1 TEACHERS’ PRODUCTIONS OF ALGEBRAIC GENERALIZATIONS AND JUSTIFICATION: IMAGES OF SPECIALIZED CONTENT KNOWLEDGE Rebekah Elliott Oregon State University elliottr@science.oregonstate.edu Kristin Lesseig Oregon State University lesseigk@onid.orst.edu Matthew Campbell Oregon State University campbmat@onid.orst.edu This study documents teachers’ productions of algebraic generalizations and justification that draw on specialized content knowledge (SCK) for teaching. Examining the entailments of teachers’ productions developing SCK in professional development (PD) is essential to advance research on teacher knowledge used in teaching. Twenty teachers’ productions of two tasks were analyzed. Results show that teachers’ productions examined mathematical relationships and structures to explain generalizations that were both mathematically valid and beyond reproach in the teacher community. Further, productions elaborated key mathematical practices drawing on and developing SCK. Implications of this research are ways of working in PD to advance teachers’ SCK. Purpose In order to create classroom experiences where students reason and justify mathematics, teachers need to understand mathematical proof 1 and know how to apply it in practice (Stylianides & Stylianides, 2006). Research on teachers’ knowledge uncovers that it is the form of proof, rather then the nature of proof and student learning that teachers notice (Knuth, 2002). Similarly, research on teachers’ knowledge of algebraic reasoning shows a number of weaknesses in understanding (Kieran, 2007). Yet, teachers’ knowledge of mathematics and their instruction impacts students’ learning (Hill, Rowan & Ball, 2005). In order to advance teachers’ knowledge of justification and its role in algebraic reasoning teachers need opportunities to construct justifications (Elliott, Lesseig, & Kazemi, 2009b; Lo, Grant & Flowers, 2008). Research on mathematical knowledge for teaching (MKT) suggests that the aim of professional development (PD) should advance teachers’ specialized content knowledge (SCK) of mathematics that is unique to the work of teaching (Elliott, Kazemi, Lesseig, Mumme, Carroll, & Kelley-Petersen, 2009; Suzuka, Sleep, Ball, Bass, Lewis, & Thames, 2009). Although this seems like a logical argument -- teachers should learn the mathematics unique to their work - - researchers have documented competing purposes of mathematics PD where teachers’ learning migrates to topics other then mathematics (Wilson, 2003). Confounding the finding that teachers’ mathematical learning is often negotiated away, is the fact that there is not an agreed upon knowledge base of the mathematics teachers need to know (Ball, Sleep, Boerst, & Bass, 2009) nor portraits of teachers’ deep understanding of algebraic reasoning (Doerr, 2004). Such images could serve professional educators learning how to facilitate PD oriented to SCK and researchers who are trying to build a knowledge base on teacher learning. This report offers images of teachers’ productions of algebraic generalizations and justification as they invoke and develop SCK and suggests ways of working mathematically in PD. To contribute to the limited understandings of teachers’ content knowledge needed for teaching, the research questions are: How do teachers’ justifications of generalizations orient them to SCK? What ways can mathematics PD take up teachers’ productions with the purpose of supporting SCK? This study examines the mathematical productions of teachers who had a long- term commitment to work on mathematics with one another. Analysis of their mathematical work provided insights on critical elements of justification that orients teachers to SCK in PD.