| In the 1990s, the National Science Foundation (NSF) funded the development of curricula based on the approach to mathematics proposed in Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, 1989). Controversy over the effectiveness of these curricula and the soundness of the standards on which they were based, often labeled the "math wars," prompted a plethora of evaluative and comparative curricular studies. Critics of these studies called for mathematics education researchers to document the implementation of these curricula (e.g., National Research Council, 2004; Senk & Thompson, 2003) because "one cannot say that a curriculum is or is not associated with a learning outcome unless one can be reasonably certain that it was implemented as intended by the curriculum developers" (Stein, Remillard, & Smith, 2007, p. 337). Curriculum researchers have used a variety of methods for documenting curricular implementation, including table-of-content implementation records, teacher and student textbook use diaries, teacher and student interviews, and classroom observations. These methods record teacher and student beliefs, extent of content coverage, in-class and out-of-class textbook use, and classroom participation structures, but do little to compare the mathematics presented in the written curriculum (the student and teacher textbooks) and the way in which this mathematics plays out in the enacted curriculum (that which happens in classrooms).;In order to compare the mathematical features in the written and enacted curricula, I utilized Sfard's Commognition framework (most recently and fully described in Thinking as Communicating: Human Development, the Growth of discourses, and Mathematizing published in 2008). That is, I compared the mathematical words, visual mediators, endorsed narratives, and mathematical routines in the written and enacted curricula. Each of these mathematical features provided a different perspective on the mathematics present in the curricula. The written curriculum in this study was represented by Investigation 3 (Multiplying with Fractions) included in Bits and Pieces II: Using Fraction Operations in Connected Mathematics 2 (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2006). Videotapes of this same Investigation recorded in a sixth grade classroom in a small, rural town in the Midwest were used as the enacted curricula for this case.;The study revealed many similarities and differences between the written and enacted curricula; however, most prominent were the findings regarding objectification in the curricula. Sfard defines objectification as "a process in which a noun begins to be used as if it signifies an extradiscursive, self-sustained entity (object), independent of human agency" (Sfard, 2008, p. 412). She proposes that objectifying is an important process for students' discursive development and that it serves them particularly well in the study of advanced mathematics. Both objectification itself and the opportunities present for objectification were more prevalent in the written curriculum than in the enacted curriculum. |
