2013 Conference Proceedings - University of Nevada, Las Vegas

(SCK), or knowledge of mathematics specifically for teaching, and (c) mathematics on thehorizon. For example, knowing how to multiply 35 x 25 using a standard algorithm is CCKexpected of most adults. Teachers, on the other hand, also need to know how to detectmathematical errors, determine if methods and solutions different from the ones they are familiarwith are valid, ask appropriate questions to probe student thinking and correct misconceptions,and use representations to make connections, all examples of SCK. Pedagogical contentknowledge includes (a) knowledge of content and students, (b) knowledge of content andteaching, and (c) knowledge of curriculum. Ma (1999) identified three periods in whichteachers’ subject matter knowledge develops (a) during their own schooling experiences(students of mathematics, K-12 and college-level), (b) during a teacher preparation program, and(c) while teaching students in the classroom. Although pre-service teachers have limited timeand experience in the classroom working directly with students, CCK and SCK can developwithout direct student interactions.Second, teacher behavior and learning is influenced by subject matter knowledge, andattitudes and beliefs towards mathematics, within a social context (Van der Sandt, 2007). Whenconsidering teacher preparation, existing knowledge and beliefs are critical factors indetermining what and how teachers learn from educational experiences and these beliefs aredifficult to change (Kajander, 2010). Furthermore, the level of mathematical competence of preserviceteachers prior to entering the preparation program greatly influences the focus of theprogram itself. If pre-service teachers do not possess mathematical competence prior to enteringthe teacher preparation program, then teacher educators must dedicate methods instructional timeto school-level mathematics. Teachers in the U.S. are caught in a cycle of low-qualitymathematics learning (Ball, 2003; Ma, 1999).Although studies with pre-service teachers have documented growth in MKT withinmathematics content courses designed for teachers (e.g. Mathematics Education of ElementaryTeachers (ME.ET), 2009; Welder, 2007), there have been limited studies on the impact of themathematics methods course on the development of MKT. By design, the objectives of amathematics methods course focus on both content and pedagogical content knowledge.Therefore, the purpose of this study was to investigate the impact of a one-semester mathematicsmethods course, and follow-up full time student teaching assignment on the development ofMKT. The focus in algebraic reasoning, in particular two underlying components of algebraicProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 34