小学数学空间与图形教学策略解析

小学数学教学中所涉及的数学知识有一类以抽象图形为主,重视学生抽象思维、几何思维的发展与提升.空间几何与图形结构对学生的逻辑推理能力、数学记忆力提出了新的要求.本文以小学数学教学中空间与图形的有关教学展开论述,探讨实现教学任务的有效方法.     

结构化视域下小学数学“图形与几何”教学例析

“图形与几何”教学贯穿整个小学阶段,它立足学生的几何直观、空间观念、推理能力等核心素养的发展,是培养学生想象思维和创造思维的重要基础。基于结构化视域,从构建“知识结构、策略结构、活动结构”三个方面,例谈小学数学“图形与几何”教学。     

小学数学几何概念教学的有效策略

几何概念是小学数学概念中的重要组成部分,也是构成小学数学基础知识的主要内容。掌握正确的几何概念,是学生学习平面图形和立体图形知识的基石,也是培养学生空间想象能力的前提。几何概念较为抽象,对于以具象思维为主要形式的小学生来说,在理解和掌握几何概念上都有很大难度。因此,小学数学教师应当重视几何概念教学。通过分析小学数学中几何概念教学的课堂实例,探究能够提高数学教学质量的几何概念教学的有效策略。     

小学数学“图形与几何”教学中思维可视化策略研究

近年来,随着小学数学教育的课程改革,越来越注重培养学生的创新思维和问题解决能力。图形与几何教学因其在学生空间感知能力、逻辑思维能力和几何直观能力的培养中的重要作用而受到关注。本研究对基于思维可视化的小学数学“图形与几何”教学设计进行了探究,提出了“图形与几何”模块的可视化“五步”教学法,即引入情境创设、合作探究、多维表达、问题解决和回顾总结。并结合流程图、微课、课件、几何画板、思维导图和学习任务单等可视化工具和技术,激发学生学习兴趣,培养创新思维和问题解决能力。     

例谈小学生空间思维的培养

“图形与几何”是小学数学课程内容的重要组成部分,其核心目标在于发展学生的空间观念,培养空间思维能力。那么,如何通过具体的教学实践将先进理念与课程目标有机结合,以促进学生空间思维的发展？现以几个教学片断为例,浅谈在小学数学教学中小学生空间思维的培养。一、注重直观感知,形成思维表象皮亚杰的认知发展理论指出：“儿童空间观念的...     

结合微课，让数学学习“深”起来——以小学数学“图形与几何”教学为例

<正>在小学数学教学中,图形与几何部分的教学内容对学生来讲一直是一块“硬骨头”。小学生的年龄尚小,还未能形成空间想象思维,也不具备良好的抽象能力,因此对几何方面的问题理解起来会有一定的难度。为了有效培养学生的数学思维,推动数学几何内容的教学效率不断提升,教师应重视对微课教学资源的使用,借助微课,     

经历探究过程 培养空间观念——以“观察物体”一课为例

空间观念是小学数学教学中的核心内容之一,也是学生学习数学时必备的基础能力,其在“图形与几何”领域中占据着重要地位。课程标准中也明确提出要将培养学生良好的空间观念作为教学的核心之一。良好的空间观念不仅能有效促进学生空间想象力和抽象思维的发展,还能更好帮助学生理解图形知识,解决实际问题,促进创新创造。因此,教师应重视学生空间观念的培养,引导其经历自主探究过程,在不断的思考与实践中逐渐树立空间意识,并以此为依托实现数学核心素养的全面提升。     

重视几何概念的形成 发展学生的空间观念——小学数学第十册长方体和正方体的教学

重视几何概念的形成发展学生的空间观念——小学数学第十册长方体和正方体的教学白宝兰九年义务教育六年制小学数学第十册第二单元开始教学立体图形——长方体和正方体。培养学生初步的空间观念是教学大纲中的要求之一,因此就要在教学中重视几何概念的形成,促进学生空间...     

