Mathematics is permeated with language; it appears in the form of new words and some old words with new meanings. There are new symbols to be able to read and consume; much information is presented in tabular or graphic form, and finally the language in a mathematics class has its own semantics, syntax and traditions of argumentation and expression. It is this language, used in the mathematics classroom, which students must absorb and develop fluency with--all while learning the mathematics expressed by this language. Traditionally, the language of mathematics has been overlooked in the classroom, as if students could learn it by just being exposed, rather than having explicit instruction. Numerous professional organizations have called for a focus on language in mathematics education, yet it appears that this important topic is overlooked in the classroom. This research project concentrated on developing a working definition of the language of mathematics and then, speculating that the reason teachers avoid teaching the language of mathematics, it developed the Language of Mathematics Teacher Self-Efficacy Scale (LoMTES), a measurement instrument to measure teacher perceived self-efficacy regarding the teaching of the language of mathematics. Bandura's socio-cognitive theory was the guiding force in developing this instrument. Bandura indicates that self-efficacy is predictive--that teachers with high perceived self-efficacy on a topic are generally capable of teaching it, while teachers with low perceived self-efficacy on a topic tend to skip over the topic or teach it in a minimal way. Self-efficacy, however, is a changeable construct; thus, this instrument could be used to identify teachers with low perceived self-efficacy regarding the teaching of the language of mathematics, which would enable the mathematics education community to explore possible interventions designed to improve student learning by improving teacher perceived self-efficacy. / Graduation date: 2004

<p>The purpose of the study was to investigate prospective &lsquo / A&rsquo / level mathematics teachers&rsquo / knowledge of the concept of a function. The study was a case study of six prospective Zimbabwean teachers who were majoring in mathematics with the intention of completing a programme leading to certification as secondary mathematics teachers. At the time of the study the six prospective teachers were in their final year of study. Prospective teachers&rsquo / knowledge of the concept of a function was assessed through task-based interviews and reflective interviews. These interviews, which were done over a period of three months, were structured to capture the prospective teachers&rsquo / subject matter knowledge and pedagogical content knowledge for teaching the concept of a function. The interviews were also meant to capture the prospective teachers&rsquo / underlining pedagogical reasons for their choices of the examples, representations and teaching approaches when planning to teach the concept.</p> <p>As part of the study a theoretical framework for understanding prospective teachers&rsquo / knowledge of the concept of a function was developed. The framework, which was developed, was used as an analytical tool in analyzing prospective teachers knowledge of the concept of a function. The results of the study indicated that the prospective teachers had a process conception of a function although some of them had given a set-theoretic definition of a function in which a function is perceived as a mathematical object. They also confined the notion of a function to sets of real numbers. Functions defined on other mathematical objects (for example, the differential operator and the determinant function) were not considered as functions by five of the six prospective teachers.</p>

<p>The purpose of the study was to investigate prospective &lsquo / A&rsquo / level mathematics teachers&rsquo / knowledge of the concept of a function. The study was a case study of six prospective Zimbabwean teachers who were majoring in mathematics with the intention of completing a programme leading to certification as secondary mathematics teachers. At the time of the study the six prospective teachers were in their final year of study. Prospective teachers&rsquo / knowledge of the concept of a function was assessed through task-based interviews and reflective interviews. These interviews, which were done over a period of three months, were structured to capture the prospective teachers&rsquo / subject matter knowledge and pedagogical content knowledge for teaching the concept of a function. The interviews were also meant to capture the prospective teachers&rsquo / underlining pedagogical reasons for their choices of the examples, representations and teaching approaches when planning to teach the concept.</p> <p>As part of the study a theoretical framework for understanding prospective teachers&rsquo / knowledge of the concept of a function was developed. The framework, which was developed, was used as an analytical tool in analyzing prospective teachers knowledge of the concept of a function. The results of the study indicated that the prospective teachers had a process conception of a function although some of them had given a set-theoretic definition of a function in which a function is perceived as a mathematical object. They also confined the notion of a function to sets of real numbers. Functions defined on other mathematical objects (for example, the differential operator and the determinant function) were not considered as functions by five of the six prospective teachers.</p>

The problem of this study was to determine if the teachers of Algebra I rated highest and lowest according to the Texas Teacher Appraisal System differed significantly in a measure of achievement. The analyses indicated that there were significant differences in achievement between the classes taught by the highest and lowest ranked teachers.

