Instructional approaches that encourage self-monitoring—or metacognition—have been shown to support learning with understanding (Donovan & Bransford, 2005). Math Pathways & Pitfalls® lessons include several structures and reminders for students to become more aware of their thinking and learning processes. For example, Math Pathways & Pitfalls lessons encourage students to consider where someone might make a pitfall as they solve a problem. Students also learn to ask themselves whether or not a solution makes sense. These opportunities for reflection help students become more conscious of how they learn and provides ways they can monitor their own learning and problem-solving.
Findings From Studies
Building Mathematics Discussions in Elementary Classrooms with Latino/a English Learners
This qualitative, mixed-methods study was conducted by external researchers Aria Razfar and Della Leavitt of the University of Illinois at Chicago.
Abstract: Drawing on Cultural Historical Activity Theory (CHAT) and Gee’s (1996) notions of primary and secondary discourses, this paper examines the use of Math Pathways & Pitfalls discussion builder stems to mediate mathematical learning and language development. Through analyses of the social organization of learning and classroom discourse conducted in the later stages of an urban classroom of Latino/a English language learners and several African American students, we examine how the solving of mathematical problems in the domain of fractions and decimals is mediated by the cultural artifacts provided by Math Pathways & Pitfalls. In particular, we focus on discussion builder stems, the pitfall narrative, and other elements of the Math Pathways & Pitfalls curriculum. We show how the participants display a multiplicity of functions, purposes, and uses as they draw on the Math Pathways & Pitfalls register to engage in mathematical problem-solving, along with participating in the broader classroom culture. Finally, we explore how Math Pathways & Pitfalls, in conjunction with other primary and secondary discourses, can lead to the development of meta-level discourses as exemplified by the pitfall metadiscourse.