Browsing by Subject "Mathematics Education"
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Item A Pathway to STEM Education: Investigating Pre-Service Mathematics and Science Teachers at Turkish Universities in Terms of Their Understanding of Mathematics Used in Science(2012-07-16) Corlu, MehmetReforms in education of Science, Technology, Engineering, and Mathematics (STEM) disciplines have been particularly critical for the economic competitiveness of Turkey. STEM education includes the set of knowledge, skills, and beliefs which are collaboratively constructed by students and teachers at the intersection of more than one STEM subject area. The overall purpose for all three studies comprising this dissertation was to investigate whether prospective Turkish mathematics and science teachers were ready to implement STEM education in terms of their integrated teaching knowledge (ITK), teaching self-efficacy beliefs, and attitudes toward mathematics and science integration. The dissertation employed a quantitative research methodology to investigate ITK and attitudes whereas teaching self-efficacy beliefs were investigated with an explanatory mixed methods study. Results from the first study suggested that the pre-service mathematics and science teachers, who were educated in an integrated teaching education program, outperformed peers in the departmentalized teacher education program in terms of their ITK. There was evidence in the second study that practical teaching experiences helped pre-service mathematics and science teachers develop high self-efficacy beliefs for mathematics and science integration. The findings of the third study indicated that the integrated teacher education program provided noteworthy benefits for pre-service attitudes toward mathematics and science integration when compared to pre-service mathematics teachers in the departmentalized program. The unique attributes of integrated mathematics and science teacher education programs, such as balanced coursework of content, pedagogy, and pedagogical content knowledge, integrated teaching courses, and the increased peer stimulation in classrooms were discussed as possible factors that explain the results. Overall, the three studies demonstrated that the pre-service mathematics and science teachers in the integrated teacher education program were ready to implement STEM education aligned with the reforms enacted by the K-12 policy-making organization while the departmentalized teacher education program, which was recommended by the higher education policy making organization, was preparing pre-service teachers as content experts of individual STEM subjects. Policy coordination in K-12 and higher education emerged as a critical factor for the success of Turkish education reforms.Item Achievement and Opportunity Gaps in Mathematics Education in Turkey Compared to European Union Countries(2010-12-08) Yetkiner, Zeynep 1978-One of the main purposes of this dissertation was to examine gender- and socioeconomic status (SES)-related mathematics achievement gaps among Turkish middle-school students compared to achievement gaps in European Union (EU) countries. A further purpose of the present study was to investigate qualified mathematics teachers? distribution in relation to student SES among Turkish middle schools. Finally, relationships between mathematics teacher quality indicators and students? mathematics achievement within Turkish middle-school classrooms were explored. In this dissertation, Trends in International Mathematics and Science Study 2007 data were used. Sample countries were Turkey, Bulgaria, Cyprus, Czech Republic, Hungary, Italy, Lithuania, Malta, Romania, and Slovenia. Achievement gaps by gender and SES were examined using Cohen?s d effect sizes and 95 percent confidence intervals. Relationships between mathematics teacher quality and students? mathematics achievement were investigated using hierarchical linear modeling. Results showed none or only negligible gender differences but substantial SES-related gaps in Turkish students? achievement in mathematics, overall, or in various content and cognitive domains. Correlations between students? SES levels and their achievement were the largest in Turkey compared to the sample EU countries. Among the sample EU countries, only Hungary had as large or even somewhat larger disparities as Turkey between low- and high-SES students? mathematics achievement. The current study also identified SES-related inequities in access to qualified mathematics teachers in Turkey. Low-SES students were more likely to be taught by mathematics teachers who had less than 3 years of experience or who did not hold a degree in mathematics or mathematics education. On the other hand, years of experience and a degree in mathematics or mathematics education were found to be substantially related to Turkish eighth-grade students? mathematics achievement. Low-SES students? mathematics teachers were also more likely to report lack of confidence in their preparation to teach various mathematics contents. To narrow achievement gaps, Turkish policy-makers can explore and benefit from policies of the countries identified in the present study as more equitable in terms of student achievement than Turkey. The current study also shows Turkish policy-makers importance of the equitable distribution of