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1.
The purpose of this cross-national study is to understand teachers’ views about the meaning of instructional coherence and the ways to achieve instructional coherence. With respect to the meaning of instructional coherence, whereas the majority of U.S. teachers paid attention to connections between teaching activities, lessons, or topics, the majority of Chinese teachers emphasized the interconnected nature of mathematical knowledge beyond the teaching flow. U.S. teachers expressed their views about ways to achieve instructional coherence through managing a complete lesson structure. In contrast, Chinese teachers emphasized pre-design of teaching sequences, transitional language and questioning based on the study of textbooks and students beforehand. Moreover, they emphasized addressing student thinking and dealing with emerging events in order to achieve “real” coherence. The findings of the study contribute to our understanding about the meaning of instructional coherence and ways to achieve instructional coherence in different cultural contexts. 相似文献
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Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding. 相似文献
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徐彦辉 《宁波大学学报(教育科学版)》2022,(5):66-072
数学理解包括三种基本形态,即:记忆性理解、解释性理解和探究性理解,这三种数学理解分别对应着“记得、晓得和明得”三种不同的状态。三种数学理解对数学学习都是有价值的,但仅有记忆性和解释性理解是不够的,探究性理解才是数学教学的最终目标。实践中,不少水平不高的教师常常只能让学生达到记忆性理解,有一定水平的教师能让学生达到解释性理解,真正让学生达到探究性理解的教师并不是很多。教师要不失时机地促进学生数学理解层级的迭代升级,促使学生最终达到探究性理解,吴文俊院士数学学习的经验对把握数学理解的三种基本形态有借鉴和启迪意义。在课堂教学中引导学生从事生动活泼的数学探索性活动常常是一个相当艰难的过程,对教师的数学探究素质提出了较高的要求,教师应努力引导学生去探求数学知识的意义和发现的过程,促使学生数学探究性理解方式的养成。 相似文献
4.
Margot Berger 《Educational Studies in Mathematics》2004,55(1-3):81-102
The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both as an object with which to communicate (like a word is used) and as an object on which to focus and to organise her or his mathematical ideas (again as a word is used) even before she or he fully comprehends the meaning of this sign. Through this sign usage, I claim that the mathematical concept evolves for that learner so that it eventually has personal meaning, like the meaning of a new word does for a child; furthermore, because the usage is socially regulated, I claim that the concept evolves for the learner so that its usage concurs with its usage in the mathematical community. In line with Vygotsky, I call this usage of the mathematical sign before mature understanding, ‘functional use’. I demonstrate ‘functional use’ of signs (manipulations, imitations, template-matching and associations) through an analysis of an interview in which a mathematics university student engages with a ‘new’ mathematical sign, the improper integral, using pedagogically designed tasks and a standard Calculus textbook as resources. 相似文献
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后现代教育理念对数学教育目的观、课程观、教学观的反思和批判产生一定的影响。关于数学教学观的反思主要体现于数学教学行为的改变：构建数学认知结构,强调学生个体的＂意识的建构＂;呈现静态知识方式,创设学生个体的＂认知的情境＂;重构思维发展模式,塑造学生个体的＂茎块式思维＂;培养问题质疑能力,强化学生个体对＂问题的反思＂;突破师生交往方式,注重师生之间的＂对话的互动＂。 相似文献
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This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching. 相似文献
8.
We adopt a neo-Vygotskian view that a fully concrete scientific concept can only emerge from engaging in practice with systems of theoretical concepts, such as when mathematics is used to make sense of outside school or vocational practices. From this perspective, the literature on mathematics outside school tends to dichotomise in- and out-of-school practice and glamorises the latter as more authentic and situated than academic mathematics. We then examine case study ethnographies of mathematics in which this picture seemed to break down in moments of mathematical problem solving and modelling in practice: (1) when amateur or professional players decided to investigate the mathematics of darts scoring to develop their “outing” strategies and (2) when a prevocational mathematics course task challenged would-be mathematics teachers’ concept of fractions. These examples are used to develop the Vygotskian framework in relation to vocational and workplace mathematics. Finally, we propose that a unified view of mathematics, outside and inside school, on the basis of Vygotsky’s approach to everyday and scientific thought, can usefully orientate further research in vocational mathematics education. 相似文献
9.
Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today’s sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers’ application of meta-cognition therefore directs and reflects their teaching-practice behaviour which influences their learners’ learning with understanding in problem-solving. The purpose of the study reported on in this article was to explore teachers’ available meta-cognitive skills in class with the intention of supporting learners’ development of mathematics in problem-solving in some selected rural primary schools in the Eastern Cape, South Africa. The participants were three teachers purposefully selected from three primary schools. Interviews were conducted with the three teachers and three lessons were observed. The interviews, as an extension of observation, focused on the teachers’ knowledge or understanding of available meta-cognitive skills and how they used these skills in helping their learners’ development of mathematics problem-solving. The findings included a detailed exploration of the teachers’ acquisition and use of specific metacognitive skills, either consciously or unconsciously, during teaching and learning processes in order to develop their mathematics learners’ meta-cognitive skills as well as in solving mathematical problems. The results of the observation showed that there was evidence of teachers applying meta-cognitive skills unconsciously in assisting their learners in problemsolving in class. The interviews confirmed this evidence of available meta-cognitive skills which the teachers usually applied in assisting their learners in problem-solving in class. Recommendations have been made regarding teachers’ methods of teaching to improve the development of such skills in the lives of their mathematics learners through problemsolving. 相似文献
10.
This study explores prospective teachers’ skills of attending, interpreting and responding to content-specific characteristics of mathematics instruction in classroom videos. Prospective teachers analyzed the mathematics instruction of two teachers through four video clips and proposed alternative instructional ways to support the teaching and learning of mathematics. The results indicated that as prospective teachers examined the teachers’ instructional practices, they increased their level of attending and interpretation to content-specific aspects of instruction rather than focusing on generic dimensions of the instruction. When they watched and compared different characteristics of teachers’ mathematics instruction, they provided more detailed and mathematical instructional suggestions. 相似文献
11.
Camilla Björklund 《Scandinavian Journal of Educational Research》2018,62(2):245-263
This is an empirical inquiry concerning children’s concept development and early mathematics teaching. The intention is to broaden the understanding of preschool children’s perceptions of the concept “half” (as 1 of 2 equal parts of a whole), in designed mathematics teaching settings. Three teachers working with 4–5-year-old children participate in an in-service program, involving continuous and cooperative reflection and theoretically designed teaching activities. Observations of pedagogical strategies and children’s responses reveal that: children show qualitatively different ways of experiencing the same concept; the ways of experiencing are critical for how the intended learning object is perceived; and the dimensions of the learning object are related to each other, suggesting a hierarchical organization of how to perceive aspects of “half.” 相似文献
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This mixed methods study investigates the ways in which secondary mathematics prospective teachers acquire skills needed to attend to, interpret, and respond to students’ mathematical thinking and the ways in which their perceived strengths and weaknesses influence their skills when this type of formalized training is not part of their program. These skills (attending, interpreting, and responding) are defined as teachers’ professional noticing of students’ thinking. Results indicate that seniors respond to students’ thinking in significantly different ways from juniors and sophomores. Converging the data highlighted inconsistencies in how participants’ were making sense of students’ mathematical thinking, as well as in participants’ self-identified strengths and weaknesses. 相似文献
13.
