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小学生的思维以具体形象思维为主,对抽象知识的理解和接受能力还比较弱。在数学教学中,教师可巧妙借助几何直观,使抽象的问题形象化、具体化,从而降低学生的学习难度,提高教学效率和教学质量,提升学生数学核心素养,为学生终身学习奠定坚实基础。文章结合教学实践,对数学教学中几何直观应用进行探研。 相似文献
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《Early education and development》2013,24(4):409-422
The results of previous research suggest that while preschool children have a beginning understanding of disabilities that involve the use of adaptive equipment, they have little awareness of disabilities such as Down syndrome which have less overt distinguishing characteristics. In this study, videotaped segments from the children's television show, Sesame Street, were used to explore children's ideas about Down syndrome and physical disability. Participants included 41 preschool children. While a majority of participating children were aware that each child in the videotapes had some difficulties performing age-appropriate tasks, children had significantly fewer ideas about why the child with Down syndrome had this difficulty. Significantly more thought that the child with Down syndrome could do more "if he tried really hard" when compared with the child with a physical disability. These results are discussed in terms of children's developing understanding of disabilities and implications for using media to teach preschoolers about people with disabilities. 相似文献
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The results of previous research suggest that while preschool children have a beginning understanding of disabilities that involve the use of adaptive equipment, they have little awareness of disabilities such as Down syndrome which have less overt distinguishing characteristics. In this study, videotaped segments from the children's television show, Sesame Street, were used to explore children's ideas about Down syndrome and physical disability. Participants included 41 preschool children. While a majority of participating children were aware that each child in the videotapes had some difficulties performing age-appropriate tasks, children had significantly fewer ideas about why the child with Down syndrome had this difficulty. Significantly more thought that the child with Down syndrome could do more “if he tried really hard” when compared with the child with a physical disability. These results are discussed in terms of children's developing understanding of disabilities and implications for using media to teach preschoolers about people with disabilities. 相似文献
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Karen C. Fuson 《International Journal of Disability, Development & Education》2019,66(2):119-132
ABSTRACTThis paper briefly overviews my research in supporting children to learn number concepts by relating number words, research-based visual supports, and math symbols. I first outline my approach to helping children build relationships between the use of concrete materials and the building of abstract concepts. I then focus on two crucial early aspects of building meanings for numbers: (1) understanding break-apart partners such as 5=3+2 that support addition and subtraction with small numbers and children’s moving on to Level 2 counting on and algebraic problem representations, and (2) the use of visual five-groups in understanding numbers 1–1000 and in drawings to support multi-digit computations. The research-based learning path of visual-spatio supports is shown and discussed for each topic, including examples of children’s math drawings for representing word problems algebraically and for multi-digit computations. I have found math drawings to be a key visual support that helps children transition to working meaningfully with symbols and words alone. I close with a brief discussion of the difficulties children have with the number line. This overview can provide a framework within which future research on number learning by individuals with trisomy 21/Down syndrome can proceed. 相似文献
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Rhonda Faragher Elena Gil Clemente 《International Journal of Disability, Development & Education》2019,66(2):111-118
ABSTRACTIn September 2017, a group of researchers met for the first conference devoted to the singular purpose of exploring a neglected field – the learning of mathematics by individuals with Down syndrome. This special issue is a result of that first meeting and identifies three emerging trends in the mathematics education of learners with Down syndrome: the goals, content, and pedagogy. Education is central to the goal of improving an individual’s quality of life and only recently has the impact of mathematics been fully comprehended. Many researchers continue to explore the development of the concept of number and there is still much to learn. As a new development, we see that interest is now expanding to explore other areas of mathematics. We still have a long way to go to understand how best to open the doors of mathematics to all learners with Down syndrome. We conclude by offering six areas requiring immediate future research in the field of mathematics and Down syndrome. 相似文献
