The problem with which this investigation was concerned is that of determining whether remedial mathematics students who receive individualized attention in small groups with many special materials would gain more knowledge in the areas of computation, concepts, problem solving, and total composite mathematics than would remedial mathematics students taught as sub-groups of regular mathematics classes.

<p> This quantitative research study investigates South Dakota middle school (grades 5-8) mathematics teachers&rsquo; perceptions of teaching competencies including general pedagogical knowledge (GPK) and mathematical pedagogical content knowledge (MPCK). The study also considered how teacher characteristics relate to teacher competencies. The study examined middle school teacher perceptions because of the importance of the mathematics concepts being taught. Teacher participants completed a voluntary 50 question electronic survey within a three-week time period. Data analysis findings include descriptive and inferential statistics on GPK, MPCK, professional development, and teacher characteristics. Respondents perceived maintaining a safe and respectful classroom to be the most important item for GPK. Respondents perceived having an adequate knowledge of mathematics to be the most important item for MPCK. Overall, GPK was perceived as more important than MPCK regardless of teacher characteristics studied. Respondents perceived professional development in the area of mathematics and mathematics education to be most important to middle school mathematics teachers. However, respondents reported that professional development was rarely provided to teachers with the exception of self-directed learning. The aim of this study was to provide current and future middle school mathematics teachers and their evaluators with a summary of how the importance of pedagogical knowledge can inform mathematics teacher practice, evaluation, and professional development.</p><p>

Please read the abstract (Summary) in the section 00front of this document / Dissertation (MSc (Mathematics Education))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted

Few terms in organisational studies inspire less agreement than leadership. It is a slippery concept and much that is written on the subject is confusing and contradictory. Early theories of leadership have, generally, reduced leadership behaviour to a concern for task balanced against a concern for the well-being of employees. This two-dimensional approach has proved to be a limited conceptualisation of leadership. In response, over the past thirty years, researchers have tried to highlight the less rationalistic, more intangible, aspects of leadership. However, there is still very little in leadership research that conveys a sense of the leader as a person. I have argued, in this study, that the reason for this lies in the fact that most leadership research has been conducted along positivistic lines and, therefore, cannot take into account the values, feelings, morals and life experiences of the human beings being studied. Thus, for the human being to take centre-stage in leadership enquiry, a different research paradigm needs to be explored. I have chosen to use phenomenological enquiry as an avenue for examining how John Stoker, the leader of the Rhodes University Mathematics Education Project (RUMEP), experiences being a leader. This is because phenomenology, in both theory and practice, privileges the nature of the meanings that people construct in their lives and that guide their actions. In adopting such a methodology my research findings have examined a number of issues that are of interest to current leadership researchers, however they have also highlighted a number of concerns that have not been explored thoroughly in the leadership literature. These include the importance of the individual leader’s action, intention and will in shaping an organisation, the complex nature of a leader’s creativity within the organisation and possible differences between educational leaders and business leaders. In adopting a phenomenological perspective the eccentricity and fulness of an individual leader’s action is expressed through the research, however, the research also focusses on how the researcher translates and evolving philosophical understanding into sound methodology. Therefore, interwoven into the discussions on leadership there are reflections on how I applied phenomenological theory. The purpose of these reflections is to deliberate on the appropriateness of applying such a methodology to the eclectic field of leadership and to show how my own developing philosophical attitude has transformed into practice.

<p> The sixth grade is very important for education stakeholders, as it marks the beginning of the transition period for students to high school. No consensus has been reached so far among scholars on whether block scheduling is the best way to provide students the time that is necessary to facilitate effective learning and the retention of knowledge. </p><p> The purpose of this quasi causal-comparative, ex-post facto study was to determine the effectiveness of block scheduling in improving the mathematical performance of sixth-grade students by using data from a selective Nebraska public school system regarding the performance of its sixth-grade students on their state assessment evaluation scores in traditional and nontraditional schedules. The researcher analyzed the results of a mathematics assessment from one school in the Nebraska public school system, using data from learners at the sixth-grade level as the specific purposeful sample. The results indicated that there were no significant differences found in student mathematical proficiency scores for each type of scheduling. This suggests that the type of scheduling of mathematics courses does not influence a student&rsquo;s mathematical achievement. This conclusion also held true when comparing the students of various races, free or reduced lunch status, and genders. Due to limitations including missing data and an intermittent block schedule, the researcher cannot conclude that block scheduling improves academic performance; further studies are recommended. </p><p>

