This thesis describes a research study that investigated the relationships between school level environment and student outcomes. The study involved 620 teachers and 4645 students from 57 Australian secondary schools in all states and territories. Student outcome measures included mathematics achievement, attitudes and beliefs toward mathematics and were collected as part of the Third International Mathematics and Science Study. Teachers perceptions of their school environment were measured using the School Level Environment Questionnaire and included variables such as student support, affiliation, professional interest, mission consensus, empowerment, innovation, resource adequacy and work pressure. Previous research has shown that factors at the school level, like environment, influence education at the classroom level and to further investigate this, data regarding the instructional practices of teachers was included in the analysis. The unique methodology used to investigate influences on student mathematics achievement is also described in this thesis. A two-step approach to modelling consisted of the analysis of two conceptually distinct models. The first was an analysis of the measurement model, which specifies the relationships between the observed variables and the latent variables. The second involved a structural equation model, which specifies the relationships among the latent variables as posited by theory and previous research. In addition, a multilevel analysis was included to further partition the variance in student outcomes between the student level, the classroom level and the school level. The results of these analysis linked particular variables of interest to improved student outcomes. / For example, teachers who felt supported and empowered were more likely to employ student-centred instructional practices and that work pressure and resource adequacy influenced the instructional approaches in the classrooms. The success attribution of students determined which method of instruction promoted positive outcomes. Furthermore, these results indicate relationships between student outcomes, attitudes and achievement, and the relationships between attitude and achievement were recursive with influences from student background variables. The multilevel analysis demonstrated the importance of the influence of factors at the classroom level in influencing student outcomes and highlighted factors at the school level that explained differences in achievement. The significance of this study is in the provision of evidence that demonstrates the effects on student outcomes and not only supports, but significantly adds to previous research. This thesis provides practical implications for teaching and for school policy that can be implemented to promote positive student outcomes. The thesis also provides a rationale for further research that would involve an investigation of the effects of change as suggested from the results of these analysis reported from this study.

The new South African national curriculum for the twenty first century adopted an outcomes-based education approach. The new curriculum represents a crucial shift in emphasis from learners concentrating on formal and procedural mathematics (with an absence of meaning) to learners making meaning of mathematics and becoming flexible mathematical thinkers, with problem solving and mathematics investigations as central focus. This study reports on an action research collaboration between two teachers and myself, a university mathematics educator. It was conducted over a period of three years. The main purpose of our collaboration, and this thesis, was to explore mathematics teacher learning in the context of the OBE-based reforms. The data were gathered through questioning, journal keeping by the two teachers and my participant observations. Using the two teachers’ reflective writings and field notes I analysed the data in two stages - narrative analysis and analysis of narratives. What emerged from the study were several issues clustered around three characteristics of teacher learning - teacher learning as situated, teacher learning as social and teacher learning as distributed. These three overlapping characteristics of teacher learning were used as heuristic devices or convenient organisers for the description, analysis and discussion of the issues that emerged. This study revealed several overarching propositions that may have applicability beyond its boundaries. The first proposition is that teachers reflect on and revise their personal practical knowledge if exposed to learning experiences that encourage them to attach meaning to and make sense of the underlying concepts of new curriculum reforms. The second proposition is that interactions with literature improve the quality of teacher learning. / The third proposition is that teachers are motivated to experiment with new ideas if they observe these ideas being modelled in practice. The fourth proposition is that teachers develop positive perceptions about learning if the expectations of multiple stakeholders (both in their classrooms and beyond the classrooms) are not contradictory. The fifth proposition is that teachers’ listening to learners’ thinking opens opportunities for explorations. The sixth proposition is that I teachers respond to learners’ learning by being more curious about classroom discussions. The seventh proposition is that teachers who play an active role in collaborative working relationships are more likely to revise their pedagogy. The eighth proposition is that true collaborative relationships take time. The last proposition is teachers who are supported are more likely to distribute their knowledge and learning. Some implications of this study are also highlighted in the last chapter.

Teaching a subject requires a teacher to understand its language, epistemology and traditions, and how these characteristics govern what is appropriate for teaching and learning. This research examines how teachers' experiences of mathematics and science subject cultures, including traditions of practice, beliefs, and basic assumptions, influence their secondary school mathematics and science teaching. Six teachers from two secondary schools were interviewed and their classroom practice observed over a period of eighteen months. The research involved observing and video recording teachers' mathematics and science lessons, then interviewing them about their practice, their views of school mathematics and science, and how they see themselves in relation to these subjects. Four themes emerged which highlight similarities and differences between the subject cultures of mathematics and science: the nature of curriculum organisation across the two subjects; the role of learning experientially through hands-on experiences; the translation of 'relevance' as a school culture imperative into teachers' conceptions of, and practices in, the subject; and the role of aesthetic understanding in how teachers experience, situate themselves within, and negotiate boundaries between the two subject cultures. Significant cultural and individual differences were found in what teachers considered to be at the core of their subject teaching. Cultural differences make the subject identifiably mathematics or science. In mathematics, supporting students to move through sequentially organised curriculum content, and the importance placed on mathematics in the school curriculum, led to a Pedagogy of Support. In science, the more topic-based curriculum, and an imperative to foster student interest in science, led to a Pedagogy of Engagement. A school culture imperative to link the subject matter to students' lives was translated differently in mathematics and science. Individual differences between teachers resulted in a diversity of practices across and within the two schools, particularly with respect to how teachers related practical work to theory. The two schools' different approaches to open-ended problem solving resulted in varying degrees of latitude for teachers to move away from traditional teaching modes. In addition, whether or not teachers had stories to tell that related the subject matter to students' lives influenced their approach to making the subject relevant. Teachers' passions, coherence in their understanding of content and pedagogy, and their identity, were shown to be integral to the way they positioned themselves in relation to the subject, and in shaping their confidence and competence. Teachers experienced different traditions within the subject cultures. Some traditions perpetuated practices that might be considered 'outdated'. Emerging traditions challenged current practices through innovation and new ways of thinking about teaching and learning. Local traditions developed within the school as expectations for practice. Teachers experienced these different traditions in the process of moving forward from basic assumptions that they saw as characterising the subject, while translating school culture imperatives, and as they developed a sense of self in relation to the subject. The significance of this research lies in its contribution to improved understanding of the demands associated with subject teaching. Findings relating to the demands associated with negotiating subject boundaries have implications for the support of teachers who are teaching 'out-of-field'. In addition, teachers' experiences of the demands associated with translating school culture imperatives into their subject teaching raise questions about the usefulness of generic descriptions of pedagogy. These findings indicate that teacher and school change processes can be informed by describing subject and individual pedagogies.

