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函数是近现代数学的基础,是中学数学中最重要,也是最复杂的概念.学生对函数本质的理解可划分为4个水平:前结构水平、单结构水平、多结构水平和关系结构水平.高一学生函数对应关系的理解整体水平偏低的原因有:函数本身的复杂性、发展性和教学的问题.数学教学中要更新教学观念,注重理解的数学教学,要掌握有利于促进理解的教学方法. 相似文献
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"教好数学"是对每一个数学教师的职业要求,如何"教好数学"是每一个数学教师每天面对的、而且是每天必须研究的课题。这里以人教版《义务教育课程标准实验教科书·数学》八年级(上)"三角形全等的判定"(第1课时)为例谈谈对"教好数学"的基本认识。一、理解数学是教好数学的前提有效、高效的教学源于教师完善的知识结构,源于教师对教学内容深刻而透彻的理解。作为数学教师,其知识结构 相似文献
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本文用现代数学的集合论观点去剖析了曲线与方程的对应关系，这不仅有利于学生对曲线与方程对应关系的理解与掌握，也培养了学生现代数学的思想、观点与方法。 相似文献
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教师在解题教学时引用的例题往往是自己在问题解决过程中经历了深刻体验的.文章结合一道反比例函数习题的解题教学,以数学问题解决过程中的有效三问帮助学生从理解题目开始,逐渐形成思路,明确执行方案,发展数学智慧.教师应该就自己解题时所经历的心路历程转化为教学形态,从而成为解题方面学生学习的典范. 相似文献
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数学模型是思维的支撑点,也是知识的附着点.学生对数学概念的理解和抽象都是针对一定的模型进行的,概念模型不仅是数学概念的典型样例,而且是数学概念表征的重要方式,人们以模型与特征捆绑的图式化表征与概念关系表征相结合的方式理解数学概念及概念体系;对数学基本事实的理解与发现则是根据模型的结构特征,建立相关概念之间的因果联系,没有数学模型,也就谈不上对反映模型特征、结构和关系的数学事实和数学原理的理解和发现;学生对数学思想方法的理解则是在解决数学问题(探索问题结构特征和关系)的过程中,以解决问题的程序为 相似文献
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新版本高中数学教材对函数内容进行了较大的调整.文章通过课堂教学实录,向读者展示了函数概念如何"从实际问题出发,结合学生的认知,归纳共性形成概念"这一过程,尝试将教学理论与教学实践相结合,力求通过精心设计教学过程,帮助学生克服概念学习中的困难,加深对函数概念的理解,提升数学核心素养. 相似文献
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<正>数学文化为核心素养的发展提供了载体。很多学者和一线教师为如何将数学文化融入数学课程与教学付诸行动,并取得了一定的成效。然而,很多冠以“数学文化”的数学课堂教学多是在教学的某一环节简单呈现数学史,实际上未能真正将数学文化融入数学教学中。究其原因,主要是对数学文化的理解不到位,没有找到切实可行的途径使数学教学有效地彰显数学文化。有学者指出,数学文化既强调将数学作为相对独立的文化系统来理解数学的本质及其发展, 相似文献
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章建跃博士指出：“高水平的教学设计要建立在如下三个基本点上：理解数学、理解学生、理解教学．其中,理解数学是指对数学的思想、方法及其精神的理解;理解学生是指对数学学习规律的理解,核心是理解学生的数学思维规律;理解教学是指对数学教学规律、特点的理解．‘三个理解’是数学教师专业发展的基石．” 相似文献
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数学概念教学是构成数学基础知识的重要组成部分，准确地理解概念是学好数学的前提，概念的引入、形成、理解、掌握、运用是数学概念教学中应该注意的问题。 相似文献
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统计分析中对应分析方法应用 总被引：6，自引：0，他引：6
通过数学方法的描述和统计软件SPSS对实例的分析,阐明了在统计分析中运用对应分析方法,可以得出正确的探索性统计分析结果,直观地揭示统计数据间的内在联系。 相似文献
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Susanne Prediger 《Journal of Mathematics Teacher Education》2010,13(1):73-93
What kind of mathematical knowledge do prospective teachers need for teaching and for understanding student thinking? And
how can its construction be enhanced? This article contributes to the ongoing discussion on mathematics-for-teaching by investigating
the case of understanding students’ perspectives on equations and equalities and on meanings of the equal sign. It is shown
that diagnostic competence comprises didactically sensitive mathematical knowledge, especially about different meanings of
mathematical objects. The theoretical claims are substantiated by a report on a teacher education course, which draws on the
analysis of student thinking as an opportunity to construct didactically sensitive mathematical knowledge for teaching for
pre-service middle-school mathematics teachers. 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
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Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The integrated theory of numerical development posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of the magnitudes to which they refer, and this magnitude understanding is central to general mathematical competence. We investigated relations among fraction magnitude understanding, arithmetic and general mathematical abilities in countries differing in educational practices: U.S., China and Belgium. Despite country-specific differences in absolute level of fraction knowledge, 6th and 8th graders' fraction magnitude understanding was positively related to their general mathematical achievement in all countries, and this relation remained significant after controlling for fraction arithmetic knowledge in almost all combinations of country and age group. These findings suggest that instructional interventions should target learners' interpretation of fractions as magnitudes, e.g., by practicing translating fractions into positions on number lines. 相似文献
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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
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数学理解的水平可以用量来刻画,而且是一个连续量,是一个模糊量。数学理解的因素一般由事实、计算、联系、分辨、表达、转化、推理、应用构成。结合数学学科和数学理解的特点提出了评价数学理解水平的定性和定量相结合的方法——加权求和法。 相似文献
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在数学教学中引入游戏教学法,可以调动学生的学习积极性,提高学生的课堂参与度。文章从提高兴趣、开展趣味数字教学,积极参与、感受数学知识的应用,趣味作业、感受数学游戏的应用,加深理解、感受知识的实践过程,训练技巧、提高解题的专业技能,综合知识、感受游戏的实际运用几方面,对引入数学游戏教学法,培养学生自主探索能力进行探究。 相似文献
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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
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J. M. Lansdell 《Educational studies》1999,25(3):327-333
This paper explores the nature of the language used when teaching mathematics to young children. It proposes that an important part of the teaching of a mathematical concept is the introduction of specific terminology. Children may need to be taught new meanings for already familiar words. The timing of these introductions to new words or meanings is critical to their understanding of the concepts being taught. It will be argued that there are two aspects of the children's learning that need to be considered. First, their understanding of the concept being introduced, and secondly, their learning the appropriate word to describe that concept. By assessing children's understanding of new mathematical concepts through their own use of the terminology, the teacher can then negotiate new meanings with them through practical experiences, introducing new word meanings only when the concepts have been understood. 相似文献