How Are Pre-service Teachers’ Educational Experiences Related to their Mathematical Knowledge for Teaching Geometry? Inah Ko University of Michigan inahko@umich.edu Amanda Milewski University of Michigan amilewsk@umich.edu Patricio Herbst University of Michigan pgherbst@umich.edu Abstract This study describes an investigation exploring relationships between pre-service teachers’ (PSTs’) mathematical knowledge for teaching geometry (MKT-G) and their educational experiences. Our data from 108 pre-service teachers from 6 universities suggest that PSTs’ experience in the classroom had the most significant effect on their MKT-G scores. The close examination of correlations between PSTs’ field experience and subsets of items reveals that PSTs’ field experience has a greater positive correlation with the amount of MKT-G used in the task of formulating problems than the amount of MKT-G used in the task of reviewing students’ work. Theoretical Framework and Objectives This paper investigates the mathematical knowledge for teaching of secondary preservice teachers (PSTs). To the extent that mathematical knowledge for teaching (MKT) is used in practice and that some measures of it show it correlates with experience (Herbst & Kosko, 2014), it is worth asking questions about this construct at the preservice stage: What is the variance of MKT among PSTs, and how much of that variance can be accounted for by components of PST training such as coursework or practicum experiences? Ball and colleagues have developed a practice-based theory of mathematical knowledge for teaching (MKT) (Ball, Thames, & Phelps, 2008), elaborating on the components of two major domains (subject matter knowledge, pedagogical content knowledge) by defining six sub- domains: common content knowledge (CCK); specialized content knowledge (SCK); and horizon content knowledge; knowledge of content and student (KCS), knowledge of content and teaching (KCT); and knowledge of content and curriculum. Ball’s group have developed measures of MKT and reported a plethora of findings (Hill, 2007; Hill, Schilling, & Ball, 2004; Hill, Rowan, & Ball, 2005; Hill, Ball, & Schilling, 2008) that describe the MKT of elementary and middle school teachers. There has been interest in the field to develop instruments specific to particular mathematical subjects for use with secondary teachers. While there is debate about how to conceptualize mathematical knowledge for teaching at the secondary level (Thompson, 2015; Speer, King, & Howell, 2015; and McCrory et al. 2012), efforts have been made to utilize Ball et al.’s (2008) framework to measure MKT for specific secondary courses. The present study builds on the work of Herbst and Kosko (2014) who developed an instrument for measuring teachers’ MKT for secondary geometry (MKT-G) which included items designed to tap into four domains of Ball’s MKT framework (CCK, SCK, KCS, KCT). With empirical data obtained from teachers’ responses on the instruments, researchers have begun investigating the relationship between elements of teachers’ subject matter