Overview:  The teacher tells students that, for their work on the problem, they will imagine that they are on a team of urban planners trying to determine where to locate a new grocery store.  The teacher begins by asking students to name some of the factors that they would need to consider to decide where would be the best location for a new grocery store in their community.  Students suggest a wide variety of factors, including population density, sales tax, and zoning laws.  After hearing these ideas, the teacher tells students that they will act as the mathematicians on the team of planners, and they should bring a mathematical perspective to identify a solution to the problem.  The teacher tells students that they will need to come up with the best mathematical solution, while also considering all of the other perspectives that would contribute to the decision-making.

Prior knowledge:  The teacher establishes a connection with students’ prior knowledge of the context of the grocery store problem.  Students in the class have a great deal of knowledge about their local community, although students likely have different levels of knowledge of the various contextual factors (Ball, 1995).  With the discussion, the teacher helps students begin to think about the many factors that would contribute to selecting a location for a new grocery store in the community.

Other points of interest:  After hearing and listing some of the many different factors that students suggest as contributing to a solution to the grocery store problem, the teacher tells students that they need to be the “mathematicians on the team,” and they need to “bring the mathematical perspective.”  The teacher’s comments may seem to indicate that a mathematical perspective towards solving the problem would be something different than a perspective taking into account the various factors students have named.  Moreover, because students are in a geometry class, the didactical contract (Brousseau, 1997) of the class may equate finding a “mathematical” solution with finding a “geometric” solution.  The teacher’s instructions may serve to limit students’ solution strategies by placing a priority on the mathematics that students have learned in school.  Students may not see things such as zoning laws and sales tax as inherently mathematical, and this may influence how students choose to work on the problem.