共查询到20条相似文献，搜索用时 312 毫秒
1.
In this paper, we use theoretical frameworks from mathematics education and cognitive psychology to analyse Cauchy’s ideas of function, continuity, limit and infinitesimal expressed in his Cours D’Analyse. Our analysis focuses on the development of mathematical thinking from human perception and action into more sophisticated forms of reasoning and proof, offering different insights from those afforded by historical or mathematical analyses. It highlights the conceptual power of Cauchy’s vision and the fundamental change involved in passing from the dynamic variability of the calculus to the modern set-theoretic formulation of mathematical analysis. This offers a re-evaluation of the relationship between the natural geometry and algebra of elementary calculus that continues to be used in applied mathematics, and the formal set theory of mathematical analysis that develops in pure mathematics and evolves into the logical development of non-standard analysis using infinitesimal concepts. It suggests that educational theories developed to evaluate student learning are themselves based on the conceptions of the experts who formulate them. It encourages us to reflect on the principles that we use to analyse the developing mathematical thinking of students, and to make an effort to understand the rationale of differing theoretical viewpoints. 相似文献
2.
基于建构主义的数学概念转变学习 总被引：9，自引：0，他引：9
概念转变学习是学生原有概念的改变、发展和重建,是学生的前概念向科学概念的转变.日常概念、概念意象、迁移等因素是数学概念转变学习中产生错误概念的主要原因.根据概念转变的途径、机制和条件理论,概念转变学习的教学策略:(1)了解学生已有知识经验,促进日常概念向科学的数学概念转变;(2)引发认知冲突,辨清新旧界限以实现数学概念转变学习;(3)重视概念生成的凝聚,构建概念网络. 相似文献
3.
随着新的教育理念的更新发展,对于数学教学的要求也不再是让学生学习基础的数学知识,而是要求培养学生的核心素养,切实培养学生应用数学知识解决实际问题的能力,为学生的全面发展奠定良好的教育基础。为此,初中教师需要结合学生的特点,主动转变教育理念,坚持以学生为主体,相信学生并且在教学时以核心素养为标准科学选择教学方法。 相似文献
4.
We analyze the interrelations between prospective and practicing teachers' learning of the mathematics of change and the development
of their emerging understanding of effective mathematics teaching. The participants in our study, who were all interested
in teaching secondary mathematics, were mathematics majors who had significant formal knowledge of the fundamental concepts
of calculus prior to taking our courses, but who often experienced and expressed procedural orientations toward the teaching
of mathematics. To address this difficulty, we developed novel computer-based activities to challenge the participants' mathematical
understandings and required them to use technology during short teaching episodes they conducted with younger students. To
analyze our participants' understandings, we developed a framework that juxtaposes the roles of the participants as students
and teachers, and their understanding of mathematics and of pedagogical strategies. Our analysis of the participants' views
from these different perspectives enabled us to see simultaneously the intertwined development of subject matter insights
and specific views of teaching.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
5.
朱琳琳 《襄樊职业技术学院学报》2012,11(4):28-30
微积分是高等数学教学的重要单元,学生在学习微积分时会接触大量的导数方程、积分和相关演算等知识,理解起来难度很大。文章列举Mathematica软件中对微积分的应用,通过这些应用可以解决学生学习数学时遇到的困难。 相似文献
6.
Although the field of educational neuroscience has grown in recent years, little research has been conducted on conceptual change and science learning through an educational neuroscience framework. Educational neuroscience is frequently used to study processes of language and mathematics cognition, but is not extensively applied to conceptual change and science learning. This review integrates insights from extant conceptual change educational neuroscience studies to inform the fields of educational psychology and science education. These new insights shed light on the persistence of misconceptions and the roles of error detection, inhibition, executive function, and memory in conceptual change. Future directions for the study of conceptual change and educational neuroscience are discussed. 相似文献
7.
In learning conceptual knowledge in physics, a common problem is the development and differentiation of concepts in the learning process. An important part of this development process is the re-organisation or re-structuring process in which students’ conceptual knowledge and concepts change. This study proposes a new view of concept development with explicit attention given to concept development from the level of knowledge-as-pieces to the level of knowledge-as-theory. The proposed new picture is based on the view that concepts are complex constructs essentially embedded in a larger system of knowledge. Three closely connected aspects require our attention: (1) conceptions of concepts, (2) conceptions of knowledge systems, and finally, (3) conceptions of the process of change. The potential advantages of this prospective are demonstrated through the re-analysis of the concept development in the well-known case of electric current and voltage. The results show that in the concept development process, both causal knowledge and coherence of the knowledge system play crucial roles. Finally, the study points out how the theoretical position proposed here directly impacts conceptions of learning and instruction as well as what solutions are sought for problems in learning—or even what is considered a problem or success in learning. 相似文献
8.
