Research on the relationship between mathematics education and society has established that societal change can have a direct effect on mathematics education. Qatar experienced a large amount of societal change since its leadership change in 1995. The literature would suggest that changes in mathematics education in Qatar would follow. The purpose of this study was to investigate the changes in mathematics education in Qatar from 1995 until 2018 and to understand the reasons for these changes. This study applied historic research methods in the form of primary source analysis. The primary sources consisted of text analysis and in-depth interviews. The texts included published reports from the Ministry of Education in Qatar and Qatari mathematics textbooks. Seven in-depth, semi-flexible interviews were conducted with educators involved with Qatar’s mathematics education system within the timeframe of interest. The findings revealed that there were significant changes in mathematics education in Qatar during this timeframe. Specifically, changes were made to the mathematics standards and curriculum, the mathematics language of instruction, mathematics assessments, and mathematics teachers’ preparation. New mathematics standards were created, and government-issued textbooks were abandoned for many years to encourage autonomy and creativity. The language of instruction in the mathematics classroom was transitioned from Arabic to English, and then back to Arabic again. New, national mathematics assessments were created to track the new mathematics reform project. They were later abandoned. The reasons for these many changes, and the challenges they created, touched on many different areas of research in mathematics education and sociology. These included policy borrowing, the language of instruction, knowledge societies, rentier societies, and the relationship between mathematics and society. The findings from this study confirmed that the rapid societal changes that occurred in Qatari society during this timeframe were mirrored by rapid changes in mathematics education within the country.

There is in effect at the present time a Florida State-Wide Ninth-Grade Testing Program. This program consists of two tests; one is the School Ability Test (SAT) and the other consists of five parts of the Iowa Tests of Educational Development (ITED). The SAT is an attempt to provide a measure of a student's ability to achieve successfully in a school program. This test provides two part scores, verbal and quantitative, and a total score which is the sum of the part scores. The quantitative section of the test is designed to give "measure of ability in certain quantitative skills of number manipulation and problem solving." Items on this test are of two kinds; one involves problem solving and the other involves numerical computation. When the SAT is mentioned in this paper, it is the quantitative section that is referred to. / Advisor: Raymond E. Schultz, Professor Directing Paper. / Typescript. / "Feb., 1960." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 29).

Set-based reasoning and conditional language are two critical components of deductive argumentation and facility with proof. The purpose of this qualitative study was to describe the role of truth value and the solution set in supporting the development of the ability to reason about classes of objects and use conditional language. This study first examined proof schemes – how students convince themselves and persuade others – of Algebra I students when justifying solutions to routine and non-routine equations. After identifying how participants learned to use set-based reasoning and conditional language in the context of solving equations, the study then determined if participants would employ similar reasoning in a geometrical context. As a whole, the study endeavored to describe a possible trajectory for students to transition from non-deductive justifications in an algebraic context to argumentation that supports proof writing. First, task-based interviews elicited how participants became absolutely certain about solutions to equations. Next, a teaching experiment was completed to identify how participants who previously accepted empirical arguments as proof shifted to making deductive arguments. Last, additional task-based interviews in which participants reasoned about the relationship between Varignon Parallelograms and Varignon Rectangles were conducted. The first set of task-based interviews found that a majority of participants displayed ritualistic proof schemes – they viewed equations as prompts to execute processes and solutions as results, or “answers.” Approximately half of participants employed empirical proof schemes; they described convincing themselves or others using a range of arguments that do not constitute valid proof. One particularly noteworthy finding was that no participants initially used deductive justifications to reach absolute certainty. Participants successfully adopted set-based reasoning and learned to use conditional language by progressively accommodating a series of understandings. They later utilized their new ways of reasoning in the geometrical context. Participants employed the implication structure, discriminated between necessary and sufficient conditions, and maintained a disposition of doubt toward empirical evidence. Finally, implications of these findings for pedagogues and researchers, as well as future directions for research, are discussed.

"Wanting to help children to overcome any fears that might be foremost in them, the writer wishes to make a study of principles of teaching arithmetic and apply in the classroom certain of these principles in an effort to help children hurdle their great fear of arithmetic"--Introduction. / "August 1956." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Advisor: Mildred Swearingen, Professor Directing Paper. / Includes bibliographical references (leaves 29-30).

"Out of genuine desire to prepare oneself to handle, in a more effective way, the teaching of eighth grade mathematics, there comes to mind such questions as these: 1. What are the needs or tasks or problems of eighth grade pupils to which arithmetic can make a contribution? 2. What content is available in the state adopted textbooks? 3. How well is this material adapted to school needs of pupils of this age? 4. What reliable tests can be found? 5. What materials and plans of a general nature can be found or developed which, if revised later to fit the specific classroom situation, may prove of help in improving the teaching of mathematics?"--Introduction. / "August, 1952." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: W. Edwards, Professor Directing Paper. / Includes bibliographical references (leaf 33).