小学数学图形与几何结构化教学的实践研究

小学数学中图形与几何的教学是培养学生想象思维和发展学生创造思维的重要基础,为了更好的使学生进行有效、系统的学习,将结构化的概念赋予到小学图形与几何的教学中。怎样才能让二者合二为一、相辅相成,切实提高小学生的逻辑思维以及想象能力,提高学生对图形与几何学习的掌握程度。本篇文章也以此为中心探究了小学数学图形与几何结构化教学的意义和价值,并且分析了具体的实践策略。     

浅谈新课改下的小学数学几何教学

正几何是小学数学教学的重要组成部分,在整个数学体系中占有非常重要的作用。随着新一轮课程改革的推进,对几何教学提出了更为明确的要求与更高的目标,明确提出小学数学教学要重视培养与发展学生的逻辑思维、空间观念。所谓空间主要表现在:能由实物的形状想象出几何图形,由几何图形想象出实物的形状,进行几何体与其三视图、展开图之间的转化;能根据条件做出立体模型或画出图形;能从较复杂的图形中分解出基本的图形,并能分析其中的基本元素     

Types of reasoning in 3D geometry thinking and their relation with spatial ability

The aim of this study is to describe and analyse the structure of 3D geometry thinking by identifying different types of reasoning and to examine their relation with spatial ability. To achieve this goal, two tests were administered to students in grades 5 to 9. The results of the study showed that 3D geometry thinking could be described by four distinct types of reasoning which refer to the representation of 3D objects, spatial structuring, conceptualisation of mathematical properties and measurement. The analysis of the study also showed that 3D geometry types of reasoning and spatial abilities should be modelled as different constructs. Finally, it was concluded that students’ spatial abilities, which consist of spatial visualisation, spatial orientation and spatial relations factors, are a strong predictive factor of the four types of reasoning in 3D geometry thinking.     

Early childhood teacher education: the case of geometry

For early childhood, the domain of geometry and spatial reasoning is an important area of mathematics learning. Unfortunately, geometry and spatial thinking are often ignored or minimized in early education. We build a case for the importance of geometry and spatial thinking, review research on professional development for these teachers, and describe a series of research and development projects based on this body of knowledge. We conclude that research-based models hold the potential to make a significant difference in the learning of young children by catalyzing substantive change in the knowledge and beliefs of their teachers.     

Spatial ability and transformational geometry

New technologies in education are placing more emphasis upon visual and spatial skills, those required to inspect, encode, transform, and construct information in visual displays. They do this by presenting students with learning material embedded in complex visual displays and hypermedia, and by requiring students to navigate through virtual space. These developments make it important for us to learn more about the underlying nature of visuospatial ability, how it is related to academic performance, and how it can be improved. This paper explores these issues in the context of instruction in transformational geometry upon geometry performance and spatial ability of Grade 7/8 students. The instructional conditions were (a) a traditional textbook approach involving paper-and-pencil tasks and verbal instruction (Traditional Group), and (b) an approach incorporating object manipulation, and visual imagery, which was designed to encourage spatial thinking (Spatial Group). Multiple regression results indicated that posttest geometry performance was predicted by pretest geometry, pretest spatial ability, and the interaction of pretest geometry and instructional condition; the interaction indicated that high prior knowledge subjects performed better in the Spatial group, low prior knowledge subjects in the Traditional group. Posttest spatial ability was predicted by handedness, pretest geometry, pretest spatial ability, and the interaction of pretest spatial ability and handedness; the interaction indicated that less right-handed subjects of low spatial ability improved on spatial ability more than their more right-handed peers.     

Encouraging Maternal Guidance of Preschoolers’ Spatial Thinking During Block Play

Spatial thinking, an important component of cognition, supports academic achievement and daily activities (e.g., learning science and math; using maps). Better spatial skills are correlated with more spatial play and more parental attention to spatial concepts. Tested here was whether informing mothers about spatial thinking and ways to encourage it would increase the spatial guidance they provide to their preschool children (N = 41; M = 5.23 years) during dyadic block play. Mothers given such instructions indeed produced more spatial language and spatial guidance than mothers asked to play as usual. In instructed dyads, children also used more spatial language; both mothers and children engaged in less pretend play. Findings offer support for designing interventions to encourage parents to foster their children's spatial skills.     