微积分思想是微积分知识的精髓,是知识转化为能力的桥梁。只有充分认识和领悟微积分思想、方法的来源,学生才能真正地理解、领会与应用微积分知识来分析、解决实际问题。在《高等数学》课程教学过程中,实施融入数学史素材,挖掘微积分思想源头,充实教学内容、更新教学设计、丰富课堂教学方式和课后练习,以求达到降低数学内容抽象性和学生学习数学的恐惧感,提升学生学习数学的兴趣与应用数学的意识和发现、分析、解决问题的能力。 相似文献
9.
In this paper I discuss my experience in using the inverted classroom structure to teach a proof-based, upper level Advanced Calculus course. The structure of the inverted classroom model allows students to begin learning the new mathematics prior to the class meeting. By front-loading learning of new concepts, students can use valuable class time for exploring and solving complex problems, with the instructor available for guidance and assistance. This paper compares student performance in the inverted classroom with student performance in the direct instruction classroom. I also share student perceptions of the inverted classroom experience. 相似文献
10.
随着新课程改革的不断深入,小学数学教师也应转变传统的教学观念,创新数学教学方法,以达到新课程改革对小学阶段数学教学目标的新要求。小学阶段的数学教学能为学生未来更好地学习数学知识打好理论基础,在这一段时间内培养学生的良好学习习惯能使学生的学习达到事半功倍的效果。因此抓住这一关键期对学生进行教育,对帮助学生形成数学思维、提高学生运用数学知识解决实际问题的能力有重要作用。基于此,本文将研究在新课改背景下小学数学教学方法的几种创新形式。 相似文献
11.
The theoretical background and different methods ofconcept mapping for use in teaching and in research on learning processes are discussed. Two mathematical projects, one on fractions and one on geometry, are presented in more detail. In the first one special characteristics of concept maps were elaborated. In the second one concept mapping allowed students' individual understanding to be monitored over time and provided information about students' conceptual understanding that would not have been obtained using other methods. Regarding the students' individual concept maps in more detail there were some additional findings: (i) The characteristics of the maps change remarkably from fourth grade to sixth grade; (ii) There is some evidence that prior knowledge related to some mathematical topics plays a very important role in students' learning behaviour and in their achievement; (iii) Concept maps provide information about how individual students relate concepts to form organised conceptual frameworks; (iv) Long-term difficulties with specific concepts are able to be traced. These findings are discussed with regard to results of other studies as well as to their implications for the teaching of mathematics in the classroom. 相似文献
12.
随着新一轮数学课程改革的进行,微积分再一次走进中学数学.微积分课程的教育价值主要有:增强了高中数学的严密性,优化了解题过程、扩展了研究范围,培养了学生解决实际问题的能力,发展了学生的数学思维能力,提高了学生的数学文化素养.要实现微积分的教育价值,需要兼顾不同层次学生对微积分的求知需求,把握高中微积分与大学微积分不同的尺度定位,防止微积分方法对高中基础知识的消极影响. 相似文献
13.
One of the factors affecting students' learning in science is their existing knowledge prior to instruction. The students' prior knowledge provides an indication of the alternative conceptions as well as the scientific conceptions possessed by the students. This study is concerned primarily with students' alternative conceptions and with instructional strategies to effect the learning of scientific conceptions; i.e., to effect conceptual change from alternative to scientific conceptions. The conceptual change model used here suggests conditions under which alternative conceptions can be replaced by or differentiated into scientific conceptions and new conceptions can be integrated with existing conceptions. The instructional strategy and materials were developed for a particular student population, namely, black high school students in South Africa, using their previously identified prior knowledge (conceptions and alternative conceptions) and incorporate the principles for conceptual change. The conceptions involved were mass, volume, and density. An experimental group of students was taught these concepts using the special instructional strategy and materials. A control group was taught the same concepts using a traditional strategy and materials. Pre- and posttests were used to assess the conceptual change that occurred in the experimental and control groups. The results showed a significantly larger improvement in the acquisition of scientific conceptions as a result of the instructional strategy and materials which explicitly dealt with student alternative conceptions. 相似文献
14.
