Participation and cognitive demand: Linking the enacted curriculum and student learning in middle school algebra

Many current policy initiatives focus on teacher qualifications and high-stakes assessments for students as a means to improve mathematics education in the United States, but this approach ignores the actual practice of teaching through which students have opportunities to learn mathematics. The present study is an effort to answer scholars' calls to focus on the enacted curriculum—what actually happens in the classroom—and the relationship between enacted curriculum and student learning in mathematics. In particular, within 12 middle school algebra classrooms from two states, each lesson focused on the introduction of variables as a means of representing changing quantities was analyzed for the levels of cognitive demand and the nature of student participation present throughout the phases of mathematical task enactments. Students' verbal participation is conceptualized through a new construct termed participatory demand, which attends to both the amount of student talk as well as the semantic nature of that talk. The results of the analyses of the enacted curriculum were then compared with class gain scores between a pre- and post-test related to the focal learning objective. Although cognitive demand in the enacted curriculum was not found to be significantly correlated with class gain scores, the nature of student participation was predictive of higher class gain scores.;Additionally, two narrative cases of teacher's task enactments are presented to illuminate issues of cognitive demand and participatory demand at a finer level of detail than the correlational analysis. Ms. Wyncott's task enactments constitute a case of declining cognitive demand and participatory demand that is not of a high mathematical nature, even though Ms. Wyncott explicitly directed students to talk with one another in small groups about their mathematical work. Ms. Albert's task enactments constitute a case of cognitive demand that is maintained at a high level and participatory demand that is of a high mathematical nature both as students work and as they look-back on their work together as a whole class. These cases include particular attention to the look-back phase of enactment because this phase is a new addition to the Mathematical Tasks Framework (Stein, Grover, & Henningsen, 1996) that was used to structure analysis.;The final chapter of this thesis summarizes the ways in which the study contributes to an understanding of the relationship between cognitive demand and participatory demand within the enacted mathematics curriculum and to the body of research on the relationship between enacted curriculum and student learning. Implications for teacher education are discussed and potential avenues of future research are identified.