<p>Mitt syfte med det här arbetet var att undersöka en grupp gymnasieelevers tankar kring sin inlärningssituation i matematik och se under vilka förutsättningar de själva tror att de lär sig bäst. Studien genomfördes med hjälp av 175 enkäter som delades ut på en gymnasieskola i Västergötland. De svarande tillhörde olika program och olika årskurser, och enkäten hade dels frågor med fasta svarsalternativ och dels några ganska öppna frågor. Resultatet kan sammanfattas med bland annat:</p><p>- att de flesta elever tror att det är viktigt att öva många gånger på samma sorts uppgifter i matematik; framför allt flickornas svar betonar detta.</p><p>- att det finns en svag positiv korrelation mellan använd tid till läxläsning i matematik och betyg i matematik även om kausaliteten är oklar.</p><p>- att det finns en stark önskan hos många elever om förståelse av matematikstoffet.</p> / <p>My aim in with this work was to examine a group of students at a secondary school and their thoughts about the teaching context in mathematics, and to see under which circumstances they self believe they learn the best. The study was accomplished with the help of 175 questionnaires, which were given to students of an upper secondary school in Västergötland. The respondents represent different categories of studies and different levels, and the questionnaire included both questions with fixed answer alternatives and a few quite open questions. The result of the survey can be summarized with:</p><p>- that most students thinks that it is necessary to exercise many times with the same type of assignments in mathematics; above all the girls’ responses emphasized this.</p><p>- that there is a slightly positive correlation between time spent on homework in mathematics and the grade in mathematics, even if the way of causality is unclear.</p><p>- that there is a strong wish among many students to understand the mathematic topic.</p>

Mathematics is much more than the manipulation of numbers. At its best, it involves simple, clear examples of thought so apt to the world we live in that those examples provide guidance for our thinking about problems we meet subsequently. We call such examples, capable of heuristic use, POWERFUL IDEAS, after Papert (1980). This article documents a child's introduction to a specific powerful idea in a computer environment. We trace his extensions of that idea to other problem areas, the first similar to his initial experience and the second more remote from it.

Thesis (Ph. D.)--Oregon State University, 1985. / Typescript (photocopy). Includes bibliographical references (leaves 151-155). Also available online.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Printout. Vita. Includes bibliographical references (leaves 275-281) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph. D.) -- University of Tennessee, Knoxville, 2006. / Title from title page screen (viewed on Feb. 2, 2007). Thesis advisor: Vena M. Long. Vita. Includes bibliographical references.

Reforms 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.

Mitt syfte med det här arbetet var att undersöka en grupp gymnasieelevers tankar kring sin inlärningssituation i matematik och se under vilka förutsättningar de själva tror att de lär sig bäst. Studien genomfördes med hjälp av 175 enkäter som delades ut på en gymnasieskola i Västergötland. De svarande tillhörde olika program och olika årskurser, och enkäten hade dels frågor med fasta svarsalternativ och dels några ganska öppna frågor. Resultatet kan sammanfattas med bland annat: - att de flesta elever tror att det är viktigt att öva många gånger på samma sorts uppgifter i matematik; framför allt flickornas svar betonar detta. - att det finns en svag positiv korrelation mellan använd tid till läxläsning i matematik och betyg i matematik även om kausaliteten är oklar. - att det finns en stark önskan hos många elever om förståelse av matematikstoffet. / My aim in with this work was to examine a group of students at a secondary school and their thoughts about the teaching context in mathematics, and to see under which circumstances they self believe they learn the best. The study was accomplished with the help of 175 questionnaires, which were given to students of an upper secondary school in Västergötland. The respondents represent different categories of studies and different levels, and the questionnaire included both questions with fixed answer alternatives and a few quite open questions. The result of the survey can be summarized with: - that most students thinks that it is necessary to exercise many times with the same type of assignments in mathematics; above all the girls’ responses emphasized this. - that there is a slightly positive correlation between time spent on homework in mathematics and the grade in mathematics, even if the way of causality is unclear. - that there is a strong wish among many students to understand the mathematic topic.