Jörg Härterich Christine Kiss Martin Mönnigmann Moritz Schulze Darup Roland Span 《European Journal of Engineering Education》2012,37(3):255-266
First-year engineering students often complain about their mathematics courses as the significance of the difficult and abstract calculus to their field of study remains unclear. We report on the project MathePraxis, a feasibility study which was designed as a means to give first-year students some impression about the use of mathematics in real practice. We aim to increase the motivation and retention rates among engineering students by connecting the contents of the first-year mathematics lectures with practical applications. We developed three projects, two of which are described in this article: an inverted pendulum considered as a model for the automated control within a Segway and a study on the optimal design of a ribbed cooler. In this article, we briefly present the mathematical content of the projects and report on their implementation. 相似文献
15.
中学数学与高数有明显的差别,授课的方式和学习方法在一定程度上也都发生了变化。对于新入学的大学生来说,想要从比较简单的、基础性的中学数学思维模式转到抽象又复杂的高数学习中难度较大。因此,要帮助新入学大学生适应这种新的变化,教会他们学会如何听课,引导学生掌握基本概念,做好预习、复习,以适应新的环境,学习好高等数学。 相似文献
16.
金卫雄 《连云港师范高等专科学校学报》2001,(4):60-62
学习数学的目的是应用，但是学校数学与现实数学之间存在很大差距，要让学生将数学应用于现实却非常之难。本文就数学应用题，到底难在何处？本文从其源头处作一番审视。 相似文献
17.
微积分是理工科的基础课程,学好微积分对后续课程的学习以及对学生专业素质的培养都具有十分重要的意义.而极限是微积分的基石,因为极限的思想和方法是解决微积分问题的工具.极限定义教学是整个微积分教学的重点和难点,是学生学习大学数学的一道障碍.提出了9个结合破解极限定义教学难题的综合性方法:感性与理性相结合;现象与本质相结合;数与形相结合;分析与综合相结合;正面与反面相结合;数列极限与函数极限相结合;理论与实践相结合;传统与现代相结合;内因与外因相结合. 相似文献
18.
随着美国公众认识到个体的数学学习与数学能力在其发展中的重要意义,"数学等于机会"等理念获得广泛认同,数学教育中的公平问题也愈加受到关注。在美国中小学,不同族裔、家庭背景、城乡区域的学生在数学学习水平上存在着明显差距。导致差距的原因错综复杂,可以从教育资源配置、家庭背景、文化观念等方面予以阐释。 相似文献
19.
Yan Ping Xin Jia Liu Sarah R. Jones Ron Tzur Luo Si 《The Journal of educational research》2016,109(4):436-447
Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of constructivist-oriented mathematics instruction involving students with LD, the authors conducted a case study to analyze teacher–student interactions during constructivist-oriented small group instruction involving a student with LD. The student demonstrated, to a certain degree, the ability to reason mathematically when provided with appropriate opportunities and prompting. However, given the limited intervention time, his reasoning and problem solving did not seem to go beyond the semiconcrete level of operation, which may have inhibited his solving of complex word problems with large numbers. Findings indicate that more efforts are needed to support students, those with LD in particular, in their transitions from concrete or semiconcrete to abstract conceptual understanding and problem solving. 相似文献
20.
Hsiao‐Ching She 《科学教学研究杂志》2004,41(2):142-164
This article examines how the Dual‐Situated Learning Model (DSLM) facilitates a radical change of concepts that involve the understanding of matter, process, and hierarchical attributes. The DSLM requires knowledge of students' prior beliefs of science concepts and the nature of these concepts. In addition, DSLM also serves two functions: it creates dissonance with students' prior knowledge by challenging their epistemological and ontological beliefs about science concepts, and it provides essential mental sets for students to reconstruct a more scientific view of the concepts. In this study, the concept “heat transfer: heat conduction and convection,” which requires an understanding of matter, process, and hierarchical attributes, was chosen to examine how DSLM can facilitate radical conceptual change among students. Results show that DSLM has great potential to foster a radical conceptual change process in learning heat transfer. Radical conceptual change can definitely be achieved and does not necessarily involve a slow or gradual process. © 2004 Wiley Periodicals, Inc. J Res Sci Teach 41: 142–164, 2004 相似文献