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1.
Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms. 相似文献
2.
Cyril Julie 《British journal of educational technology : journal of the Council for Educational Technology》1991,22(2):99-109
There is widespread belief that computers should be used for the teaching and learning of mathematics. Research indicates that computers are primarily used in mathematics classes: (1) to reinforce previously taught concepts, (2) to allow students to construct computer programs to simulate mathematical techniques known to the student and (3) to explore mathematical microworlds encompassing mathematical ideas and concepts normally known to the student. Furthermore, it is said that pre-service teachers should experience the learning of mathematical ideas and concepts of which they had no prior experience in environments in which computers are just one of the resources available for exploring and experimenting with these ideas and concepts. How should these learning environments be constructed so that pre-service teachers are sensitised to the value of doing mathematics in such environments? Is a student's understanding of novel mathematical concepts enhanced when s/he explores it in a computer-enriched environment? An experiment with pre-service teachers was carried out in a college of education for blacks in South Africa. This article describes the insights gained from this experiment. 相似文献
3.
Educational Studies in Mathematics - This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in... 相似文献
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5.
张磊 《南昌教育学院学报》2011,26(6):114-114,118
本文通过对数学问题解决过程中惯性思维存在现状的分析和探讨,对指导学生跳出惯性思维局限作初步的研究。旨在为教师和研究者提供帮助,解决学生在学习过程中存在的各种思维障碍。 相似文献
6.
M. Kathleen Heid Glendon W. Blume Rose Mary Zbiek Barbara S. Edwards 《Educational Studies in Mathematics》1998,37(3):223-249
Understanding students' understanding of mathematical ideas can inform mathematics teaching, and task-based interviews are
one way in which teachers can learn more about their students' understandings. The CIME project was designed to empower mathematics
teachers to use interviews to understand their students' mathematical understandings as well as to prepare teachers to use
technology-intensive curricula. This study examined the influences on three high school mathematics teachers as they learned
to use task-based interviews to understand students' mathematical understandings. The areas of teacher knowledge and conceptions
that influenced the teachers we studied were: teachers' mathematical understandings and knowledge of technology and the perceived
importance of curriculum topics; teachers' views of knowing mathematics; teachers' perceptions of students' characteristics
and needs; and teachers' perceptions of interviewing and the role of questioning in interviews.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
7.
《International Journal of Educational Research》2002,37(2):195-210
Historically, content preparation and pedagogical preparation of teachers in California have been separated. Recently, in integrating these areas, many mathematics methodology instructors have incorporated children's thinking into their courses, which are generally offered late in students’ undergraduate studies. We have implemented and studied a model for integrating mathematical content and children's mathematical thinking earlier, so that prospective elementary school teachers (PSTs) engage with children's mathematical thinking while enrolled in their first mathematics course. PSTs’ work with children in the Children's Mathematical Thinking Experience (CMTE) may enhance their mathematical learning. Preliminary study results indicate that the sophistication of CMTE students’ beliefs about mathematics, teaching, and learning increased more than the sophistication of beliefs held by students enrolled in a reform-oriented early field experience and that experiences considering children's mathematical thinking provided PSTs with increased motivation for learning mathematics. 相似文献
8.
Applied mathematical problem solving 总被引：1，自引：0，他引：1
Richard Lesh 《Educational Studies in Mathematics》1981,12(2):235-264
A case is presented for the importance of focusing on (1) average ability students, (2) substantive mathematical content, (3) real problems, and (4) realistic settings and solution procedures for research in problem solving. It is suggested that effective instructional techniques for teaching applied mathematical problem solving resembles mathematical laboratory activities, done in small group problem solving settings.The best of these laboratory activities make it possible to concretize and externalize the processes that are linked to important conceptual models, by promoting interaction with concrete materials (or lower-order ideas) and interaction with other people.Suggestions are given about ways to modify existing applied problem solving materials so they will better suit the needs of researchers and teachers. 相似文献
9.
