations in Delaware. Jenni Green (a pseudonym), the teacher he was observing, had been participant in an intensive summer institute, and Manon wanted to find out if any of the summer's workshop lessons had had an effect on her work. decided that I would look for 'residue' from the summer professional development across grades and units, writes Manon in case study published on LSC-net, an interactive website for the project leaders of the Local Systemic Change (LSC) initiative, funded by the National Science Foundation (NSF) since 1995. In particular, I was seeking evidence that our emphasis on the instructional model, the launch-investigate-summarize lesson cycle, was finding root in actual practice. (1) A LESSON IN FACTORING Jenni Green used to teach sixth grade. This year, was an eighth-grade mathematics teacher. According to Manon, she did have special concerns about particular students, e.g., one 14-year-old had baby and often stayed home to care for it. But when these kids were in school, Jenni was prepared to help them focus on learning mathematics. Manon's visit to her classroom came at what Jenni described as a very critical moment in the Mathematics in Context curriculum algebra unit, Building Formulas. (2) Manon continues: This was the lesson in which factoring was first introduced. We agreed that it was seminal concept, gatekeeper to success in more formal algebra course. As the name of the unit suggests, building situations were used to introduce algebraic representations. Section B, Basic Patterns, exploited the context of construction with bricks to introduce representation for rows of bricks involving Standing, S, and Lying, L, bricks. For example, the length of [a simple] pattern, made up of two Standing [bricks] and one Lying brick, might be represented symbolically as 2S + L. A such as this one might be repeated to produce longer string of bricks. And that new configuration might be represented as either three groups of two Standing and one Lying--3(2S + L)--or, dropping the reference to the pattern, as 6S + 3L. Before the students arrived, Jenni had described the approach planned to take to introduce her lesson. She decided to challenge her students to identify the basic pattern in longer string and then determine how many times that was repeated. As the first students entered the room, Jenni apparently made up her mind to try something different. Seated at the overhead projector, Jenni wrote 15S + 10L and asked, How can I figure out what the is in this case? Immediately, Ellen, diminutive girl in the front row, answered, Five ... it fits into [15] ... three times. For 10, it will be 2. Initially caught off guard by both the promptness and content of Ellen's response, Jenni recovered and asked, So the is repeated how many times? She drew 15 Standing and 10 Lying bricks on the overhead and, indicating in the drawing, said, I'll try to clarify Ellen's thinking ... for every three Standing, there are two Lying bricks ... pretty cool. I like that Ellen! Then, looking quite pleased and shifting her gaze from to the rest of the class, said, Ellen stole my thunder! …