Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

Effects of age on learning a spatial motor task in younger and older adults individualizing their knowledge of results schedule

Self-controlled KR practice has revealed that providing participants the opportunity to control their KR is superior for motor learning compared to participants replicating the KR schedule of a self-control participant, without the choice (e.g., yoked). The purpose of the present experiment was two-fold. First, to examine the utility of a self-controlled KR schedule for learning a spatial motor task in younger and older adults and second, to determine whether a self-controlled KR schedule facilitates an increased ability to estimate one’s performance in retention and transfer. Twenty younger adults and 20 older adults practiced in either the self-control or yoked condition and were required to push and release a slide along a confined pathway using their non-dominant hand to a target distance. The retention data revealed that as a function of age, a self-controlled KR schedule facilitated superior retention performance and performance estimations in younger adults compared to their yoked counterparts.

Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

Experiencing Manipulative Material for the Teaching and Learning of Mathematics

This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.

Building Leadership: The Knowledge of Principals in Creating Collaborative Communities of Professional Learning

Research literature is replete with the importance of collaboration in schools, the lack of its implementation, the centrality of the role of the principal, and the existence of a gap between knowledge and practice--or a "Knowing-Doing Gap." In other words, there is a set of knowledge that principals must know in order to create a collaborative workplace environment for teachers. This study sought to describe what high school principals know about creating such a culture of collaboration. The researcher combed journal articles, studies and professional literature in order to identify what principals must know in order to create a culture of collaboration. The result was ten elements of principal knowledge: Staff involvement in important decisions, Charismatic leadership not being necessary for success, Effective elements of teacher teams, Administrator‘s modeling professional learning, The allocation of resources, Staff meetings focused on student learning, Elements of continuous improvement, and Principles of Adult Learning, Student Learning and Change. From these ten elements, the researcher developed a web-based survey intended to measure nine of those elements (Charismatic leadership was excluded). Principals of accredited high schools in the state of Nebraska were invited to participate in this survey, as high schools are well-known for the isolation that teachers experience--particularly as a result of departmentalization. The results indicate that principals have knowledge of eight of the nine measured elements. The one that they lacked an understanding of was Principles of Student Learning. Given these two findings of what principals do and do not know, the researcher recommends that professional organizations, intermediate service agencies and district-level support staff engage in systematic and systemic initiatives to increase the knowledge of principals in the element of lacking knowledge. Further, given that eight of the nine elements are understood by principals, it would be wise to examine reasons for the implementation gap (Knowing-Doing Gap) and how to overcome it.

The art of drawing in perspective : made easy to those who have no previous knowledge of the mathematics /

Mode of access: Internet.

The role of the learning community in the development of discipline knowledge and generic graduate outcomes

In this paper we describe a study of learning outcomes at a research-intensive Australian university. Three graduate outcome variables (discipline knowledge and skills, communication and problem solving, and ethical and social sensitivity) are analysed separately using OLS regression and comparisons are made of the patterns of unique contributions from four independent variables (the CEQ Good Teaching and Learning Communities Scales, and two new, independent, scales for measuring Teaching and Program Quality). Further comparisons of these patterns are made across the Schools of the university. Results support the view that teaching and program quality are not the only important determinants of students' learning outcomes. It is concluded that, whilst it continues to be appropriate for universities to be concerned with the quality of their teaching and programs, the interactive, social and collaborative aspects of students' learning experiences, captured in the notion of the Learning Community, are also very important determinants of graduate outcomes, and so should be included in the focus of attempts at enhancing the quality of student learning.