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Recent initiatives in mathematics education reform have identified proof and reasoning practices as critical for all grades of mathematics (NCTM, 2000; CCSSO, 2010). Successful enactment of these ambitious practices depends, in part, on teacher conceptions of proof and justification. This study examines middle school teacher conceptions of justification along three dimensions: What is justification? What is the purpose of justification? What are teacher proficiencies with justification? Data for this analysis is drawn from twelve middle school math teacher participants in the JAGUAR project and includes interview transcripts, justification assessments, and participation in workshops. One important result from this case study analysis is that teachers viewed justification as a mathematical practice, one that centers on why something works or is true mathematically, as well as a pedagogical practice, one that centers on communication of student reasoning. Motivation Using proofs to establish the validity of mathematical results is critical for the practice of mathematics. Yet many math teachers think of proof as a specific skill independent from content, with little relation to “every-day” mathematics instruction (Hanna, 2000; Knuth, 2002b; Ross, 1998; Wu, 1996). Over the past several decades math education researchers and policy makers have argued for greater integration of proof and justification into mathematics instruction. Schoenfeld (1994) argued that “proof is not a thing separable from mathematics, as it appears to be in our curricula; it is an essential

Development of Middle School Teachers' Knowledge and Pedagogy of Justification: Three Studies Linking Teacher Conceptions, Teacher Practice, and Student Learning