qualified mathematics teachers in closing the mathematics achievement gap in middle schools.Item Authoritative discourse in the middle school mathematics classroom: a case study(Texas A&M University, 2005-11-01) Harbaugh, Adam PaulAccording to the National Council of Teachers of Mathematics (NCTM) standard of communication, ??Instructional programs from pre-kindergarten through grade 12 should enable all students to...communicate their mathematical thinking coherently and clearly to peers, teachers, and others?? and students need to learn ??what is acceptable as evidence in mathematics?? (NCTM, 2000, p. 60). But do teachers have a clear understanding of what is acceptable or do they believe that the only acceptable explanations are the ones that they themselves gave to the students? Can teachers accept alternative forms of explanation and methods of solution as mathematically accurate or do they want students to simply restate the teachers?? understandings of mathematics and the problem? The focus of this dissertation is the authoritative discourse practices of classroom teachers as they relate to individual students and large and small groups of students. In this case study, I examine the interactions in one eighth-grade mathematics classroom and the possible sharing of mathematical authority and development of mathematical agency that take place via the teacher??s uses of authoritative discourse. A guiding objective of this research was to examine the ways a teacher??s discursive practices were aligned with her pedagogical intentions. The teacher for this study was an experienced eighth-grade mathematics teacher at a rural Central Texas middle school. The teacher was a participant in the Middle School Mathematics Project at Texas A&M University. Results of an analysis of the discourse of six selected classes were combined with interview and observation data and curriculum materials to inform the research questions. I found that through the teacher??s regular use of authoritative discursive devices, mathematical authority was infrequently shared. Also the teacher??s uses of authoritative discourse helped create an environment where mathematical agency was not encouraged or supported. The teacher??s use of various discursive devices helped establish and maintain a hierarchy of mathematical authority with students at the lowest level reliant on others for various mathematical decisions.Item Factors Supporting College Mathematics Sucess: Orientation, Voice, and Technological Pedagogical Content Knowledge(2013-08-09) Alpert, Anna PatThe purpose of this study was to examine factors supporting college mathematics success. First, effect of a brief high school orientation to mathematical technologies used for college placement testing was examined. Secondly, the voice of participants in this orientation was heard. Finally, bootstrapped orientation data were presented to teachers and instructors of introductory statistics courses as a scaffold to their technological pedagogical content knowledge (TPCK) as these teachers and instructors strive to actively engage students to achieve college mathematics success. Many entering college students are placed into developmental mathematics classes based on scores from college placement assessments that allow extremely limited use of calculating technology and have various time constraints. Students in a rural central Texas 3A high school that were enrolled in Algebra II course were given pre- and post- tests in Arithmetic and Algebra. Each 20-minute test contained 15 mathematical content questions and one qualitative question. The post-test was given approximately a week after the pre-test. During the week, students were provided time to explore review material using only pencil and paper for the arithmetic review, and a four-function calculator on the algebra review questions. Effects of the orientation were analyzed using mean scores, confidence intervals, effect size, and GLM for whole-group and sub-groups. A paired samples t-test was calculated. These effects were discussed. A case study involving participants of the orientation was conducted. Twelve participants were interviewed after each had entered college. Five themes emerged from these interviews: (1) Knowledge of College Mathematics, (2) Technology and Mathematics, (3) Mathematics Tests/Assessments, (4) Teaching and Learning Mathematics, and (5) Mathematical Experiences, Hopes and Dreams. Each theme is discussed. Using Microsoft Excel, bootstrapping is presented to instructors of first year introductory statistics courses in support of student success as instructors? technological pedagogical content knowledge is developed. A course project demonstrating and developing application of computational technology by bootstrapping confidence intervals at the 95 % level using Microsoft Excel is presented. Data from the orientation were further analyzed in the bootstrapping project. Confidence intervals were empirically calculated from bootstrapped resamples of the mean. The number of resamples used was 250 at each of three levels: Over-sampling, at-sampling, and under-sampling. Graphs of bootstrapped confidence intervals, using the Rule of Eye 4, showed statistically significant differences between pre-test and post-test scores for all pairs of data sets.Item Initial full-time classroom teaching experiences for