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The Using Math Pathways & Pitfalls to Promote Algebra Readiness project aims to create and test student activities and professional development that specifically target key misconceptions that are barriers to algebra readiness. The three goals of the project are to 1) develop an MPP book and companion materials dedicated to algebra readiness content and skill, 2) investigate how MPP transforms pedagogical practices to improve students’ algebra readiness and metacognitive skills, and 3) validate MPP’s effectiveness for improving students’ algebra readiness at a large scale.
The newly-developed materials and professional development are grounded in five research-based principles: confronting pitfalls (to confront misconceptions), sense-making (to make implicit understandings explicit), building discussions (to engage students in rigorous, respective discourse), capturing key ideas (to build shared knowledge), and visualizing and representing (to support flexible thinking and connections among mathematical ideas).
Ten lessons for the book were created and revised using an iterative process. In the previous year the project team had drafted and field-tested eleven lessons. Pilot teachers provided feedback through teacher logs and interviews and external math experts reviewed each lesson. Based on this feedback, the development team made revisions including content and formatting changes. During the 2015-2016 school year, thirteen 7th grade math teachers piloted the new MPP lessons in authentic classroom settings. All teachers participated in the professional development that included four-day summer workshop in August, one follow-up Saturday session in January, an evening webinar in April, and a final in-person evening session in May.
Twenty-seven classroom observations were conducted during the 2015-2016 school year at eight Bay Area middle schools. The observations were distributed among the thirteen participating teachers, with each teacher being observed at least twice. As each Math Pathways & Pitfalls lessons are two days in length, the classroom observations focused on one class period for both days of the lesson. One or two researchers attended each observation and conducted a forty-five minute follow up teacher interview after day two of the observation. Observers took notes and made recommendations about changes to either the professional development or the instructional materials. These recommendations were discussed during project “reconciliation meetings” in which final decisions were made regarding lesson revisions. Overall, interviews and observations revealed that the materials were feasible for use in authentic classroom settings, and effectively prompted students to address misconceptions and engage in productive classroom discussions.
Through iterative design, the MPP project is producing research-based materials to increase student learning of core concepts in algebra readiness. Though the project focuses on middle school math, our studies also examine the validity of the pedagogical approach of MPP. The MPP lesson structures are designed to help students confront common misconceptions, dubbed “pitfalls,” through sense-making, class discussions, and the use of multiple visual representations. If the pedagogical approach of MPP proves to be successful at the middle school level, the lesson structures can serve as an effective framework that may extend across content areas in mathematics to other disciplines.