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1.
Mathematics education researchers have investigated mathematics anxiety in prospective elementary teachers. While many of these studies have focused on the bodily sensations and emotions of mathematics anxiety, particularly those felt in assessment situations, opportunities remain to investigate how prospective elementary teachers interpret their experiences with mathematics anxiety and connect them over time to compose personal histories of mathematics anxiety. Currently, over 90 % of elementary teachers in US schools are women, and women have been shown to suffer more from mathematics anxiety than do men. In this article, I analyze how one woman prospective elementary teacher described, explained, and related her experiences of mathematics anxiety across her personal narratives of learning mathematics as a K-12 student and of learning to teach mathematics as a college student in a teacher preparation program. My research demonstrates that experiences of mathematics anxiety may persist beyond assessment situations to influence women prospective elementary teachers’ larger mathematical histories. I also show that women prospective elementary teachers may interpret mathematics anxiety as specific fears (e.g., loss of opportunities for social participation) and may develop particular coping strategies related to those fears. Finally, I point out that while a coping strategy may be used consistently across K-12 mathematics learning and undergraduate teacher preparation, and may even offer a woman prospective elementary teacher some relief from mathematics anxiety, it may also limit her mathematics learning and professional development. To conclude, I present implications of my research for mathematics teacher educators.  相似文献   

2.
A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers’ mathematical and pedagogical knowledge. The analysis of teachers’ reflections on their learning explored teachers’ understanding of mathematical connections and their appreciation of mathematical structure. The findings indicate that a professional learning program about senior secondary mathematics can enable practicing teachers to deepen and broaden their knowledge for teaching junior secondary mathematics and develop their practice to support their students’ present and future learning of mathematics. Further research is needed about professional learning approaches and tasks that may enable teachers to imbed and develop awareness of structure in their practice.  相似文献   

3.
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical modeling is treated more as a venue for learning other mathematics than as an instructional goal in its own right. From this perspective, we are compelled to ask how learning of mathematics beyond modeling may occur as students generate and validate mathematical models. We consider a diagrammatic model of mathematical modeling as a process that allows us to identify how mathematical understandings may develop or surface while learners engage in modeling tasks. Through examples from prospective teachers' mathematical modeling work, we illustrate how our diagrammatic model serves as a tool to unpack the intricacies of students’ mathematical experience while engaging in modeling tasks.  相似文献   

4.
Recent applications of technology to mathematics education have been designed with cognitive and constructivist theoretical perspectives in mind, viewing mathematical learning as the acquisition of knowledge through the construction of meanings and connections between concepts. With the advent of increasingly flexible communication technologies, there is both the need and opportunity to consider how they might be utilised, particularly since emergent socio-cultural theories advocate learning in mathematics as an inherently social activity where understanding is developed and negotiated collaboratively. The need to examine effective technology-facilitated learning arose in the context of a research project, currently underway in a number of secondary schools in the state of Victoria and funded by the Australian Research Council. It is investigating the learning needs of pupils who are absent from school for prolonged or intermittent periods owing to chronic illness yet continue with their school studies. An emerging understanding of the significant difference between computer-mediated contact for mere information exchange and communication for teaching and learning has led to a consideration of socio-cultural perspectives on effective mathematical learning and a focussed investigation of technologies able to facilitate them. Early data have demonstrated the potential of videoconferencing, online whiteboarding and interactive whiteboard application sharing, but which require particular resources, aligned infrastructure and teacher support. This article explores issues surrounding the use of such technologies for collaborative mathematical learning in a context where online interaction is being considered for the learning support of pupils unable to attend school.  相似文献   

5.
Students’ concerns about mathematics can significantly affect their ability to learn the subject. In particular, their anxieties and attitudes can greatly affect how they perceive their own mathematical competence, and in return, this may make them reluctant to pursue mathematical studies. Many researchers believe in the role of active learning environments in reshaping students’ perception of and emotions about mathematics. This paper reports the results of an investigation on the effect of one such environment. As a result of being exposed to an active learning environment, a group of 21 cohort students showed opinion changes from a pre- to post-survey statements significantly on emotion and noticeably on confidence and perception statements. There was, however, no statistically significant change observed on the opinions of a group of 41 traditional students.  相似文献   

