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Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits and limitations. In this paper, I examine prototypes in a context in which they seem to play an important role: graphical representations of the calculus concept of the definite integral. I use student data to empirically describe the makeup of the definite integral prototype image, and I report on the frequency of its appearance among student, instructor, and textbook image data. I end by discussing the possible benefits and drawbacks of this particular prototype, as well as what the results of this study may say about prototypes more generally. [ABSTRACT FROM AUTHOR]

Technology is available and accessible in many mathematics classrooms. Adopting technology to support teaching and learning requires teachers to change their teaching practices. This paper reports the responses of a diverse cohort of 92 secondary mathematics teachers who chose to respond to an Australian state-wide survey (Mathematics with Technology Perceptions Survey) developed using a Theory of Planned Behaviour framework. The items discussed in this paper targeted mathematics teachers’ perceptions of possible barriers and enablers to their intention to use technology in their teaching. The responses are varied but, overall, strength of agreement with enablers outweighed agreement with perceived barriers. However, it is clear that despite an overall positive attitude towards the use of technology for teaching mathematics, some perceived barriers to change are notable. It is, therefore, helpful if those responsible for professional development, promoting the use of technology, recognise and address these barriers as well as working to strengthening enablers. [ABSTRACT FROM AUTHOR]

This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education conference proceedings. Some regional sources from various parts of the world were also included. We investigated who was writing, from and in what settings, with what theoretical frameworks, and with what sorts of study designs for what core questions. We also examined the range of findings and conclusions produced in these studies. Our analysis presented here focuses on four themes that stood out from our initial investigation of almost 300 published papers, and systematically elaborated through a focused study of a 160 papers across key journals and conference proceedings in the field. From this vantage point, the paper offers a reflection on the current state of the field of mathematics teacher education research. Our aim is to stimulate discussion that can support the development of the field, not make final pronouncements about its nature. [ABSTRACT FROM AUTHOR]

This paper examines the contribution of quality mathematics teaching to student achievement gains. Quality of mathematics teaching is assessed through teacher demonstration of the five strands of mathematical proficiency, the level of cognitive task demands, and teacher mathematical knowledge. Data is based on 1907 grade 6 students who sat for the same test twice over an interval of about 10 months. The students were drawn from a random selection of 72 low- and high-performing primary schools. Multi-level regression shows the effects of quality mathematics teaching at both individual and school levels, while controlling for other variables that influence achievement. Results show that students in low-performing schools gained more by 6 % when mathematics instruction involved high-level cognitive task demands, with two thirds of all the lessons observed demonstrating the strands of mathematics proficiency during instruction. The implication to education is that quality of mathematics instruction is more critical in improving learning gains among low-performing students. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explore middle school in-service mathematics teachers' ability (1) to identify and explain students' actions in pattern generalization and (2) to account for the variation in teachers' explanations of students' actions in terms of task and teachers' factors. Two questionnaires were developed: (1) a questionnaire to measure teachers' ability to identify students' actions while finding the nth term in the pattern generalization and (2) a questionnaire to measure teachers' ability to explain students' actions in different tasks. The two questionnaires were given to a sample of 83 middle school in-service mathematics teachers from 22 schools in Lebanon. Analysis of data shows that teachers seemed to have the ability to identify students' actions while finding the nth term in the pattern generalization and that teachers' explanations of students' actions in different tasks are lacking in terms of identifying variable-related counting elements. The results of stepwise multiple regression show that teachers' ability to explain students' actions to find the general term depends on their ability to explain students' step-by-step counting or drawing. [ABSTRACT FROM AUTHOR]

This paper (1) presents a conceptual framework for analyzing the mathematics addressed in probability lessons and (2) uses the framework to compare the mathematics that two teachers with contrasting teaching approaches addressed in class when teaching the topic of probability. One teaching approach aimed to develop understanding; the other emphasized mechanistic answer finding. Class work on 193 problems was analyzed qualitatively and quantitatively, showing some similarities and some differences in the mathematics that the two teachers offered to students. The differences found seemed to be linked to the teachers’ teaching approaches. The findings suggest that teachers who adopt different teaching approaches, to some extent, make available to learn different mathematics even when they use the same textbooks. [ABSTRACT FROM AUTHOR]

