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Thesis (M.A.)--Boston University. This thesis was written in conjunction with Dennis J. Roberts, Mary Lee McLaughlin and Robert F. Pierce. / Statement of the problem: It is the purpose of this thesis to formulate plans for a guided tour throughout Western Europe for secondary-school teachers with emphasis on present and past mathematical and allied science contributions. This study will serve as an answer to four fundamental questions: 1. What are the resources available in Europe of value to mathematics teachers? 2. From the standpoint of marginal utility, which of these would be the most important? 3. where are they to be found? 4. How long would it take to see each of them profitably in a limited amount of time? [TRUNCATED]

The computer is an essential tool for the teaching of Numerical Analysis, since even simple methods involve complicated arithmetic. However, lecturers have been finding difficulties in formulating courseworks for undergraduate courses because the computing aspects tend to consume a great amount of the student's time, and hence divert his attention from the mathematical principles of the exercise. This project therefore instigated an investigation into how the learning of Numerical Analysis may be improved. After having established a learning model for Numerical Analysis, an assessment of the conventional teaching methods was performed, showing that these are not effective in furnishing the student with practical experience on the subject. A national survey of Numerical Analysis courseworks manifested that some lecturers attempted to overcome this problem by replacing the traditional coursework with interactive computer programs. The possible roles that may be assigned to the computer as an interactive teaching device were thus examined, leading to the conviction that the computer's. function must rest in, providing all students with the opportunity to easily execute the numerical methods, and to stimulate them to undertake a thorough critique of their subject. The educational objectives given to the teaching programs are: initiate or increase the amount of student- lecturer communication¡ produce all aspects of problem solutions; maximise the student's enthusiasm; accommodate all students; exhibit a user-friendly disposition; require no pre-usage training; involve no machine dependent code; be useful in all practical learning situations. A study of the programming features which are necessary for the real isatian of these objectives revealed that the methodology for designing the man-machine interaction for educational software requires further research and development. Through the development of three teaching packages (on ordinary differential equations, I inear simultaneous equations, and numerical integration) it became possible to derive a methodology for the design of the man-machine interface for simulation-type programs, whose design elements, which fall in one or more of the categories of learner control, motivation, and informative representation, are explained in terms of the psychological theories of learning. The methodology is proposed on the basis that the experiments carried out in real classroom situations proved that the form of the man-machine interaction enabled the programs to fulfil their educational objectives. Furthermore, it was discovered that the teaching programs have several advantages over the traditional coursework technique, in that they enhance the student's knowledge of Numerical Analysis to a greater extent, as well as increase the amount of student-lecturer contact, without expending more of the student's time.

Thesis (Ed.M.)--Boston University

<p> Previous research focused on characteristics of effective teachers, teacher recruitment or new pathways to teaching (Ball &amp; Forzani, 2009; Ronfeldt et. al., 2014). However, there is a gap in the research regarding the best path to prepare secondary math teachers. Universities create a customized path of preparation based on their beliefs within the scope of a set of standards given by organizations such as the National Council for Teachers of Mathematics or National Council for Accreditation of Teacher Education. Further research supports the necessity for both content and pedagogical knowledge (Ball, 2000; Graham &amp; Fennell, 2001; NCATE, 2010; Thames &amp; Ball, 2010). Therefore, the purpose of this qualitative case study pursues to increase the research by uncovering perceptions of secondary math teacher preparation with the standards, content knowledge, and content pedagogical knowledge. The study included two universities&rsquo; programs to gain awareness as to the interpretations of novice teachers, cooperating teachers, and University professors of the pre-service training program used to prepare future secondary mathematics educators. The findings suggest: while only the Mathematics Education Professor at both Universities were the only study participants to have a vast knowledge of the standards it did not seem to impede on the overall preparation of the novice teacher. Novice and Cooperating teachers lacked the vision for the purpose and value of upper level math classes required for the degree. Both Novice and Cooperating Teachers wanted an increase in opportunities for real-world content pedagogical situations along with differentiation, coteaching, and Special Education. Novice teachers acknowledged the need for relationships with University professors and peers in their path toward preparation. Lastly, Mathematics Education Professors stated value in making connections between courses and research to high school math. Furthermore, the finding suggest for teacher preparation program: to prepare secondary math teachers for the current culture of mathematics education, content and pedagogical courses should not be separated and a push to increase program enrollment should be a priority.</p><p>

