| This study analyzes the uses of real-world contexts in mathematics lessons in the classrooms of four teachers across two school years at an urban high school. Drawing upon a framework of culturally relevant mathematics pedagogy, this dissertation focuses on how real-world contexts are connected to teaching mathematics for understanding, centering mathematics instruction on students’ experiences and classroom participation, and developing students’ critical consciousness. Analysis of real-world contexts in lessons focuses on the extent to which they are adapted from curricular sources and the role that lessons play within the lesson. For those real-world contexts which are at the center of a mathematics lesson, the nature of the mathematical modeling in which students engage is analyzed. Finally, the extent to which students and the teacher participate in the process of elaborating key features of the context whether in terms of experiences, perceptions, or opinions, is also considered. These different categories for real-world contexts are then used to compare three different measures of the lesson. These include the cognitive demand of the main mathematical task, different ratings of the instructional environment, and the distribution of class time in terms of the participation categories offered to students. Results point at the promise of real-world contexts as the basis for motivating metaphors to explore noncontextualized mathematical procedures and concepts, the need to structure lessons so that students can develop models rather than apply given models, and the importance of elaboration in supporting student understanding and participation. |