6.
The use of the history of mathematics in teaching has long been considered a tool for enriching students’ mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of research conducted over four semesters in which I sought to characterize what prospective mathematics teachers (PMTs) understand about the topics that they will be called upon to teach in the future and how that teaching might include an historical component. In particular, I focus on how the study and application of the history of solving quadratic equations illuminates what PMTs know (or do not know) about this essential secondary school algebraic topic. Additionally, I discuss how the results signal important considerations for mathematics teacher preparation programs with regard to connecting PMTs' mathematical and pedagogical knowledge, and their ability to engage in historical perspectives to improve their own and their future students' understanding of solving quadratic equations.  相似文献   

7.
Subject matter knowledge for teaching and the case of functions   总被引：2，自引：0，他引：2  
Interest in teachers' subject matter knowledge has arisen in recent years. But most of the analysis has been general and not topic-specific. This paper shows how one may approach the question of teachers' knowledge about mathematical topics. It demonstrates the building of an analytic framework of subject matter knowledge for teaching a specific topic in mathematics and then uses the concept of function to provide an illustrative case of a paradigm for analyzing subject matter knowledge for teaching. The choice of the aspects, which form the main facets of the framework, was based on integrated knowledge from several bodies of work: the role and importance of the topic in the discipline of mathematics and in the mathematics curriculum; research and theoretical work on learning, knowledge and understanding of mathematical concepts in general and the specific topic in particular; and research and theoretical work on teachers' subject matter knowledge and its role in teaching. An application of the framework in the case of the concept of function is described and illustrated by anecdotes drawn from a study of prospective secondary teachers' knowledge and understanding of functions.Recipient of a Sir Charles Clore Post-Doctoral Fellowship.  相似文献   

8.
In this report, I examine resources and their use in school mathematics. I do so from the perspective of mathematics teacher education and with a view to the practice of school mathematics. I argue that the effectiveness of resources for mathematical learning lies in their use, that is, in the classroom teaching and learning context. The argument pivots on the concepts of school mathematics as a hybrid practice and on the transparency of resources in use. These concepts are elaborated by examples of resource use within an in-service teacher education research project in South Africa. I propose that mathematics teacher education needs to focus more attention on resources, on what they are and how they work as an extension of the teacher in school mathematics practice. In so doing, the report provides a language with which mathematics teacher educators and mathematics teachers can investigate teachers' use of resources to support mathematical learning in particular and diverse contexts. This revised version was published online in September 2006 with corrections to the Cover Date.  相似文献   

9.
ABSTRACT

This article suggests that there are important connections between design and technology and mathematics curricula and that these are not fully made in the United Kingdom National Curriculum. Using three examples, the authors show how there are real opportunities in design and technology teaching for incorporating mathematical learning, but that all too often these are lost because they are not made explicit. Again, the authors argue that too much mathematics teaching is dominated by abstract investigation rather than practical problem‐solving. They conclude by suggesting that teaching should transcend subject boundaries and be concerned with real‐life situations.  相似文献   

10.
概述了问题解决样例学习研究的进展,评述了已有样例学习理论的价值,提出了学生可以通过数学运算样例学习新的运算规则的理论解释,并用自己已有的实验研究结果论证了理论解释的科学性。认为学生可以通过精心设计好的数学运算样例并根据已知的数学运算规则顿悟或推断出新的数学运算规则。关键运算步骤的样例设计是数学运算规则样例学习的关键。根据数学运算规则的逻辑特点,可以分别采用分解法、逆运算法和解释法设计运算样例中的关键步骤,从而促进学生对新运算规则的顿悟和运用。  相似文献   