The purpose of the current study was to test the theory of action hypothesized for the Mathematics Formative Assessment System (MFAS) based on results from a large-scale randomized field trial. Using a multilevel structural equation modeling analytic approach with multiple latent response variables decomposed across student, teacher, and school levels of clustering, the current study found evidence of effects of MFAS that were consistent with the MFAS theory of action. First, assignment to the treatment condition was associated with higher mean student mathematics performance and a higher prevalence of small group instruction compared to schools assigned to the control condition—both of which are outcomes hypothesized to result from MFAS use. Also, a positive association between teacher-level mathematics knowledge for teaching and student mathematics performance was found in the current study, which is consistent with the interrelation of constructs specified in the MFAS theory of action. However, evidence of the particular linkages of MFAS use→teacher knowledge→classroom practice→student mathematics performance and the putative cascade of effects that would substantiate the mechanisms of change posited in the MFAS theory of action were not detected in the current study. Thus, positive effects of MFAS on teacher and student outcomes were substantiated; however, as to how the effects of MFAS on teachers transfer to improved outcomes for students remains to be empirically demonstrated. Based on my review of the results from the current study and consideration of the literature on formative assessment as it relates to the design of MFAS tasks and rubrics, I discuss a proposed modification to the theory of action that specifies the addition of a direct path from MFAS use to student mathematics performance, in addition to the indirect path currently specified. / A Dissertation submitted to the Department of Educational Leadership and Policy Studies in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2016. / June 29, 2016. / Dynamic Assessment, Formative Assessment, Mediation Analysis, Multilevel Structural Equation Modeling, Multisite Cluster Randomized Field Trial / Includes bibliographical references. / Laura B. Lang, Professor Directing Dissertation; Barbara R. Foorman, University Representative; Carolyn D. Herrington, Committee Member; Jeffrey A. Milligan, Committee Member.

Statistically skilled workers are highly demanded in today's world, which means we need high-quality statistics education. There has been a continuously increased enrollment of statistics students. At the college level, introductory statistics courses are typically taught by professors who often hold a strong qualification in mathematics but may lack formal training in statistics education and statistical analysis. Existing literature claims that a unique way of thinking--statistical thinking or reasoning--is essential when teaching statistics, especially at the introductory level. To elaborate and expand on the issue of statistical thinking, a qualitative study was conducted on 15 mathematics teachers from a local community college to discuss differences between statistics and mathematics as academic disciplines and exemplify two types of thinking--statistical thinking and mathematical thinking--among mathematics teachers who teach college-level introductory statistics. Additionally, the study also inspected mathematics teachers' pedagogical ideas influenced by each type of thinking, some of which were recognized as "pedagogically powerful ideas" that transcend students' conceptual understanding about statistics. The study consisted of two online questionnaires and one interview. In the two online questionnaires, participants explored and rated five technology options for teaching statistics and self-evaluated their technology, pedagogy, and content knowledge. During the interview, participants solved nine statistical problems designed to elicit statistical thinking and addressed pertinent pedagogical questions related to each problem's statistical concept. A framework that hypothesizes aspects of mathematics teachers' statistical thinking and mathematical thinking in statistics was created, summarizing the prominent differences in problem-solving, variability, context, data production, transnumeration, and probabilistic thinking. Select responses from participating mathematics teachers were provided as examples of each type of thinking. Furthermore, it was revealed that mathematics teachers with a different type of thinking tended to cover different statistical topics, deliver the same statistical concept in different ways, and assess students' knowledge with different emphases and standards. This study's results have implications: if statistics is to be taught by mathematics teachers, statistical thinking is required to implement pedagogically powerful ideas for furthering meaningful statistical learning and to unveil the differences between statistics and mathematics.

The study examines the role of music in the lives and work of 20th century mathematicians within the framework of understanding the contribution of affect to mathematical thinking. The current study focuses on understanding affect and mathematical identity in the contexts of the personal, familial, communal and artistic domains, with a particular focus on musical communities. The study draws on published and archival documents and uses a multiple case study approach in analyzing six mathematicians. The study applies the constant comparative method to identify common themes across cases. The study finds that the ways the subjects are involved in music is personal, familial, communal and social, connecting them to communities of other mathematicians. The results further show that the subjects connect their involvement in music with their mathematical practices through 1) characterizing the mathematician as an artist and mathematics as an art, in particular the art of music; 2) prioritizing aesthetic criteria in their practices of mathematics; and 3) comparing themselves and other mathematicians to musicians. The results show that there is a close connection between subjects’ mathematical and musical identities. I identify eight affective elements that mathematicians display in their work in mathematics, and propose an organization of these affective elements around a view of mathematics as an art, with a particular focus on the art of music. This organization of affective elements related to mathematical thinking around the view of mathematics as an art has implications for the teaching and learning of mathematics.

