Teachers must have specific knowledge of a subject and how to teach it to promote learning in their students (also known as pedagogical content knowledge). Research has shown that project-based curriculum can be an effective way for teachers to leverage this knowledge into deeper student understanding and application readiness, but observations about when and how this happens in the classroom have not been adequately documented. In this study we will explore teaching and learning in a middle-school boat-building curriculum focused on real-world application of math concepts. The boat-building program took place over one week, included seven students, and was taught by three teachers. The teaching phase of this study examined how the three boat-building teachers applied their pedagogical content knowledge (PCK) through a participant observation case study. The three teachers had diverse training and teaching backgrounds. At the completion of the course these teachers were interviewed on their prior teaching experiences and training to determine how they acquired their pedagogical content knowledge. The learning part of this study involved a pre- and post-test application task completed by the students. After all students completed the application task, each was interviewed to see what, if any, knowledge or approach these teachers used had an impact on the ability of the students to do the task. Analysis of the pre-post assessments showed that students were not able to make statistically significant gains over the one week of instruction. However, students did note many aspects of instruction that they thought helped them. Additionally, students showed gains in assessing importance of geometry in design, the vocabulary associated with scale, geometry, and woodworking, and creating context for prior instruction. For the teachers, higher scores on the PCK rubric did align with a greater amount of experience teaching. Also, the two more experienced teachers influenced each other and the third teacher regarding student learning and instructional approach.

The purpose of this research study is to describe and analyze the self-reported experiences of exemplary high school mathematics teachers who underwent personal and professional transformations in order to develop and use a standards-based, constructivist (SBC) teaching paradigm in their classrooms. These teachers were all past recipients of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST), an award that required them to demonstrate that their mathematics instruction was rigorous in the manner described by the NCTM standards. The following research questions are addressed: (a) What are the paths SBC secondary mathematics teachers who received the PAEMST pursued to become highly effective?, (b) What obstacles and challenges did they encounter and how were these obstacles overcome?, and (c) What sustained them on their journeys? The research methodology used to be a narrative inquiry. Following a wide survey of PAEMST recipients, five volunteer participants were chosen for the study. Data were collected from each participant using a one-to-one interview and the written section of each participant's PAEMST application. A narrative was written for each participant describing the path they had followed to become a highly effective high school mathematics teacher. The narrative was sent to each participant, and a follow-up interview was conducted via telephone amending the narrative to reflect the participant's additions and deletions. From the five amended narratives, eight themes were identified: (a) influences; (b) education; (c) professional development; (d) NCTM standards; (e) teaching style: beginning, current, or end of a career; (f) obstacles; (g) personality traits and personal beliefs; and (h) student influence. Several of the themes were supported by previous research. However, this research study discovered two new findings. First, the five participants had common characteristics and beliefs: (a) belief in their students, (b) persistence, (c) belief that professional development is vital for teacher growth, and (d) passion about mathematics and about conveying that passion to their students. The second research finding pertained to the influence that their own students had on all of the five participants. All the participants purposely sought out their students' thoughts about the classroom curriculum and about the instruction they received. The teachers considered their students part of the classroom learning community, and they honored and acted on their input. Finally, in addition to describing the trajectory of five PAEMST winning teachers, this study offers recommendations for students studying to become high school mathematics teachers, teacher educators, and educational researchers. For these students, their teaching preparation courses need to be taught adhering to the four principles of learning: activity, reflection, collaboration and community. According to this research, the model of teacher preparation courses that emphasize the teaching of the above four principles using a traditional teacher-directed method does not prepare future mathematics teachers for the use of SBC teaching in their classrooms. Suggestions about further research are addressed.

The Teaching Abstract Algebra for Understanding (TAAFU) project was centered on an innovative abstract algebra curriculum and was designed to accomplish three main objectives: to produce a set of multi-media support materials for instructors, to understand the challenges faced by mathematicians as they implemented this curriculum, and to study how this curriculum supports student learning of abstract algebra. Throughout the course of the project I took the lead investigating the teaching and learning in classrooms using the TAAFU curriculum. My dissertation is composed of three components of this research. First, I will report on a study that aimed to describe the experiences of mathematicians implementing the curriculum from their perspective. Second. I will describe a study that explores the mathematical work done by teachers as they respond to the mathematical activity of their students. Finally, I will discuss a theoretical paper in which I synthesize aspects of the instructional theory underlying the TAAFU curriculum in order to develop an analytic framework for analyzing student learning. This dissertation will serve as a foundation for my future research focused on the relationship between teachers' mathematical work and the learning of their students.

M.Ed. (Psychology of Education) / Please refer to full text to view abstract

This study is limited to the mathematics performance of two intact groups of culturally deprived kindergarten students, mostly blacks, with a few whites and Mexican-Americans, who were enrolled at Robert E. Lee Elementary School (Denton, Texas) for the entire school year of 1970-1971. The purposes of the study are to compare the effectiveness of two methods of teaching mathematics to culturally disadvantaged children and to check for interaction of treatments when these children are classified by sex.

This study is an attempt to determine how a course in general mathematics can satisfy some of the needs of youth. The purpose of this study is to find out how the course in general mathematics can be made to contribute effectively to pupil growth, and how well the present course is contributing to pupil growth.

The problem of this study was to evaluate the effectiveness of prescriptive teaching of arithmetic to seventh grade pupils who were achieving at least one year below grade level in mathematics.

The purposes of this study were (1) to compare the achievement levels of students enrolled in a beginning college mathematics course when taught by (a) closed-circuit television followed by student-assisted study periods, (b) closed circuit television followed by access to videotape replay with no supervised study periods, (c) closed-circuit television followed by unsupervised study and discussion, and (d) regular lecture-recitation methods conducted by the television instructor, and (2) to ascertain the students' attitudes toward their instructor, course, and method of instruction.

This study has two purposes. The first is to compare the academic skills achievement in reading and mathematics of students participating in a performance contracting program with the academic skills achievement of students not participating in the performance-based program. The second is to determine whether those students participating in the performance contracting program show a significantly different level of achievement (higher or lower) than the control group approximately four months after the conclusion of the program.

The purpose of this study was to determine the interrelationship of self-concept and attitude toward mathematics to academic achievement in the areas of arithmetical computation, concepts, and application.