11.
In this paper, we aim to contribute to the discussion of the role of the human body and of the concrete artefacts and signs created by humankind in the constitution of meanings for mathematical practices. We argue that cognition is both embodied and situated in the activities through which it occurs and that mathematics learning involves the appropriation of practices associated with the sets of artefacts that have historically come to represent the body of knowledge we call mathematics. This process of appropriation involves a coordination of a variety of the semiotic resources??spoken and written languages, mathematical representation systems, drawings, gestures and the like??through which mathematical objects and relationships might be experienced and expressed. To highlight the connections between perceptual activities and cultural concepts in the meanings associated with this process, we concentrate on learners who do not have access to the visual field. More specifically, we present three examples of gesture use in the practices of blind mathematics students??all involving the exploration of geometrical objects and relationships. On the basis of our analysis of these examples, we argue that gestures are illustrative of imagined reenactions of previously experienced activities and that they emerge in instructional situations as embodied abstractions, serving a central role in the sense-making practices associated with the appropriation of mathematical meanings.  相似文献   

12.
Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on bite-sized learning objectives and a tendency for mathematics teachers to path-smooth their students’ learning. I argue that a reductionist mathematics pedagogy severely restricts students’ opportunities to engage in authentic mathematical thinking and deprives them of the enjoyment of solving richer, more worthwhile problems, which would forge connections across diverse areas of the subject. I attribute the rise of a reductionist mathematics pedagogy partly to an assessment-dominated curriculum and partly to a systemic de-professionalisation of teachers through a performative accountability culture in which they are constantly required to prove to non-specialist managers that they are effective. I argue that pedagogical reductionism in mathematics must be resisted in favour of a more holistic approach, in which students are able to bring a variety of mathematical knowledge and skills to bear on rich, challenging and non-routine mathematical tasks. Some principles for achieving this are outlined and some examples are given.  相似文献   

13.
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14.
Particularly in mathematics, the transition from school to university often appears to be a substantial hurdle in the individual learning biography. Differences between the characters of school mathematics and scientific university mathematics as well as different demands related to the learning cultures in both institutions are discussed as possible reasons for this phenomenon. If these assumptions hold, the transition from school to university could not be considered as a continuous mathematical learning path because it would require a realignment of students’ learning strategies. In particular, students could no longer rely on the effective use of school-related individual resources like knowledge, interest, or self-concept. Accordingly, students would face strong challenges in mathematical learning processes at the beginning of their mathematics study at university. In this contribution, we examine these assumptions by investigating the role of individual mathematical learning prerequisites of 182 first-semester university students majoring in mathematics. In line with the assumptions, our results indicate only a marginal influence of school-related mathematical resources on the study success of the first semester. In contrast, specific precursory knowledge related to scientific mathematics and students’ abilities to develop adequate learning strategies turn out as main factors for a successful transition phase. Implications for the educational practice will be discussed.  相似文献   

15.
Mathematics education research must enable adjustment to new conditions. Yet such research is often conducted within familiar conceptualisations of teaching, of learning and of mathematics. It may be necessary to express ourselves in new ways if we are to change our practices successfully, and potential changes can be understood in many alternative, sometimes conflicting, ways. The paper argues that our entrapment in specific pedagogic forms of mathematical knowledge and the styles of teaching that go with them can constrain students’ engagement with processes of cultural renewal and changes in the ways in which mathematics may be framed for new purposes, but there are some mathematical truths that survive the changing circumstances that require us to update our understandings of teaching and learning the subject. In meeting this challenge, Radford encountered a difficulty in framing notions of mathematical objectivity and truth commensurate with a cultural–historical perspective. Following Badiou, this paper distinguishes between objectivity, which is seen necessarily as a product of culturally generated knowledge, and truth, as glimpsed beyond the on-going attempt to fit a new language that never finally settles. Through this route, it is shown how Badiou’s differentiation of knowledge and truth enables us to conjure more futuristic conceptions of mathematics education.  相似文献   

