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53 5 integrative learning in a data-rich Mathematics Classroom Mike Burke i wanted to let you know that i was actually moved by your final snapshot. i’m accustomed to thinking critically about language and its sources, but it had never occurred to me that the ability to do mathematical equations might be a feature of (or requirement for!) emancipated thinking. i felt jealous of your students. for the past few years, i have been designing, and assigning, data-based integrative writing assignments in my mathematics classes. each assignment presents the students with a data set 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 then use this work as a basis for any conclusions that they reach. The opening quote is a thoughtful response to a description of this work (in the form of a Keep toolkit Snapshot) from a bright, well-educated young woman. it is fair to conclude from the quote, i think, that nowhere in her education (an ivy league education followed by an advanced degree) has this young woman encountered the idea that mathematics has any bearing at all on political, social, or even environmental issues. This quote thus stands as a rather disturbing indictment of us, the higher education mathematics community. What her education lacks (and she is not atypical of our college population) has come to be called quantitative literacy (Ql). There appears to be surprisingly little agreement about what, specifically, constitutes quantitative literacy. in a general discussion of Ql, The Case for Quantitative Literacy, the Quantitative literacy design team writes that “[q]uantitative literacy is more a habit of mind, an approach to problems that employs and enhances both statistics and mathematics. . . . Unlike mathematics, which is primarily about a platonic realm of abstract structures, numeracy is often anchored in data derived from and attached to the empirical world” (2001, p. 5). lynn Steen writes that quantitative literacy is “intertwined with political, scientific, historical or artistic contexts. here Ql 54 | Courses that Foster Integrative Learning adds a crucial dimension of rigor and thoughtfulness to many of the issues commonly addressed in undergraduate education. . . . Ql is not a discipline but a literacy, not a set of skills but a habit of mind” (2004, p. 22). randall richardson and William McCallum argue that “[q]uantitative literacy cannot be taught by mathematics teachers alone, not because of deficiencies in teaching but because quantitative material must be pervasive in all areas of students’ education” (2004, p. 17). for this reason, the writing-across-thecurriculum model seems to offer a promising approach. in this spirit, Steen considers a quantitative literacy course at the college algebra level, perhaps focusing on mathematical modeling rather than on preparation for calculus. Such a course could focus on “data, technology, and quantitative communication. it could serve as the hub of a campus-wide Ql program in much the same way as freshman composition anchors writing-across-the-curriculum programs” (2004, p. 39). i find that through my work i have arrived at much the same conclusions, doubtless by a more circuitous route. My initial motivations were quite modest; i wanted to improve the way i taught functions. about a decade ago, the harvard Calculus project popularized the “rule of Three,” the idea that we should routinely examine functions from three different perspectives: numerically (as a table of values), geometrically (as a graph), and analytically (as an equation or formula). as i thought about the “rule of Three,” i realized that a spreadsheet is the natural tool for the study of functions because the user of a spreadsheet uses formulas to build tables, and then the spreadsheet quickly constructs an accurate graph. The beauty of the spreadsheet is that it helps students move from one perspective on a function to another, and thus easily view a particular function from all three. So i began my thinking for this work a number of years ago with this idea: the use of a spreadsheet should help my students come to a deeper understanding of the mathematical concept of a function. at the same time, i had three other ideas that nicely dovetailed with the use of a spreadsheet. i wanted my students, for motivational purposes, to see some genuine applications of the mathematics they were studying. i...

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