Project Summary: My Carnegie project is a "vision of the possible" centered on the question "What would a mathematics course which used data-based integrative assignments look like?" I constructed a sequence of six data-based integrative assignments for use in my Precalculus and Calculus classes this year. I was initially interested in the question of how I could use these assignments to reinforce the mathematics the students were studying, but my interests broadened as the year progressed. It became apparent that the integrative assignments had the potential to refocus the mathematics courses in interesting ways, not all of which were strictly mathematical. So what would a mathematics course which used data-based integrative assignments look like? Although I have no definitive answers, I have a number of preliminary thoughts on this question.

Motivation: My original motivation for this work was relatively narrow. I wanted to create supplementary assignments for mathematics classes, involving spreadsheet work with functions, to support the mathematics being studied. My focus shifted as the year progressed. My use of data-based integrative assignments has raised additional pedagogical issues: the use of data, the care that we must take in drawing conclusions and making decisions, and the cultivation of a kind of scientific thinking. I am very much interested in exploring these issues with my students. For a more complete look at my motivation, click the link below. Motivation

The Integrative Assignments: Each of the six integrative assignments provides data about an important issue. Students are asked to analyze the data mathematically by constructing a mathematical model, and then to use a spreadsheet to implement the model. They are to produce a written paper in which they present their model (with a table and a graph) and to use this work as a basis for any conclusions that they reach. The students are expected to present the mathematical calculations involved in deriving the model as an appendix to the paper. Thus, the assignments require integration of at least three disciplines: mathematics, writing, and the discipline of the data being analyzed. Students find the kind of thinking required by these assignments to be quite foreign and difficult. Integrative assignments of this sort both expose my students' weaknesses in ways that are not ordinarily apparent and, ultimately, lead to deeper, more thoughtful work. The issues explored by the assignments are: Global Warming I The Population of Ireland Radiocarbon Dating Global Warming II Nuclear Waste World Population For a look at the assignments, click the link below. The Assignments

Thoughts about the Assignments: As I reflect on my experience assigning data-based integrative assignments in a mathematics classroom, some pedagogical issues seem central. I needed to figure out how I, as a mathematics teacher, could grade written work. I had to learn how to frame the assignments in such a way that they opened up thought, rather than shut it down. I needed to think about what I should do when I encountered students with preconceptions. I thought long and hard about whether or not I should encourage (or even allow) students to do additional research on the topics being addressed. Finally, the breakdown of the mathematical model presented another pedagogical challenge; I had to think about how to address a number of issues associated with the failure of the model. For a discussion of these, and other, issues, click the link below. Thoughts about the Assignments

Evidence: My primary source of evidence is the written papers from my students. In addition, I asked my students to reflect on the experience each time they handed in a paper. Close reading of the papers and reflections reveals interesting insights into the difficulties and struggles my students faced as they worked on the written assignments. For a look at the evidence, click the link below. Evidence

Concluding Thoughts: I began this project with the goal of creating data-based, integrative assignments to supplement to the mathematical work the students were doing in my classroom. But the issues raised by these assignments were fascinating, compelling, and complex. I found myself thinking about the role of data in decision making, the care that we must take when we draw conclusions, and the interplay between data, preconceptions, opinion, and belief. I have come to think that the assignments are beginning to encourage in my students a scientific way of thinking, to give my students a new (for them) worldview that incorporates the use of data and evidence, and that uses mathematics and careful reasoning to reach conclusions. I think that perhaps these lessons about thinking are as important (or perhaps more important) than the mathematics we ordinarily teach. For a more complete discussion, click the link below. Concluding Thoughts