Supporting Middle School Mathematics Specialists’ Work: A Case for Learning and Changing Teachers’ Perspectives

Abstract:In this paper, we highlight one whole-class discussion that took place in a middle school mathematics Rational Number and Proportional Reasoning course, one of the six mathematics courses teachers take to complete our state-wide middle school mathematics specialist program. Statistical measures indicate that teachers made gains in their understanding of concepts and substantial gains in their views of teaching and preparedness. We provide a microanalysis of one of the lessons, to explain, in part, how they might have made this progress. To develop our argument, we coordinate a social analysis with an analysis of the types of specialized mathematical knowledge that teachers might have considered as they engaged in these discussions. As we will illustrate, these types of classroom discussions provided teachers opportunities to consider new visions for mathematics learning and teaching.Keywords: Proportional Reasoning, Mathematics Specialists, Professional Development, Middle School MathematicsProfessional development initiatives that provide continuing, quality support for middle school teachers have received renewed attention in recent years. For instance, Smith, Silver and Stein (2005) stated that due to students' lower-than-expected perfonnance on national and international assessment? (p. xi) the National Science Foundation provided financial support for developers to create new middle school mathematics cunicula (e.g,, MathScape, Connected Mathematics Project & Mathematics in Context). that offered new innovations in teaching and learning mathematics (Reys, Reys & Chavez, 2004}. Providing new curricula and professional development around implementing these curricula can be catalysts for teachers to further develop (or change] practices, make connections among ideas, and better support student learning (Reys, et al., 2004]. However, if teachers do not develop new kinds of practices they may not be able to successfully implement innovative curricula. As Smith, Silver and Stein (2005] state with regard to implementing new middle school curricula,In short, new curriculum materials are unlikely to have the desired impact on student learning unless classroom instruction shifts from its current focus on routine skills and instead focuses on developing student understanding of important mathematics concepts and proficiency in solving complex problems, (p. xi ]Schifter and Lester (2005] mirror Smith et al.'s (2005] position. Speaking about teachers' participation in the Developing Mathematical Ideas programs, they state that if teachers do not "construct new visions for mathematics, mathematics learning and the mathematics classroom" (Schifter & Lester, p. 97], instructors will not be able to implement these curricula in ways that the developers intend.Schifter and Lester's (2005] position is a useful way to frame our work in our statewide mathematics specialist program for middle school teachers. One of the aims of this work is to help teachers, when needed, to make shifts in their instructional practices so that they can effectively serve as mathematics teacher leaders, who we refer to as mathematics specialists. Our goal is to prepare middle school teachers such that once they successfully complete this program, they will be well positioned to provide ongoing, longterm, classroom-based professional development for fellow teachers in their school buildings.Throughout the program, we know that the course instructors played a key role in helping teachers reflect more deeply about different aspects of their work (cf. Ball, Thames & Phelps, 2008). For instance, teachers reported that course instructors played a key role in helping them develop deeper understandings in the first two courses (Numbers & Operations; Rational Numbers and Proportional Reasoning) (Moffet, Fitzgerald & Smith, 2011]. Additionally, teachers made statistically significant gains in their understanding of mathematics content as well as how to better teach these content ideas (p