Every year of the program, each participant will attend two weeks of full-day intensive summer workshop on mathematics content as well as full-day workshops during each academic year with a focus on curriculum implementation. Participants will receive four graduate credits per year for their participation in the program. The workshop sessions will be taught using a student-centered collaborative learning model with participants working in small groups supported by five mathematics faculty members rotating among the groups to maximize participant and faculty interaction. Small-group work will be followed by large-group discussion. Each day of the summer workshop will focus on a specific mathematics topic, via three types of sessions:
Problem-Based Inquiry (PBI)
Participants will deepen their understanding of a specific content topic through problem solving. Each workshop day will begin with a PBI session in which participants work in small groups on rich problems designed to spark and sustain conversation about, and exploration of, a specific piece of the school curriculum. These sessions will engage the teachers in analyzing solutions and methods, exploring representations, communicating and making mathematical arguments. A primary source of problems for these sessions will be problems that the UWO mathematics faculty have collected and developed for their mathematics content courses for elementary and middle school education majors. For example, a PBI session on fractions might begin with the following problem: At a school dance, 1/3 of the boys are dancing with 2/5 of the girls. What fraction of the students are dancing? While this seems to be a simple question, the solution is not found by simply adding, subtracting, multiplying or dividing the two given fractions. This problem generates discussion about the concept of the “unit,” the meanings of fraction, representations and models of fractions, and beliefs and misconceptions regarding rational numbers.
Focus on Children’s Thinking
We will then study children’s thinking and misconceptions about the specific content topic, as identified in the research literature. Participants will appraise children’s methods and discuss whether they are correct and generalizable. We will view video clips of children thinking aloud as they solve problems in order to better understand the ways children reason mathematically. We will also discuss how to respond to common student questions (as established in the research literature) related to the content and address how to assess student written work (constructed response) in mathematics. For example, participants will study samples of children’s work on the problem “Find a fraction between 1/2 and 2/3 and justify your answer,” and discuss the mathematical work associated with teaching fractions (e.g. Ball et al, 2005).
Connections to the Curriculum
Finally, each day participants will study how the specific content topic is treated in the various curricula used by the partner districts. We will analyze activities and discuss the underlying concepts and the purpose and motivation for their approach. Participants will present their ideas for how they teach the content in the classroom. A key component of these sessions will be the focus on making connections in mathematics, not only the connections among the mathematics content studied in the PBI sessions and the curriculum, but also connections among mathematics concepts. To strengthen their abilities to see and understand connections, participants will make “connection maps” to facilitate a discussion of how the mathematics content studied that day is related and connected to other content, concepts, problems and procedures.
While making connections to children’s thinking, the curriculum and to teaching strategies, the professional development workshops will be driven by mathematics content. Each year of the program there will be a different content focus: Number and Algebraic Thinking in year one, Geometry and Measurement in year two, and Probability and Statistics in year three. While each year will have an identified focus, connections among mathematics topics and concepts will be stressed throughout the program. For example, Ratio, Percent and Proportion, fundamental mathematics concepts that have been identified by both the teachers in our survey and the partner district administrators as a need for our teachers and students alike, will be addressed each year as they arise in the various contexts.
Academic Year Follow Up
During the academic year workshops participants will study an upcoming unit from their curriculum, work collaboratively in teams to identify the key content and concepts underlying the unit, and develop strategies and lessons to implement in the classroom that will have a high level of cognitive demand for student understanding. The participants will be charged with implementing these lessons in their classrooms. The next one-day workshop will then begin with sessions where participants reflect and discuss the mathematical issues arising from the previous lesson implementation.
Each participant will be observed in their classroom at least once each year by one of the mathematics faculty, who will act as a coach for mathematical depth and accuracy of the lessons, and level of cognitive demand and press for student understanding. Each coaching session will include a pre-lesson conference, a classroom observation of the lesson and a postlesson conference to discuss suggestions. The participant will write both a pre-observation plan outlining the goals and strategies of the lesson and identifying specific focal points of attention for the teacher and coach, and a post-observation reflection on the lesson. The goal of this coaching component of the progam is to enrich and refine the teacher’s mathematics knowledge for teaching. We will use Content-Focused Coaching, as defined by West & Staub, 2003 as our guiding model. “Content-Focused Coaching centers on students’ learning in the lessons but also about teachers’ learning from the process. In the short term, teachers refine how they teach particular lessons to specific groups of students. In the long term, they develop professional habits of mind and general teaching expertise” (West & Staub, 2003, p. 2).