Academic journal article The Professional Educator

Inner-City Teachers' Perceptions in a Lesson Study for Critiquing Mathematical Reasoning

Academic journal article The Professional Educator

Inner-City Teachers' Perceptions in a Lesson Study for Critiquing Mathematical Reasoning

Article excerpt

This study describes the perceptions of four teachers at the beginning stages of Common Core Mathematics implementation in a historically underperforming school district. The overarching goal was to understand the collaborative inquiry experience in a lesson study that focused on teaching the mathematics practice "Construct viable arguments and critique the reasoning of others" (CCSSI 2010). The recently adopted Mathematics Common Core Standards in California have been challenging for many teachers who have changed their approach to instruction to emphasize a deeper level of rigor and intensity required by the standards. These standards emphasize conceptual understanding of mathematical processes and problem solving in non-routine situations (CCSSI 2010). In addition to the content standards, eight mathematical practices address the reasoning and communication skills that should be developed across each grade level. These practices represent key processes and proficiencies in problem solving (see Figure 1).

For many teachers more accustomed to using traditional direct-instruction models that focused on more procedural methods, these mathematics practices may be uncharted territory: How do I teach this ? How do I assess this? What is this practice standard really expecting students to do? Some teachers may have simply assumed they were already teaching the mathematics practices, without a clear way to assess their students' achievement. Or perhaps some just generally approached the practices randomly throughout instruction, without a clear plan or focus on a specific practice. Oftentimes, teachers may not prioritize these practices over content knowledge and grade-level number skills.

Four teachers in an inner-city school grappled with how they could teach these mathematics practices to students who typically struggled in number skills and problem solving. This paper will describe how their perceptions of student learning and understanding of the specific practice standard developed through a collaborative learning process.

Conceptual Framework

Teacher Learning

From the situative perspective, teachers learn in particular social and physical contexts in interactive systems with "authentic activities" (Putnam, & Borko, 2000). Authentic activities are defined by Brown, Collins, and Duguid (1989) as the "ordinary practices of a culture" (p. 34), or as "authentic practices" that are not separated from the situations where they are developed (Clayden et al., 1994). Key findings of effective professional development include more teacher ownership of learning, meaningful application to their unique contexts (Darling Hammond, 1995), content knowledge focus, active learning with meaningful discussion, planning and practice, and learning activities that are connected with classroom goals/activities (Garet et al., 2001; Schon, 1991). Along with the importance of clear learning goals and attention to student thinking (Fennema et al., 1996; Hiebert, 1999), teacher learning is sustained and self-generative when engaged in practical inquiry (Franke, Carpenter, Levi, & Fennema, 2001; Kazemi & Franke, 2004). Critical discussions challenging teachers' pre-existing assumptions and intentionally "provoking disequilibrium" are also important to teacher learning and professional growth (Ball, 1996).

Urban School Reform

Many urban schools statistically have more teacher shortages, higher percentage of poor and minority students, higher rates of mobility, and lower standardized achievement scores (Jacob, 2007). For many teachers in underperforming urban schools, daily teaching activities may be compounded by students' disruptive behaviors, lack of parent participation, learning gaps, and chronic stress due to poverty, hunger, or surrounding gang activities (Jensen, 2009; Predmore, 2004). Also prevalent in many failing urban schools is organizational irrationality, demoralization, and endemic frustration (Payne, 2008). …

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