interns and student teachers: factors contributing to their mathematics teaching development(2009-05-15) Piccolo, Diana LynneIn 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.Item Teacher Perceptions of Change in Leadership Roles and Activities as a Result of Participation in a Science Education Leadership Program(2010-10-12) Hobson, MargaretTeacher leadership has emerged as a component of the movement to increase student achievement in science and mathematics. The Information Technology in Science Center for Teaching and Learning (ITS Center) was funded by the National Science Foundation with the goal of developing science education leaders. This study explored the changes in teachers' descriptions of their leadership in their school settings before and after their participation in a science education leadership program and the aspects of their science education leadership. A study of teacher-participants in Cohort II of the ITS Center was conducted to investigate how they demonstrated leadership in their school settings and to what extent these teachers attributed changes in their leadership to their ITS Center experience. Participants in this study were 15 classroom teachers who participated in Cohort II of the ITS Center. Quantitative and qualitative methodologies were used. These teacher-participants completed a Teacher Leadership Roles Survey as a part of their application to participate and then again one year after their ITS Center participation. Their primary leadership roles were to serve as a source of knowledge and a generator of new ideas for their fellow teachers. Their major activity was to develop curricular/instructional materials. However, the change in their leadership roles and activities was highly variable. As the literature indicates, demonstration of teacher leadership is highly dependent on context. The participants who greatly increased their leadership roles and activities moved into new, formal leadership roles following their ITS Center experience. Participants who greatly decreased their leadership roles and activities had changed school campuses or districts. A case study was conducted of two teachers demonstrating a great increase in leadership. They identified the components of the ITS Center experience that contributed to increased leadership roles and activities as: relationships developed with fellow teachers, graduate students, and university faculty; extended time for engagement in ITS Center activities; accountability for implementation of ITS Center Instructional Frameworks and Practitioner Research Plan; and their increased understanding of educational research and the role it plays in evidence-based decision making.Item Transformation from Developmental Mathematics Student to Mathematics Teacher: Narratives of Adult Learning Experiences(2010-01-16) Wright, Gary L.The purpose of this study was to gain a better understanding of the experiences of developmental mathematics students who, after successful completion of their developmental courses, chose a career in teaching and to gain a better understanding of how those experiences helped shape their decision to go forward with a career in mathematics education. With the intention of exploring the text and the context of the experiences of former developmental mathematics students as they have reflected on them and storied them so as to make meaning of them, I determined that a qualitative methodology was indicated; and the qualitative method selected was narrative analysis. Altogether 13 respondents met the criteria and were interviewed. Interviews conducted during the spring and early summer of 2008 were recorded, transcribed, and analyzed for data relevant to the goals of this study. Analysis revealed that developmental mathematics students not only have the capacity to become competent students but they have the potential of becoming outstanding teachers and scholars. This potential is closely tied to affective qualities, such as self-efficacy, which are often profoundly impacted and enhanced by a teacher or mentor. The developmental student who has chosen a career in education frequently views the teacher/mentor as (i) a role model who he/she desires to emulate thereby extending that profound impact, and/or as (ii) a hero for whom future endeavors are viewed as a form of payback. The narratives also revealed that women developmental students typically had greater struggles and difficulties in meeting their educational goals because they bore the responsibility for caring for children and, in most cases, for their family?s financial support. Areas of study that warrant further investigation were uncovered while doing this research and include (i) an identification of teaching methodologies that both enhance mathematics capability and also bring a greater self-awareness of the increased capability, (ii) a determination of the impact of faculty/institutional behaviors and attitudes on adult developmental mathematics students who dropped out of their programs and did not complete their college education, (iii) the characteristics of the educational experiences of single mothers who passed through developmental mathematics and on to the teaching profession, and (iv) a deeper understanding of the teacher recruitment potential of cooperative learning groups, tutoring centers, and supplemental instruction.