The overall purpose of this concurrent mixed methods study was to develop an online performance assessment using content questions taken from a reputable seventh and eighth grade standardized assessment that effectively evaluated and allowed preservice middle grades mathematics teachers to demonstrate their mathematics knowledge for teaching in the four main content strands of algebra, probability and statistics, geometry, and number and operations. In addition, this study examined differences in mathematics knowledge for teaching in enrollment characteristics, in courses taken and currently taking, and in three different cohorts, each at different stages in the program, of 122 preservice middle grades mathematics teachers at a large public university in central Texas. Constant comparative analysis and descriptive statistics revealed average scores on the seventh and eighth grade content questions. The middle grades preservice teachers’ content understanding and pedagogical understanding responses indicated several misunderstandings and misinterpretations in the middle grades mathematics they were tested on. Content knowledge, content understanding, and pedagogical understanding together made up a preservice teacher’s mathematics knowledge for teaching. The study revealed that although preservice middle grades teachers could answer a content question correctly; they did not necessarily understand the process they used to arrive at their answer. In addition, their lack of explanation and knowledge of how to complete the problem correctly was transferred to their pedagogical understanding of the same problem. There was a general indication of increasing mathematics knowledge for teaching for each content strand across enrollment characteristics (freshmen, sophomore, etc.) and cohorts. However, there was a noticeable decrease in average mathematics knowledge for teaching scores during middle grades preservice teachers’ junior year. Special integrated mathematics and pedagogy courses (MASC) and the middle grades methods course had the greatest affect on preservice teachers’ mathematics knowledge for teaching each content strand scores. Recommendations are also included in the study which may be used to help shape reform initiatives in teacher education programs throughout the United States.

Doctor of Philosophy / Curriculum and Instruction Programs / David S. Allen / This study examined pedagogical content knowledge (PCK) and Mathematics knowledge for teaching (MKT) from a perspective that blends existing definitions, questions, and methodologies into a unique method of collecting and analyzing data. Many studies on MKT have been done using qualitative methodology, usually with the researcher interviewing or testing individual teachers and analyzing that data using qualitative methods. A smaller number of studies have attempted to measure MKT using a quantitative approach, often times involving paper pencil tests with multiple choice and some open ended questions. Current research is also heavily weighted towards pre-service elementary teachers in the area of MKT for division by fractions (Depaepe et al, 2013). Although it may be true many pre-service elementary teachers have difficulties with division by fractions (Li & Kulm, 2008; Ma, 1999; Tirosh, 2000), we do not know if these problems persist for in-service elementary teachers or with secondary teachers at any stage. This study used a survey created by the researcher as a synthesis of existing questions from research on MKT with regards to division by fractions. This survey was delivered through an online format. The qualitative data in this research was then coded into quantitative data using a rubric developed by the researcher producing MKT scores that could be analyzed using statistical methods and generalized to a larger population. This study examined the Mathematical Knowledge for Teaching held by elementary, middle, and secondary in-service teachers in the domain of division by fractions. In particular this research asked if there was a relationship between the educational background, training, and experience of teachers and their MKT. Multiple analysis including independent t-tests, independent one-way ANOVAs, and Multiple regression analyses revealed that Middle school teachers and teaching at a middle school were significant predictors of increased MKT scores when compared with other groups of teachers. The type of teaching license, the type of degree held, total experience, and grade level experience were all found to have no significant relationship to MKT scores.

With the implementation of No Child Left Behind legislation and a push for reform curricula, prospective teachers must be prepared to facilitate learning at a conceptual level. To address these concerns, an exploratory mixed methods investigation of twenty-eight prospective middle grades teachers’ mathematics knowledge for teaching geometry and mathematical connection-making was conducted at a large public southeastern university. Participants completed a diagnostic assessment in mathematics with a focus on geometry and measurement (CRMSTD, 2007), a mathematical connections evaluation, and a card sort activity. Mixed methods data analysis revealed prospective middle grades teachers’ mathematics knowledge for teaching geometry was underdeveloped and the mathematical connections made by prospective middle grades teachers were more procedural than conceptual in nature.