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Raisa Guberman 《International Journal of Science and Mathematics Education》2016,14(4):739-755
One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs. 相似文献
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《学校用计算机》2013,30(1-2):85-104
Summary PCLogo and Geometer's Sketchpad are powerful tools that may be used by mathematics teachers who want to integrate technology with geometry instruction in the elementary classroom. The purpose of this study was to examine the usefulness of PCLogo and Geometer's Sketchpad to stimulate thinking about geometric concepts in elementary age children. We used a collective case study design that included four cases, two girls (ages 8 and 10) and two boys (ages 10 and 11). All participants were trained to use PCLogo and Geometer's Sketchpad to construct geometric shapes and measure the attributes of the shapes. After the training, participants used these technologies as tools to stimulate thinking about geometric concepts. As a result of our observations of children's performances as they reasoned about geometric concepts, we developed a learning model for teaching children about geometry. 相似文献
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Psychologists, philosophers, and educators have traditionally interpreted the phenomenon of insight learning as the result of the sudden comprehension of abstract/conceptual ideas. The present article shows that such phenomenon may also follow and emerge from the kinetic movements of the human body; that is, we conceptualize insight learning as a post-kinetic phenomenon. Further, it is suggested that kinetic movement constitutes the ground of all human knowing. To illustrate this innovative conceptualization of insight learning, we present the analysis of an exemplary classroom episode taken from a two-year longitudinal video-based ethnographic project. Our project is concerned with elementary students?? mathematical knowing and learning. In the episode, which was selected among other structurally similar examples, three children are sorting geometrical objects. The evidence shown is interpreted as support for the theory of mathematics in the flesh, a radical approach to embodied cognition. In contrast to other embodiment/ enactivist theories in the field of mathematics education, we suggest that the kinetic movement of the human body constitutes a necessary condition for the emergence of abstract mathematical knowledge, and more specifically for the emergence of geometrical insight. 相似文献
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数学课程内容具有抽象性是普遍的共识。通过数与单位以及单位化眼光的案例分析,得到抽象性在数学课程与教学中表现为主观的差异性。利用具身认知理论对学生生成以及加法交换律的分析,得到隐喻思维有益于对抽象内容的理解和意义的丰富。进一步得到数学教学中的两点启示:一是将隐喻思维融入学习,有益于抽象内容意义的理解与丰富;二是面对异样生成和错误应当采取接纳的态度,并使之成为教学资源。 相似文献
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Jill Porter 《International Journal of Disability, Development & Education》2019,66(2):133-150
ABSTRACTThe focus of much mathematics teaching has been on the acquisition of counting, an area where children with Down syndrome can experience particular difficulties. Research with typically developing children has highlighted how early awareness of quantity provides a strong platform for the acquisition of later mathematical skills and programmes of early intervention have been introduced. Many of these studies are embedded in the work and traditions of developmental and cognitive psychology and can be difficult to access. Consequently, this is an area that has been largely ignored in the curricula of children with Down syndrome. This paper seeks to make this literature more available. It systematically reviews previous research with children with Down Syndrome on these early foundations. It considers seemingly contradictory findings in the light of differences in tasks, their presentation and instructions, and the responses required, in order to draw conclusions and reflect on the implications for teaching and learning. Some of these propositions are in contrast to existing practices and call for further research to test their effectiveness. 相似文献
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In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics.