This study investigated how teacher education assignments can be designed to support beginning teachers in learning to do the work of teaching. We examined beginners' formative assessment practices—in particular, their eliciting and interpreting of students' mathematical thinking—in the context of an elementary mathematics methods assignment, and the ways in which the scaffolds provided shaped their practice. We found that the scaffolds differentially supported their practice and suggest strategic improvement of the focus and organization of different types of scaffolds. Findings from the study contribute to the conceptualization and design of scaffolds for practice-based learning opportunities in teacher education. 相似文献
10.
Patrick W. Thompson Marilyn P. Carlson Jason Silverman 《Journal of Mathematics Teacher Education》2007,10(4-6):415-432
We examine the role of tasks that have the intended effect of teachers re-conceiving the mathematics they teach as comprising a coherent body of meaningful ideas. We ground our discussion in ideas of trigonometry and modular functions and draw from a professional development research project to illustrate our approach. In this project, many teachers experienced dissonance that was rooted in their commitments to their curricular knowledge of trigonometry. Teachers who built new meanings into a coherent whole were those who coordinated them at a micro level. Teachers who saw implications of their own reasoning for student learning were also successful at expressing that reasoning in natural language. We saw a similar pattern in the case of teachers' creation of meanings for action and process conceptions of mod(f(x),g(x)). Teachers who gained insight into implications of their own activities for student learning were the teachers who reasoned at a micro level in regard to the meaning of mod, who coordinated that meaning with a covariational perspective on the behavior of functions, and who expressed that coordination in natural language. We conclude that a primary feature of tasks that promote teachers' construction of coherent mathematical meanings is that they support an overall effort to have teachers engage in the coordination of meanings in the context of explaining significant ideas and relationships. 相似文献
11.
Alan H. Schoenfeld 《Journal of Mathematics Teacher Education》2017,20(5):415-432
This article characterizes my use of video as a tool for research, design and development. I argue that videos, while a potentially overwhelming source of data, provide the kind of large bandwidth that enables one to capture phenomena that one might otherwise miss; and that although the act of taping is in itself an act of selection, there is typically enough shown in a video that it rewards multiple watching and supports the kinds of arguments over data that are essential for theory testing and replication. In pragmatic terms, video presents phenomena in ways that have an immediacy that is tremendously valuable. I discuss ways in which videos help students and teachers focus on phenomena that might otherwise be very hard to grapple with. This article begins with a brief review of my uses of video, almost 40 years ago, for research and development in problem solving. It then moves to the discussion of very fine-grained research on learning and decision making. The bulk of the article is devoted to a discussion of the teaching for robust understanding (TRU) framework, which was derived in large measure from the extensive review of classroom videotapes, and which serves as the basis for an extensive program of pre-service and in-service professional development. The professional development relies heavily on the use of videos to convey the key ideas in TRU, and to help teachers plan and review instruction. 相似文献
12.
周春荔 《首都师范大学学报(社会科学版)》2002,(Z1)
本文简要回顾了 2 0世纪 80年代以来 ,我国数学教育界部分学者、教师自觉学习与应用数学方法论指导数学教学方法改革的历史足迹 ,其中“贯彻数学方法的教育方式 ,全面提高学生素质”的数学教育实验 (简称MM教育方式实验 )已从无锡拓展到湖北、天津、北京、新疆等十余个省市。这对进一步推进数学素质教育提供了重要启示。 相似文献
13.
Laurie D. Edwards 《Educational Studies in Mathematics》2009,70(2):127-141
Spontaneous gesture produced in conjunction with speech is considered as both a source of data about mathematical thinking,
and as an integral modality in communication and cognition. The analysis draws on a corpus of more than 200 gestures collected
during 3 h of interviews with prospective elementary school teachers on the topic of fractions. The analysis examines how
gestures express meaning, utilizing the framework of cognitive linguistics to argue that gestures are both composed of, and
provide inputs to, conceptual blends for mathematical ideas, and a standard typology drawn from gesture studies is extended
to address the function of gestures within mathematics more appropriately.