This paper describes the experience of a group of 17 prospective mathematics teachers who were engaged in a series of activities aimed at developing their awareness of creativity in mathematics. This experience was initiated on the basis of ideas proposed by the participants regarding ways creativity of school students might be developed. Over a period of 6 weeks, they were engaged in inventing geometrical concepts and in the examination of their properties. The prospective teachers’ reflections upon the process they underwent indicate that they developed awareness of various aspects of creativity while deepening their mathematical and didactical knowledge. [ABSTRACT FROM AUTHOR]

There is an increasing awareness of the social dimension in mathematics teacher education. Collaboration and co-operation are regarded as key factors in professional development. In this paper I will analyse some tensions that might arise when the professional development of mathematics teachers is considered a collective enterprise. I will present phenomenological group interview as a method that is designed to reveal the collective character of teacher development. Some primary teachers’ collective reflections on an ongoing professional development process will be interpreted by focusing on the concepts of routine and collective orientation. The discussion is centred on the ambivalence of routines, as facilitators of practice, and collective orientations, as socially-agreed-upon knowledge base, for mathematics teachers’ professional development. [ABSTRACT FROM AUTHOR]

This paper outlines some theoretical categories (i.e. the meso-, topo-, chrono- geneses, the “milieu”, the didactical contract and the learning games), providing a model to study mathematics teacher’s action. In order to show what this model brings to the didactical analysis, we present the action of two teachers, on the same content, and we attempt a threefold description, covering different scales of analyses of the teaching processes. To amplify the phenomena that are to be observed, we suggested the teachers include the “Race to 20” situation in their teaching. We expect that implementing an unusual teaching device should lead the teachers to take decisions and explain them more easily than in everyday lessons. [ABSTRACT FROM AUTHOR]

In research on teachers’ beliefs, a distinction is often made between what teachers state (“professed beliefs”) and what is reflected in teachers’ practices (“attributed beliefs”). Researchers claim to have found both consistencies and inconsistencies between professed and attributed beliefs. In this paper, methods and research designs typically used in studies of teachers’ beliefs are examined. It is asserted that, in some cases, the perceived discrepancy between professed and attributed beliefs may actually be an artifact of the methods used to collect and analyze relevant data and the particular conceptualizations of beliefs implicit in the research designs. In particular, the apparent dichotomy can be the result of a lack of shared understanding between teachers and researchers of the meaning of terms used to describe beliefs and practices. In addition, it is asserted that it is inappropriate to classify any belief as entirely professed since researchers make various attributions to teachers through choices about data collection, theory, analysis of data, and presentation of findings. Moreover, the emphasis on classifying beliefs in this manner may be inhibiting researchers from developing a more comprehensive understanding of teachers’ beliefs. Traditional and alternative methods are described, a data example is provided to illustrate the claims, and implications for future research are discussed. [ABSTRACT FROM AUTHOR]

The crisis in UK mathematics education, both in schools and universities, has been widely reported in the national media. A recent study shows that 26% of full-time mathematics teachers in UK schools have no qualification in the subject, and that 31% of all UK schools' mathematics teachers are now over the age of 50. The crisis in school mathematics has impacted on much of the university sector, with some departments under threat of closure and widespread difficulties experienced in student recruitment. The availability of attractive careers for mathematics graduates impacts upon the numbers choosing to enter teaching, thus risking a spiral of decline. Furthermore, studies suggest that UK mathematics graduates often lack confidence in several key skills essential for teaching, such as presenting information effectively, working in teams, and written communication. This paper recounts the development of a unit of study in the Faculty of Mathematical Studies at the University of Southampton, England, in conjunction with a new initiative, the Undergraduate Ambassadors Scheme, which seek to address the crisis in UK mathematics education through the training and placement of final year undergraduates as teaching assistants in local schools. This with a view to promoting mathematics to the broadest possible constituency as a university choice, whilst simultaneously developing those key transferable skills in which undergraduates regularly feel least confident, and allowing undergraduates to experience a flavour of teaching as a career option. [ABSTRACT FROM AUTHOR]

This paper offers for discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics. From this perspective, such learning occurs in many different situations -- mathematics and teacher preparation courses, pre-service field experiences, and schools of employment. By participating over time in these varied contexts, mathematics teachers refine their conceptions about their craft -- the big ideas of mathematics, mathematics-specific pedagogy, and sense of self as a mathematics teacher. This framework guides a research project that traces the learning trajectories of teachers from two reform-based teacher preparation programs into their early teaching careers. We provide two examples from this research to illustrate how this framework has helped us understand the process of learning to teach. [ABSTRACT FROM AUTHOR]