信息技术在立体几何教学中的应用探究

立体几何需要学生进行大量的空间想象,这给基础较差的学生带来了很大的困扰。而信息技术以其丰富的表现力和强大的交互功能,可以高效快速地向学生呈现动态图形,具有很高的教学价值以及应用意义。教师通过运用信息技术的方法教学立体几何,可以更加直观、立体以及动态化展示空间几何体,对开发学生空间思维以及几何思想具有重大意义。     

Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials

The study that informs this article was undertaken to investigate the benefits and limitations of using pre-constructed,web-based, dynamic geometry sketches inactivities related to deductive proof at the secondary school level. Two distinct themes emerged from analysis of the results– first, the relationship between the activities and the development of geometric thinking skills, and second, the relationship between the design of the materials, and the exploration process. This article focuses on the latter. An analysis of the data showed that task question and sketch provision must work together to create an environment for exploration. It also indicated that explicit attention to visual interpretation and exploration using change is required in order for students to benefit fully from their experiences with pre-constructed dynamic geometry sketches. This article draws attention to the idea that pre-constructed dynamic sketches(whether web-based or not) and accompanying materials are central elements of the learning activity of which they are a part,and therefore, that decisions about their design have the potential to support or impede the development of exploration strategies and geometric thinking skills. An examination of student responses to particular questions in light of visual and dynamic geometry research suggests that through the materials we may be able to improve students' use of the mathematical investigation process in exploring pre-constructed dynamic geometry sketches. This revised version was published online in August 2006 with corrections to the Cover Date.     

DIVERSIFYING OUR PERSPECTIVES ON MATHEMATICS ABOUT SPACE AND GEOMETRY: AN ECOCULTURAL APPROACH

School mathematics tends to have developed from the major cultures of Asia, the Mediterranean and Europe. However, indigenous cultures in particular may have distinctly different systematic ways of referring to space and thinking mathematically about spatial activity. Their approaches are based on the close link between the environment and cultural activity. The affinity to place strengthens the efficient, abstract, mathematical system behind the reference and its connection to the real world of place and a holistic worldview. This paper sets out to present an overview of various approaches to aspects of space and geometry by drawing on linguistic and cultural literature, my collaborative research in Papua New Guinea, and from personal communications with indigenous colleagues in Australia and elsewhere. This diversity provides a challenge by which teachers can deconstruct their thinking about mathematics and subsequently to review the content of teaching and to be more responsive to the diversity of cultural backgrounds of students. To assist with recognising ecocultural mathematics on space and geometry, 4 principles are established and discussed on language structures, reference lines and points, measures of space and worldviews and interpretations of space as place.     

直觉思维的训练和培养

注重对学生进行非逻辑思维能力的培养,对克服学生思维的单向性,发展创新思维具有十分重要的意义．因此,在教学中,只有在重视逻辑思维训练的同时,加强直觉思维能力的培养,才能培养出现代科技发展需要的开拓型人才。     

准正弦空间通道的环境调节功能

人在无所依靠、空旷的空间环境中独处时,轻松的感觉是短暂的,随着时间的推移将由轻松变为松散、到无所适从,定向思维能力迅速下降.在合适的空间环境中,可以使人的注意力从涣散转而集中.如果采用具有正弦特点的空间通道,可以将人的注意力柔性地收拢起来、定向地指向一定方向.     

解析几何课程中重要数学思想方法探究

解析几何里蕴涵着丰富的数学思想方法,其为数学思想方法的教学提供了一个很好的知识平台。师专数学专业主干课程《解析几何》中的数学思想方法可按核心数学思想方法和一般数学思想方法来划分。