Thomas J. Cooney 《Educational Studies in Mathematics》1999,38(1-3):163-187
This article addresses issues related to the ways teachers learn mathematics and the teaching of mathematics and the relevance of those ways to their professional development. Preservice teachers' understanding of school mathematics lacks sophistication, a situation that needs to be addressed in mathematics teacher education programs. What is critical is the means by which they encounter and explore the mathematics they will be teaching. Fundamentally, their mathematical experiences need to be congruous with the kind of teaching we would expect of a reflective, adaptive teacher. The article contains both practical and theoretical considerations of how these experiences might be structured. Theoretical orientations for conceptualizing teachers' belief structures are offered as a foundation for conceptualizing teachers' ways of knowing. The moral dimension of teacher education is considered as a backdrop for understanding how teachers come to know.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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This study investigates Chinese and U.S. teachers’ cultural beliefs concerning effective mathematics teaching from the teachers’ perspectives. Although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching. The sample of U.S. teachers put more emphasis on student understanding with concrete examples, and the sample of Chinese teachers put more emphasis on abstract reasoning after using concrete examples. The U.S. teachers highlight a teacher’s abilities to facilitate student participation, manage the classroom and have a sense of humor, while the Chinese teachers emphasize a teacher’s solid mathematics knowledge and careful study of textbooks. Both groups of teachers agree that memorization and understanding cannot be separated. However, for the U.S. teachers, memorization comes after understanding, but for Chinese teachers, memorization can come before understanding. These differences of teachers’ beliefs are discussed in a cultural context. 相似文献
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《Teaching and Teacher Education》2001,17(2):213-226
Beliefs and practices related to mathematics were assessed for 21 fourth- through sixth-grade teachers. At the beginning and the end of the school year teachers’ beliefs about (1) the nature of mathematics (i.e., procedures to solve problems versus a tool for thought), (2) mathematics learning (i.e., focusing on getting correct solutions versus understanding mathematical concepts), (3) who should control students’ mathematical activity, (4) the nature of mathematical ability (i.e., fixed versus malleable), and (5) the value of extrinsic rewards for getting students to engage in mathematics activities were assessed. (6) Teachers self-confidence and enjoyment of mathematics and mathematics teaching were also assessed. Analyses were conducted to assess the coherence among these beliefs and associations between teachers’ beliefs and their observed classroom practices and self-reported evaluation criteria. Findings showed substantial coherence among teachers’ beliefs and consistent associations between their beliefs and their practices. Teachers’ self-confidence as mathematics teachers was also significantly associated with their students’ self-confidence as mathematical learners. 相似文献
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Nicole L. Louie 《Educational Studies in Mathematics》2018,97(1):55-69
This paper responds to the burgeoning literature on mathematics teacher noticing, arguing that its cognitive orientation misses the cultural and ideological dimensions of what and how teachers notice. The author highlights Goodwin’s concept of professional vision as a way of bringing analyses of culture and power into studies of teacher noticing. The case of a high school algebra teacher who learned to notice the mathematical strengths of students from marginalized groups is used to illustrate how this might be done. The teacher’s noticing involved not only cognitive processes like attending to, interpreting, and deciding how to respond to students’ thinking, but also managing dominant ideologies that position students—especially students from non-dominant communities—as mathematically deficient rather than as sense-makers whose ideas should form the basis for further learning. The paper advances the field’s capacity for understanding the challenges that teachers face as they attempt to notice in ways that are ambitious as well as equitable. 相似文献
18.
Mathematical proofs are not only the focus of every country’s mathematics curriculum reforms, but also the subject of research
on mathematics education. This paper is based on a survey of mathematics teachers, the goal of which was to investigate the
understanding of mathematical proofs of secondary school math teachers, their levels of mathematical proofs, and their ability
to comprehensively teach mathematical proofs. Preliminary results of the survey provide insight into several characteristic
aspects of Chinese secondary school teachers’ literacy of mathematical proofs. 相似文献
19.
Joan Ferrini-Mundy Gail Burrill William H. Schmidt 《Journal of Mathematics Teacher Education》2007,10(4-6):311-324
Improving mathematics education in the United States has taken many forms. Our work has focused on two aspects: the content knowledge of teachers and a well-articulated coherent curriculum. Our aim was teacher “capacity building” that is enabling teachers to teach to coherent and significant mathematical curricular goals and describe the implementation in a large-scale project based at Michigan State University. We highlight the design, structure and use of mathematics teacher learning tasks that were intended to improve teachers’ capacity to teach to these goals and note how the teachers’ perceptions of the structure and sequencing of mathematics itself affect the ways they organize mathematics in their teaching and the ways they teach. 相似文献
20.
数学史的教育价值日益凸显,但数学史在教学中的作用远未发挥,关键原因是数学教师的数学史素养普遍不高.重视数学教师数学史素养的研究和提升成为当务之急.根据SOLO理论,可把数学教师的数学史素养划分为5个水平.维果斯基的概念形成理论有助于从心理学角度揭示数学教师数学史素养提升的内在机制.数学教师数学史素养水平划分及相关研究,可以丰富数学教师专业素养的理论内容,为提升数学教师的数学史素养提供参考。 相似文献