<p> This study focused on student achievement in remedial math through online and traditional delivery modes at Northwest Mississippi Community College. Student participants were interviewed through a semi-structured interview process to determine perceived influences and challenges that affected success in remedial math courses. The perceived influences and challenges that emerged from interview data were used to comparatively analyze online and traditional classroom modality of instruction. The acquired interview data provided for a systematic process to determine if there was a significant difference in student achievement in remedial math based on modality of instruction. A grounded theory methodology was used as a construct for this comparative study. </p><p> The population for consideration was freshmen and sophomore students who attempted a remedial math course online and/or in a traditional classroom format. Participants were interviewed in a face-to-face setting. The study was guided by two research questions: 1.) what are the perceived influences that aided in your academic success in remedial math taken online or in a traditional classroom format at Northwest Mississippi Community College? 2.) What are the challenges that hindered your academic success in remedial math courses online or in traditional classroom format at Northwest Mississippi Community College? </p><p> According to the perceptions of the participants in the study, there was no significant difference in student achievement in remedial math online compared with traditional classroom instruction based on influences that aided in success. Furthermore, there was not a significant difference in challenges that hindered academic success among students who attempted remedial math online and in the traditional classroom.</p><p>

<p> Students in the United States have historically struggled with mathematics, especially with problems that require higher-order thinking Even struggling students, however, often show considerable interest in the arts. Unfortunately, the literature sheds almost no light on how the arts might be useful in helping students become proficient in rigorous mathematics.</p><p> I created <i>Beautiful, Beautiful Math (BBM)</i> to both intrigue students and require them to use higher-order thinking In <i>BBM</i> lessons, students interact with an object of art in order to learn mathematics. </p><p> My overarching research question was: "How can objects of art be used as effective catalysts for higher-order thinking in mathematics lessons?" In this study, "higher-order mathematical thinking" was operationally defined as having students actively engaged, working and talking together, on math tasks that require high levels of Webb's Depth of Knowledge. Three research sub-questions informed this study: 1. What do exemplary <i>Beautiful, Beautiful Math (BBM)</i> lessons look like? 2. To what extent do <i> BBM</i> lessons result in students' higher-order thinking in mathematics? 3. What are key design features and other implementation factors that need to be in place for BBM lessons to have the desired outcomes?</p><p> A constructivist learning philosophy coupled with recent cognitive psychology research informed my study. Using an action research methodology, three teachers participated in two cycles of creating <i>BBM</i> lessons. I collected eight sources of data: The Performance Assessment for Quality Teaching (PAQT) scores for each lesson, including a baseline lessons and two <i>BBM</i> lessons for each participant; video recordings of the <i>BBM</i> lesson implementations; lesson plans; audio recordings of planning sessions; audio recordings of post-lesson debriefs; audio recordings of my post-study interviews with the participants; student survey responses; and my researcher's journal. I then created tables of the PAQT scores merged with the lesson plans, which helped me search for patterns among the different lessons. Additionally, I wrote narratives of each teacher's experiences with <i>BBM</i>, which became a rich source of information.</p><p> Results show that <i>BBM</i> lessons increased higher-order thinking across all three teachers when compared with their "typical" baseline lesson. The cognitive rigor of the mathematical tasks showed especially strong growth. Additionally, students were highly engaged and active in mathematical discourse. Those <i>BBM</i> lessons determined to be "exemplary," based on their extremely high PAQT scores, had several important design features in common, including strong integration between the work of art and the mathematics content, the use of Visual Thinking Strategy questions, and a cycle of problem solving. Inquiry-based pedagogical practices and the culture and climate of the classroom and school were found to be additional keys to the success of <i> BBM</i> lessons.</p><p> Products from this study include: a set of instructions that will allow other teachers to create <i>BBM</i> lessons; a <i>BBM</i> workshop that I facilitated at the local art museum for math and art teachers from around our county; a collection of twelve <i>BBM</i> lessons for the museum's library and website; and collaboration between one of the teachers and myself to design a workshop for a fall NCTM conference.</p>