In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research
on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate
the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests
that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms
where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional
approaches that support the learning of mathematics through the process of guided reinvention. 相似文献
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Maxwell Peprah Opoku Richard Tawiah Elvis Agyei-Okyere Shaibu Osman Sally Adwoa Afriyie 《International Journal of Disability, Development & Education》2019,66(2):218-232
ABSTRACTThe recent development of making secondary school education free in Ghana has raised concerns about the level of preparedness of teachers to teach students with diverse needs in one classroom. Significantly, mathematics is one of the core areas that the Ghanaian government has prioritised, and it has institutionalised mechanisms to encourage participation by many students. Accordingly, this qualitative study aimed to document the level of preparedness of mathematics teachers to support the teaching of students with Down syndrome in secondary school classrooms. Twenty-seven mathematics teachers from 14 schools, made up of 18 males and nine females, took part in the study. We found that participants were in favour of implementation of inclusive education. However, regarding the prospect of teaching students with Down syndrome, most of the participants thought that the regular secondary school classroom is not a suitable environment for these students to access education, especially due to a number of challenges. The need for the government to support schools with appropriate teaching materials and facilities is discussed extensively. 相似文献
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《Early childhood research quarterly》2004,19(1):159-166
Big Math for Little Kids, a comprehensive program for 4- and 5-year-olds, develops and expands on the mathematics that children know and are capable of doing. The program uses activities and stories to develop ideas about number, shape, pattern, logical reasoning, measurement, operations on numbers, and space. The activities introduce the mathematical ideas in a coherent, carefully sequenced fashion, and are designed to promote curiosity and excitement about learning and doing mathematics. The program produces playful but purposeful learning of deep mathematical ideas, and encourages children to think about and express their mathematical thinking. Throughout the program, great emphasis is placed on the development of mathematical and mathematics-related language. Our observations suggest two broad questions for future research: What kinds of competence can children develop in the context of a rich mathematics environment? In what ways can mathematics learning promote language and literacy? 相似文献
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赵海祥 《佳木斯教育学院学报》2012,(1):192-193
《初中数学课程标准(2011版)》指出,数学课程能使学生掌握必备的基础知识和基本技能,培养学生的抽象思维和推理能力,培养学生的创新意识和实践能力数学的发散性思维能力是"问题解决"的基础,是培养数学推理能力和创新意识前提要求。数学发散性思维作为用学科自身的品质陶冶人、启迪人、充实人。"问题解决"是人的高级数学思维。高级思维的学习,可以使学生充分享受思维的快乐,可以让思维自由飞翔。本文就初中数学发散思维的培养谈几点体会,通过创设问题情景、设置开放性试题、发挥学科优势等教学策略,着力培养初中学生的数学发散性思维能力,实现有效教学。 相似文献
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数学直观是数学学习的一种重要策略，是以数学直观符号为基本构成要素、以信息加工过程的直观性为形态的认知方式。借助图式可以使抽象知识具体化、使复杂知识简洁化、使单一知识多元化、使特殊知识一般化，从而有助于探索解决问题的思路，在整个数学学习过程中发挥着非常重要的作用。 相似文献
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高等数学教学中极限的求取是一种重要的、基本的运算方法,但对于高职高专的学生而言,由于知识结构方面相对比较薄弱,数学学习基础不牢固,对于抽象概念的理解与熟练应用也存在一定难度,因而探讨常用的运算方法并总结规律,对于有效教学和提高学习理解程度具有重要意义。 相似文献
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几何直观作为核心概念之一,对于深入理解和掌握相关数学知识起到了重要的作用。在低年段解决问题教学中,让题意在几何直观中明了;使难点在几何直观中破解;促思维在几何直观中提升。从而帮助学生分析问题、思考问题、解决问题,不仅提高学生解决问题的能力,而且逐步培养学生良好的思维品质和数学素养。 相似文献
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This study builds on previous investigations that have compared the mathematics achievement of Asian and American students by analyzing the arithmetical learning contexts of children in Taiwan and in the United States. To this end, interviews were conducted with parents and teachers to identify cultural beliefs about learning arithmetic, ten lessons were video-recorded in one classroom in each country to identify classroom social interaction patterns, and interviews were conducted with children to identify the level of sophistication of their arithmetical concepts. Consistent with previous research, the arithmetical understandings of the Chinese children were found to be generally more advanced than those of their American counterparts. The analysis of the other data sources indicates that these differences in understanding reflect two significant differences in the sociocultural context within which Chinese and American children learn arithmetic. First, the arithmetical learning activities in which the Chinese children engaged at home and in school appeared to give them greater opportunities to construct consistenst arithmetical concepts. These differences in the arithmetical learning activities used in the two countries in turn appear to reflect different cultural beliefs about what constitutes normal or natural development when children learn arithmetic. Second, the obligations the Chinese children attempted to fulfill in order to be effective in the classroom were such that they had greater opportunities to explain and to reflect on their arithmetical interpretations and solutions. This in turn gave them greater opportunities to reorganize their thinking and construct increasingly sophisticated arithmetical concepts. 相似文献