Electronic supplementary material The online version of the original article (doi:) contains supplementary material, which is available to authorized users. 相似文献
14.
This paper considers the kind of pedagogical knowledge and principles involved in the operationalisation of knowledge of children's mathematical thinking as a process of dynamic assessment. Using a case study of a particular child, this paper explores planning and instruction for a child determined by a detailed and informed interpretation of the child's conceptual understanding through a dynamic process. It presents as a case study the observations of a teacher who had undertaken professional development in children's mathematical thinking, theoretically informed by Cognitively Guided Instruction and Maths Recovery. The observations revealed the child's mathematical understanding and how the teacher used this knowledge dynamically to inform teaching. The paper outlines the kind of knowledge required of teachers to enact this dynamic process in mathematics teaching and argues for the centrality of this to the development of inclusive practice. 相似文献
15.
Responding to mathematical problems is a core activity in classrooms. The problems that teachers select determine the mathematical content, processes and nature of mathematical inquiry occurring in classrooms and thereby contribute to the development of mathematical skills and dispositions. Selecting, designing or reformulating mathematical problems is a critical skill, then, for prospective and practising teachers. This study explores the influence of a mathematical letter writing initiative in developing the problem posing skills of 28 prospective primary teachers. We examine the characteristics of mathematical problems designed by prospective teachers, and their understandings of what constitutes a good mathematical problem, prior to and following completion of a 12-week letter writing initiative with 10–11-year-old children. Analysis of the data reveals the benefits of engaging in the initiative as evidenced in improvements in several problem characteristics. There was an increase in the number of multiple approach and multiple solution problems and in the level of cognitive demand of problems posed. The challenge of posing non-traditional problems, alongside the competing demands of building in opportunities for success, may have diminished participants’ ability to evaluate and attend to the cognitive demand of problems.
相似文献16.
Bert van Oers 《Educational Studies in Mathematics》2010,74(1):23-37
In the attempt to improve mathematical thinking for safeguarding our future societal needs, there is a worldwide tendency in schools to start training mathematical and arithmetical operations at an earlier age in children’s development. Recent theoretical developments and empirical research have pointed to alternative ways of approaching early mathematical thinking. In these latter approaches, mathematical development in the early developmental stages is seen as an emerging process in the context of children’s own activities that contributes to meaningful learning and stimulation of children’s cultural identity (Bildung approach). The discussion between the training approach versus the ‘Bildung’ approach is still intemperately going on. In this article, some outcomes of a research programme (based at the Free University Amsterdam) are discussed that present empirical studies and their theoretical background (cultural–historical theory, elaborated in an educational concept called ‘Developmental Education’) that demonstrates the promising potentials of promoting mathematical thinking through supporting young children’s appropriation of schematic representations and notations in the context of play. 相似文献
17.
Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers’ views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result of continuous connection making. However, in contrast to the popular view which separates understanding into conceptual and procedural, Chinese teachers prefer to view understanding in terms of concepts and procedures. They place more stress on the process of concept development, which is viewed as a source of students’ failures in transfer. To achieve mathematical understanding, the Chinese teachers emphasize strategies such as reinventing a concept, verbalizing a concept, and using examples and comparisons for analogical reasoning. These findings draw on the perspective of classroom practitioners to inform the long-debated issue of the meaning of mathematical understanding and ways to achieve mathematical understanding. 相似文献
18.
Götz Krummheuer 《Educational Studies in Mathematics》2013,84(2):249-265
This paper deals with one aspect of the endeavor to generate a theory of the development of mathematical thinking of children in the early years ages 3 to 10. By comparing two scenes, one from preschool and one from a first grade mathematics class, the relationship between diagrammatic and narrative argumentations among children and teachers is reconstructed and related to possible developmental trajectories of mathematical thinking. Theoretically, I attempt to implement these developmental paths in a concept of an “Interactional Niche in the Development of Mathematical Thinking.” 相似文献
19.
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
20.
There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article
reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in
an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students
from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working
on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical
ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’
mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity.
The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development
of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning. 相似文献