This study investigates relationships between gender and achievement as well as gender and attitudes in a computer-integrated first year college mainstream calculus course in comparison with a similar non-computer-integrated course. The investigator analyzed data from pilot and experimental studies conducted at the University of Connecticut at Storrs in 1989-1993 and 1993-1994, respectively, in order to compare the calculus courses with respect to student achievement and attitudes with a focus on gender. Both quantitative and qualitative methods were employed. Quantitative research instruments included common final examination scores and an attitude questionnaire; data were analyzed by ANOVA/ANCOVA and Chi-Square. Students were also interviewed to gain insights into their attitudes about their calculus course experience. The samples sizes of the experimental and control groups, respectively, were as follows for each analysis: common final examination score, Fall 1989 (25, 19), Spring 1990 (30, 26), Fall 1993 (102, 107), Spring 1994 (46, 84); the 1989-1993 study of number of subsequent courses (for which calculus is a prerequisite) and achievement in those courses, (54, 42); the 1993-1994 attitude survey, (93, 70); and interviews, (21, 19). Results of the achievement study indicated that students in the computer-integrated course performed significantly better on the common final exam in Fall 1993 and suggested that female students in the computer-integrated calculus course benefited more than any other subgroup. In the 1989-1993 pilot study, there was a significantly higher mean number of subsequent courses taken by male students than by female students; however, female students' mean average grades in subsequent courses were significantly higher than mean average grades of male students. The results of the attitude survey and interviews indicated that the students in the experimental group tended to use calculators and computers more often for solving problems. Furthermore, the study revealed that the majority of respondents enjoy solving mathematics problems and believe that: calculus is useful and can be applied to real world problems; there is more than one way to solve a problem; and gender does not affect a person's potential to be a scientist or an engineer. Overall, results of the investigation suggest that a computer-integrated calculus course is effective in the teaching of calculus. Recommendations and suggestions for future research are offered.

This research study was motivated by a hypothesis, generated on the basis of formal and informal observations, personal and professional experiences, discussions with prospective teachers and a pilot study conducted by this author; that pre-service teachers have a high level of mathematics anxiety and negative attitudes about mathematics. The primary purpose of this research was to examine the relationship between mathematics anxiety and pre-service teachers. The secondary purposes of this study were to examine the relationship between anxiety and performance and to examine the relationship between math anxiety, test anxiety, and stereotype threat. A quantitative experimental research design was used to investigate the research questions. The population consisted of prospective teachers at colleges and universities in Louisiana. The sets of data are mathematics anxiety of prospective teachers, a test anxiety inventory and a mathematics performance task. A personal data questionnaire was used to gather demographic information and attitudinal information about the participants. The implications of this study for elementary teacher education programs point to increased attention on the mathematics anxiety of pre-service teachers. This process is two-fold. One, it is recommended that pre-service teachers be made aware of their mathematics anxiety level and their attitudes about mathematics and two, it is recommended that teacher education programs acknowledge and address the importance of these affective variables and their role in pedagogy.

This dissertation presents results of a formative evaluation of AnimalWatch, an intelligent tutoring software system for 9–12 year-olds, which teaches whole numbers and fractions by adapting the difficulty of problems to students' performance. Results come from a macro-analysis of 350 students using AnimalWatch in two different schools during three years. Data from these studies were integrated to analyze the system's overall effectiveness, as well as gender and cognitive development differences in interactions with the system, particularly in relation to the help component. In general, it was found that students reduced their mistakes as they progressed in the tutoring session, and improved their attitudes towards mathematics after using the system. However, a rigorous study of the internal components of AnimalWatch showed that the system can be further improved to maximize its positive impact. Students saw too many easy problems, and this may explain the fact that they hardly reached the last topics in the system. In addition, students benefited differently from alternative kinds of feedback provided, depending on the level of abstraction within the help component and the amount of help. An analysis of help effectiveness for students of different gender and cognitive development showed that girls were more sensitive to amount and structure of help than to level of abstraction in the provided help. On the other hand, boys of low cognitive development were affected by level of abstraction in the help. While boys were being selective about the kinds of help they were willing to see, girls would obediently go through each of the hints provided.