This mixed-methods study examined the extent to which teacher performance and student performance measures correlated, and to understand which specific practices of mathematics teachers in Grades 3-5 related to student performance. Research was conducted at five elementary schools in a large, urban north Texas school district. Data sources included component scores and recorded evidence from observation rubrics, interviews with campus administrators, and value-added modeling (VAM) student growth scores. Findings indicated a modest relationship between teacher performance levels and student performance levels. Lack of access to individual teacher VAM data, per district policy, might have impacted the strength of the relationship. Interviews with administrators and an examination of the evidence cited in the observation rubrics identified specific practices associated with highly rated mathematics teaching. Differences in administrators’ experience levels with both mathematics instruction and the observation instrument might have influenced rubric scores and the level of specificity shown in evidence statements.

The purposes of the study were: to determine the relationship between class size and academic achievement among university students in first-semester calculus classes, and to compare opinions about the instructor, course, and classroom learning environment of university students in small first-semester calculus classes with those in large classes. The sample consisted of 225 university students distributed among two large and two small sections of first-semester calculus classes taught at the University of Texas at Arlington during the fall of 1987. Each of two tenured faculty members taught a large and small section of approximately 85 and 27 students, respectively. During the first week of the semester, scores from the Calculus Readiness Test (CR) were obtained from the sample and used as the covariate in each analysis of covariance of four periodic tests, a comprehensive final examination, and final grade average. The CR scores were also used in a logistic regression analysis of attrition rates between each pair of large and small sections of first-semester calculus. Three semantic differentials were used to test the hypotheses relating to student opinion of the instructor, course, and classroom learning environment. It was found that for both pairs of large and small first-semester calculus classes there was no significant difference in the adjusted means for each of the four periodic tests, the final examination scores, the final grade averages, and the attrition rates. It was also found that the means of the student evaluation of the course by students in small and large classes were not significantly different, and the results of the student evaluations of the instructor and classroom learning environment by students in small and large first—semester calculus classes were mixed.

There is a considerable body of literature on the challenges faced by learners who speak an African language at home but who are taught through the medium of English. Less research has focused, however, on contexts where isiXhosa-speaking learners have Afrikaans as their Language of Learning and Teaching (LoLT), especially in Foundation Phase classrooms where teachers may not speak their learners’ home language. Such learners face the triple challenge of simultaneously learning a second language, learning to read in that language, and also learning new content and concepts through it. Using a multiple case study design, this investigation explores the mathematics teaching practices of Afrikaans-speaking Grade 3 teachers teaching isiXhosa-speaking learners through the medium of Afrikaans. Separate contextual profiles of the teaching practices of the participating teachers at the three schools are presented. Data were derived from school, classroom, and lesson observations (at least five complete mathematics lessons of each teacher), plus interviews with the teachers and with their school principals. By drawing on Vygotskian sociocultural theory and the interactive model of second language acquisition, this study highlighted the teaching practices of the three teachers as they mediated their learners’ mathematical conceptual development. An inductive data analysis approach was used to isolate recurring themes and patterns. Four main themes were identified: structuring of teaching and learning, facilitating of interaction, language use and implementation of mediating strategies. Analysis of the data shows that all three teachers’ language use displayed high levels of modified input, and high levels of context-embedded support. The levels of scaffolded learner talk were, however, found to be much lower than the levels of teacher talk, especially as far as academic registers were concerned. The teachers’ mediation strategies also displayed high levels of teacher-directed input which, on the whole, did not provide optimal opportunities for learners to develop independent levels of academic discourse. The study highlights the need for further research to inform teacher education and development with regard to more effective support structures to assist teachers with the sorts of challenges outlined above.