16.
Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for teaching in the classroom. However, limited inquiry has explored how to best prepare EMSs and how program features and learning activities influence their development. This mixed-method study identifies some of the interrelated benefits from a K-5 Mathematics Endorsement Program designed to prepare EMSs through examining changes in mathematical beliefs, specialized content knowledge (SCK), and classroom teaching practices during the program. Data (n = 32) were collected over the 2-semester program via belief surveys, a content knowledge assessment, observations of teaching practices, and individual interviews from elementary teachers participating in the program. The findings show some changes in beliefs can be made relatively quickly, other shifts in beliefs take more time and continued support, and changes in SCK and adoption of various aspects of standard-based pedagogy require considerably greater opportunities to learn. The described program features and learning experiences provided a context for these changes and offer considerations for EMS preparation programs.  相似文献   

17.
The data reported in this article come from a large project whose goal was to explore how Latin American students in Catalonia, Spain use their two languages—Spanish and Catalan—to support their learning of mathematics in small groups with other students who are Spanish- or Catalan-dominant. For 5 years, lessons from bilingual mathematics classrooms in three public secondary schools were video-recorded and transcribed. In the presentation of findings, I discuss three language practices that emerged from the analyses of several classroom instances as follows: (1) caution with mathematical vocabulary, (2) invention of terms, and (3) word-for-word translation. One example is chosen to represent each practice and some of its situated effects. The first two examples support the view that the experience of language difficulties, either real or presumed, contributes to generating opportunities that may be beneficial to mathematics learning. The third example, where the focus on the mathematics is hindered, points to a contrasting finding. Unlike other studies in the field, which have reported the difficulties and obstacles that arise in learning and teaching due to bilingualism in the classroom, I propose a change of focus through the conceptualization of language as a potential for thinking and doing, and particularly for learning and teaching mathematics.  相似文献   

18.
Thematic work that integrates different knowledge areas is considered suitable for developing young children’s knowledge and skills in early childhood education. This paper reports evidence from a survey of early childhood teachers’ work with mathematics and art integrated in thematic work. In this study, we aim to explore how teachers perceive mathematics learning and teaching integrated with art. Data for analysis were collected from a questionnaire answered by 27 early childhood teachers from Finland and Sweden. Influenced by a sociocultural theoretical framework, the analysis concerns the teachers’ expressed goals for learning and their strategies for achieving these goals. The analysis reveals qualitatively different approaches to the learning goals addressed by the teachers – process-oriented, product-oriented, development-oriented and providing awareness – which, respectively, seem to generate different meanings of mathematical learning integrated with art. This study offers an overview of teachers’ approaches to teaching mathematics and art in thematic work, and of how different approaches may influence what mathematical meaning is offered to children to explore.  相似文献   

19.
This study investigates how four prospective teachers interpret and use textbooks while learning to teach mathematics during university coursework and practicum teaching. Results indicate that prospective teachers had varied approaches to using textbooks ranging from adherence, elaboration, and creation. Factors influencing how they engaged with texts include their practicum classroom setting, access to resources, and their understanding of mathematics. Preservice teachers' attempts to modify textbook lessons raised pedagogical, curricular, and mathematical questions for them that were not easily answered by reference to the textbooks or teacher's guides. Findings indicate that the practicum can, however, challenge preservice teachers to be creative and flexible users of curriculum materials.  相似文献   

20.
Mathematics can be perceived as being a difficult subject to learn due to the conceptual leaps required to understand particular mathematical topics. In some areas of mathematics, part of the difficulty may be associated with applying sufficient imagination to visualize a particular mathematical concept, and applying sufficient visio–spatial abilities to apply the concept to practical use. In this paper we examine the potential use of animation as an aid for the teaching of mathematical concepts at undergraduate level. An experiment was conducted with a group of UK undergraduate computing students to ascertain if and how animation can potentially be used to support the teaching of mathematical concepts in areas such as rotational symmetry and matrices. In general, the results of the experiment appeared to indicate that animated learning materials can prove more useful than static representations for such topics.  相似文献   

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