In the Teaching Principle (National Council of Teachers of Mathematics [NCTM], 2000), it explained that development and utilization of pedagogical content knowledge required teachers to continually increase their knowledges of mathematics content and pedagogy. This study researched the amalgamation of multi-faceted factors and inter-relatedness of pedagogical content knowledge (PCK), content knowledge for teaching mathematics (CKTM), and mentoring support perceptions throughout elementary and middle level student teachers’ and interns’ initial full-time teaching experiences. In the first article 13 elementary and seven middle grade student teachers’ are examined based on differences between pedagogical content knowledge and content knowledge for teaching mathematics. Standardized difference scores were calculated and compared using multivariate contrasts on certification level. Results showed statistically significant differences (p < .01) on all three CKTM domains but no statistically significant differences were found on any of the five Classroom Observation and Assessment for Teachers (COPAT) domains. Both groups had the highest mean difference in the CKTM number/concept domain. COPAT results showed middle grade level pre-service teachers primarily had all positive mean differences, in comparison to the elementary level pre-service teachers, which had all negative mean differences. In the second article the mathematics mentoring support perceptions of 11 first year teachers who participated in a year-long urban internship program were examined. Semi-structured interviews revealed that district and grade level campus mentors provided the most mathematics instruction and pedagogically-based support to both groups of interns. Middle school level interns relied more on their team of mathematics teachers and elementary level interns received more mathematical content support from their district mentor than did middle level interns. Pedagogical support was greatest in the areas of lesson design and implementation of classroom management strategies. In the third article 14 elementary and six middle level student teachers were observed and interviewed on general and content-specific pedagogical skills and perceptions. Results indicated both groups of student teachers perceived themselves as most competent in having lesson plans ready, routines evident, and utilizing studentcentered instruction. Conversely, both groups felt least competent in getting students on task quickly, using a variety of teaching strategies, using critical thinking skills, and handling inappropriate behavior effectively.

Thesis advisor: Lillie Richardson Albert / The purpose of this research is to identify the categories of South Korean elementary teachers' knowledge for teaching mathematics. Operating under the assumption that elementary teachers' knowledge for teaching affects students' learning, eleven South Korean elementary teachers volunteered to participate in this study. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers' knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. A notable conclusion of this study is that Pedagogical Content Knowledge might not be the sum of the other categories of knowledge for teaching mathematics. These findings may be connected to results from relevant studies in terms of the significant role of teachers' knowledge in their mathematics instruction. This study contributes to the existing literature in that it provides empirical bases for understanding teachers' knowledge for teaching mathematics and reveals the relationship among categories of knowledge for teaching mathematics. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Lynch School of Education. / Discipline: Teacher Education, Special Education, Curriculum and Instruction.

This study investigated the impact expectancy beliefs had on third through fifth-grade teachers’ instructional teaching practices. These instructional teaching practices included how teachers used their pedagogical content knowledge, specifically their content knowledge for teaching mathematics and formative assessment, to make scaffolding decisions while supporting students in mathematics intervention. The investigation included the analysis of stratified sampling procedures, expectancy beliefs, observations, and self-reported scaffolding ratings. A multiple case study was conducted to understand how four participants, the teachers in the study, expected students to perform in mathematics intervention along with the participants’ pedagogical content knowledge and the impact those beliefs and knowledge had on scaffolding practices. Scaffolding practices highlighted in this study were the teachers’ use of cognitive activation, mathematical discourse, and handling errors productively. Findings suggested that even though teachers demonstrated having content knowledge for teaching mathematics and effective use of formative assessment the teachers still scaffolded just-in-case students might need it during mathematics intervention. The results also suggested that teachers relied upon their expectancy beliefs of students to make scaffolding decisions more than the teachers relied upon their own pedagogical content knowledge. Additionally, this study found that a scaffolding workshop focused on teacher actions may impact the teachers’ self-reported ratings and in turn the teachers’ scaffolding practices. Discussion of the findings in relation to the current literature and their implications was provided. Continued research was suggested to examine how teachers self-rate their scaffolding practices pre- and post-scaffolding workshops and the impact that may have on teachers’ scaffolding practices. These findings add to the research in the field of mathematics education in equitable teaching practices, mathematics intervention, and scaffolding practices.

The purpose of this study is to examine the effects of a mathematics teaching methods course on pre-service elementary mathematics teachers&rsquo / content knowledge for teaching mathematics (CKTM). In order to accomplish this purpose, pre-service mathematics teachers&rsquo / understanding of basic concepts and procedures in school mathematics, use of mathematical definitions, presentation of mathematical content to students, identification of common errors, misconceptions and solution strategies and evaluation of unusual solution methods were examined with the help of a multiple choice test. The data were collected from 43 senior pre-service mathematics teachers from a teacher education program at a large public university in Ankara. The participants were given an 83-item test to measure their content knowledge for mathematics teaching at the beginning and after the methods course. The purpose of the pre- and post-test assessment was to measure the amount of change in the participants&#039 / knowledge for mathematics teaching. The test was developed and piloted at the University of Michigan in the USA for Learning Mathematics for Teaching (LMT) Project. Quantitative data analysis techniques were used to answer the research questions. The results indicated that there was a significant effect of the mathematics teaching methods course on pre-service teachers&rsquo / content knowledge for teaching mathematics. Moreover, the findings showed that there is no significant mean difference between male and female pre-service teachers, and between the pre-service teachers who have taken at least one mathematics teaching elective course and the ones who have not taken any elective course related to mathematics teaching in terms of their CKTM. Also, the study showed that there is a significant positive relationship between pre-service teachers&rsquo / CKTM and their academic achievement on undergraduate mathematics content courses. The study is expected to make important contributions to the literature by providing information about whether the methods courses significantly contribute to pre-service teachers&rsquo / understanding of knowledge for mathematics teaching. Moreover, the findings of the study is hoped to inform teacher educators and policy makers about the needs and improvements in teacher preparation programs.