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Research over the past twenty years supports the teacher as the critical factor in the implementation of educational programs. The primary purpose of this mixed design study was to determine teachers' perceptions in implementing the required Algebra I program that was mandated by the state of Virginia in 1995. The research was examined through the lens of the recommendations of the National Council of Teachers of Mathematics (NCTM): communicating mathematically, making mathematical connections, becoming mathematical problem solvers, and reasoning mathematically. This study was limited to ninth grade Algebra I teachers in a school division in Virginia. Two Concerns Based Adoption Model (CBAM) instruments were used in this research. The Stages of Concern (SoC) Questionnaire determined the teachers' concerns regarding implementation of the required Algebra I program. The Levels of Use (LoU) focused interview data supported the teachers' areas of concern. In addition, the grounded theory method was used to analyze the observation and interview data. Results were presented as narrative descriptions from which major categories of concerns emerged. Findings revealed that the NCTM recommendations of communicating mathematically, making mathematical connections, becoming mathematical problem solvers, and reasoning mathematically were not implemented in the required Algebra I program. Teachers were unaware that the required Algebra I program was designed to meet the needs of a changing population. This study supports the need for comprehensive and ongoing training for teachers if the needs of a more diverse population are to be realized in a required Algebra I program.

Thesis (M.Ed.)--University of Hong Kong, 1984. / Includes bibliographical references (leaf 126-128). Also available in print.

With the dynamics of the growing population of native Spanish-speaking students in America’s public schools, two-way dual language immersion programs are increasing in number. A series of observations and interviews in a dual language program by the researcher led to the identification of the use of visuals as a prevalent component integrated in instruction. This dominant instructional strategy led to questions of how visuals might affect student performance. Previous studies had not focused specifically on questions with a visual prompt and questions without a visual prompt. The purpose of this study was to answer several questions focused on differences in student performance on nonvisual and visual questions. The research questions used to achieve this purpose included a comparison of Mathematics TAKS Test scaled scores for students in a two-way dual language immersion program and students enrolled in a monolingual educational program, an analysis comparing these two groups of students on nonvisual and various categories of visual questions, an analysis of the performance of both groups of students based on the comparison of nonvisual questions to subsets of visual questions, and an analysis of an interaction effect and main effects of question type and group based on educational setting. A quasi-experimental design with static-group comparison was used for the purposes of this study. Data were collected from the Texas Education Agency [TEA] for all students who took the Spring 2009 version of the Grade 3 or Grade 4 Mathematics TAKS Test in English or Spanish. Data from a total of 6,904 students were used in the study. Data were analyzed based on descriptive statistics and ANOVAs. A statistically significant difference was found in overall scaled score comparisons between the two groups of students on the Spanish version of the Grade 4 Test. Major findings of the study included a higher performance shown on most subsets of visual questions compared to nonvisual questions for both groups of students involved in this study. Two-way dual language immersion students scored higher than students in a monolingual English program on most subsets of visual questions, but no interaction effect occurred between question type and group.

<p> The purpose of this study was to determine the effects of theories of intelligence and an intervention of incremental mindset training on students' attitudes toward statistics and their mastery of content in an introductory statistics college course. The sample was 547 undergraduate students at a small, faith-based, liberal arts college in the Midwest.</p><p> A pretest-posttest design was used for the three instruments implemented. The Comprehensive Assessment of Outcomes in a first Statistics course (CAOS) assessed students' statistical literacy. The Student Attitudes Towards Statistics - 36^&copy; (SATS^&copy;) assessed six components of students' attitudes toward statistics including affect, cognitive competence, difficulty, effort, interest, and value. The Theories of Math Intelligence Scale - Self Form (TMIS) assessed students' mindsets toward mathematics. Students in the treatment group received four brief incremental mindset training sessions throughout the semester. The initial mindset categorization had no significant effect on the difference in mean SATS^&copy; or CAOS gain (<i> p</i> &lt; .05); the power to detect a difference was limited due to a low response rate.</p><p> Students in the treatment group decreased at a rate greater than students in the control for the component of effort on the posttest SATS^&copy; assessment when the pretest was controlled for, <i>F</i>(1, 138) = 14.778, <i>MSE</i> = 10.954, <i>p</i> &lt; .001. The remaining components produced no significant differences between groups (<i>p</i> &lt; .05). Students in the control group also improved more on their mastery of statistics as assessed by the posttest CAOS when the pretest CAOS was controlled for, <i>F</i>(1, 297) = 6.796, <i> MSE</i> = .100, <i>p</i> = .010.</p><p> Analysis revealed that females gained more than males in the treatment group on the SATS^&copy; component of value, &micro;_Diff = 0.829, <i>t</i>(28)= 3.123, <i>p</i> = .004. The remaining components of the SATS^&copy; assessment did not produce statistically significant results (<i>p</i> &lt; .05).</p><p> Recommendations for practice include creating classrooms that support growth mindsets and the design of mindset training. Recommendations for research include replication of the current research in statistics and other mathematics courses. A final recommendation calls for an examination of the differences by gender on the SATS^&copy; assessment. </p>