This study highlighted factors informing instructors’ instructional beliefs and practices and the activities that help students engage in and develop a deep understanding of mathematics. The study also described instructors’ instructional activities and curricular practices when teaching mathematics and an interdisciplinary curriculum that integrates mathematics with other subjects. Through a qualitative phenomenological approach, surveys, semi-structured interviews, and analyses of instructional activities using an adapted version of the Teaching for Robust Understanding in Mathematics (or TRU Math©) framework characterized the experiences of 13 instructors, from elementary through college years, who taught mathematics as a subject and within an interdisciplinary lesson. The study revealed several factors that informed instructors’ beliefs, practices, and activities (B, P, & A) about teaching mathematics and interdisciplinarity through descriptions and synthesis of meanings and TRU Math analyses of artifacts. Instructors felt strongly about helping students value learning, making mathematics meaningful and joyful, and saw their students as capable problem solvers. They utilized activities to illuminate thinking and understanding of mathematics and used assessments to communicate mathematics. T he study also revealed three significant ways that instructors engaged in interdisciplinarity as seen through the practices of the Constructors, Curators, and Connectors, and referred to accordingly as the 3C’s framework. These interdisciplinary characterizations reveal instructors’ practical ways of using various approaches to practice interdisciplinarity. It also showed how frameworks like TRU Math helped assess an interdisciplinary activity’s potential to foster a deep understanding of mathematics content. The conclusions offer implications for research and practice.

We analyzed the contribution to the stimulus control in learning from the antecedents and the contingent consequences in this research. In the first experiment, we analyzed the stimulus control strengths of the preferred visual antecedent targets and prosthetic reinforcers in skill acquisition. The preferred- (PA) and non-preferred-visual-antecedent-stimuli (NA) were paired with two contingent consequences. In the conditions paired with the consequence of praise-for-correct-response (PC), researchers praised correct responses and implemented a correction procedure contingent on incorrect responses. In the conditions paired with the math-for-correct-response (MC), the procedure was the same except that a correct response was followed by presenting a non-preferred activity of doing a math problem. We measured the acquisition rates and maintenance of responses of PA and NA across the two consequence conditions. The results showed that all participants acquired the PA faster regardless of the consequence conditions. The findings suggest that the see-say correspondence of the PA may function as a stronger reinforcer in skill acquisition than the contingent consequence of prosthetic reinforcer delivered by the instructor. In the second experiment we controlled the reinforcement from the antecedent stimuli and conducted a component analysis of skill acquisition consequences. In the learn unit (LU) condition, researchers praised correct responses and implemented a correction procedure contingent on incorrect responses. In the praise-only-for-correct-responses (PC) condition, researchers delivered contingent praise for correct responses and ignored incorrect responses. In the correction-only-for-incorrect-responses (CI) condition, researchers ignored correct responses and implemented the correction procedure contingent on incorrect responses. We manipulated this independent variable across educational and abstract stimuli and measured acquisition rate, duration, and maintenance of responses. The results showed that the LU and CI conditions were both effective on teaching listener responses and were more effective than the PC procedure. The results suggested that the correction procedure was probably necessary and sufficient for skill acquisition and maintenance. Since the stimulus set sizes in the previous experiments were randomly decided, in the third experiment we conducted a systematic replication of Kodak et al.’s (2020) and Vladescu et al.’s (2021) research on the effects of stimulus set sizes on skill acquisition. We manipulated the stimulus set sizes by teaching three, six, and 12 sight words simultaneously during learn unit instruction. Researchers taught participants until the participant’s responding reached the acquisition criterion for 12 different sight words per set size condition. The acquisition criterion was set for an individual operant, whereby when accuracy met criterion for a single sight word, that sight word was replaced in the following session. The results showed that the set-size-three was more efficient than the set-size-six and -twelve in acquisition, which were more consistent with Vladescu et al.’s findings, but not consistent with Kodak et al.’s findings. However, the set-size-twelve reliably produced the highest maintenance levels for all participants. The opposing acquisition and maintenance results suggest further discussion on the definition of “effectiveness” in learning. To sum up, the results of these studies demonstrated that the strengths of stimulus control were a function of the synergistic reinforcement strengths across multiple correspondences of motivating operations, discriminative stimuli, and the contingent consequences.