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刘艳霞 《中国教育技术装备》2023,(11):111-113
数学概念是数学教学的理论基础和底层逻辑,是数学知识体系建立的基础,学生在数学的解题逻辑上必须先从数学概念入手,以数学概念作为解题的开端和突破口。而对于职业院校的学生来说,数学是学科知识中比较难理解的一门学科,数学概念教学质量对于学生打好数学基础有重要作用。从我国职高学校数学概念教学入手,论述数学概念的重要性、原则以及我国职高数学概念教学面临的问题,并提出相应的解决策略。 相似文献
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数学概念是数学的基石，帮助学生理解、掌握数学概念是数学教学的一项重要任务。本文通过对“概念同化教学模式”和“APOS理论教学模式”的比较，就在数学概念教学中，应如何帮助学生正确、有效地掌握数学概念提出相关建议。 相似文献
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理论经济学的数学化关键在引入数学思维 总被引：2，自引：0，他引：2
理论经济学的数学化,一个重要前提是需要真正理解数学思维,而只有理解了数学,数学思维才能相应地产生出来,在对哲学的概念反思和数学的演绎推理进一步认识的过程当中,还可以引申到认识物理学,生物学,经济学三学科的关系,有关理论经济学研究如何使数学思维的应用达到最优等问题,则必须通过已有的研究实践活动去考察分析。 相似文献
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Pirie-Kieren数学理解模型直观地描述了学生数学理解的过程和本质,是从认知的观点全面认识数学理解的理论.本文从创设问题背景,引发积极理解意向;创设探究活动,促进产生概念表象;创设反思对比,引导认识概念本质;创设应用问题,促使获得理性认识这四个方面,阐述如何运用Pirie-Kieren数学理解模型设计弧度制的教学,拟对高中数学概念的教学策略进行探讨,从而构建促进关系性理解的数学课堂. 相似文献
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夏繁军 《中学数学教学参考》2023,(4):14-17
分析课程标准对本章的定位,明确本章的核心概念、数学思想方法,着重发展的数学核心素养,需要转变的重要观念,再对数学概念进行分级抽象概括,逐步提取数学大概念。设计指向数学大概念理解的基本问题,用问题驱动学生逐步理解数学大概念。 相似文献
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在数学学习中,数学理解占有非常重要的作用,而数学理解又以数学概念理解为前提和基础。而现行的高中数学教材中不断涌现的密集而又抽象的数学概念,给刚刚步入高中阶段的学生带来了沉重的理解负担。本文作者旨在对高中学生的数学概念理解状况进行问卷调查,探索影响学生数学概念理解的因素,并提出了改善学生数学概念理解的几点教学建议。 相似文献
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在数学学习中,如何理解重要的数学概念是非常重要的学习环节,我们以对三角函数概念的理解为例,提供了理解数学概念的思路． 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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数学概念学习中,概念理解是首要的;认知心理学研究表明,学生数学概念的获得是一个对概念心理表征的构建过程;相关的数学概念表征的调查研究也证明了数学概念表征与概念理解是相互促进、相互制约的;根据学生在数学概念学习中,对因概念表征缺失引起的概念理解障碍进行认知分析。 相似文献
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This article discusses two mechanisms through which understanding static mathematical concepts (basic and more advanced mathematical concepts) in terms of fictive motions or motion events enhance our understanding of these concepts. It is suggested that at least two mechanisms are involved in this enhancing process. The first mechanism enables us to employ both the motor system and the visual system as two contributing cognitive resources to process the static concept. When one representation of a mathematical concept is transformed into another representation, there is a shift in the mode of processing. This shift facilitates the process of employing new cognitive resources such as the motor and visual systems. The second mechanism, which is a special form of mental simulation, enables us to simulate the process of formation of the static concept, which, in turn, makes it easier for us to understand the structure and properties of the static concept. 相似文献
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美国数学教育家杜宾斯基提出的APOS理论是一种建构主义的数学学习理论,他将数学概念的建构分为Action、Process、Object、Scheme四个阶段.在对该理论的认识基础上,结合高职学生数学学习认知的心理特点,对化工专业高等数学概念的教学进行探讨,并就如何进行数学概念教学设计作了探索,使学生主动建构其概念体系. 相似文献
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Making the transition to formal proof 总被引：1，自引：0，他引：1
Robert C. Moore 《Educational Studies in Mathematics》1994,27(3):249-266
This study examined the cognitive difficulties that university students experience in learning to do formal mathematical proofs. Two preliminary studies and the main study were conducted in undergraduate mathematics courses at the University of Georgia in 1989. The students in these courses were majoring in mathematics or mathematics education. The data were collected primarily through daily nonparticipant observation of class, tutorial sessions with the students, and interviews with the professor and the students. An inductive analysis of the data revealed three major sources of the students' difficulties: (a) concept understanding, (b) mathematical language and notation, and (c) getting started on a proof. Also, the students' perceptions of mathematics and proof influenced their proof writing. Their difficulties with concept understanding are discussed in terms of a concept-understanding scheme involving concept definitions, concept images, and concept usage. The other major sources of difficulty are discussed in relation to this scheme.This article is based on the author's doctoral dissertation completed in 1990 at the University of Georgia under the direction of Jeremy Kilpatrick. 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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Ability stereotyping in mathematics 总被引：1，自引：0，他引：1
Kenneth Ruthven 《Educational Studies in Mathematics》1987,18(3):243-253
Ability is a concept central to the current practice of mathematics teaching. However, the widespread view of mathematics learning as an ordered progression through a hierarchy of knowledge and skill, mediated by the stable cognitive capability of the individual pupil, can be sustained only as a gross global model, and is of limited value in describing and understanding the particular cognitive capabilities of individual pupils in order to plan, promote and evaluate their learning. In effect, individual pupils, and groups of pupils, are subject to ability stereotyping; characterisation in terms of a summary global judgement of cognitive capability, associated with overgeneralised and stereotyped expectations of mathematical behaviour, and stereotyped perceptions of an appropriate mathematics curriculum. 相似文献
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This paper applies APOS Theory to suggest a new explanation of how people might think about the concept of infinity. We propose cognitive explanations, and in some cases resolutions, of various dichotomies, paradoxes, and mathematical problems involving the concept of infinity. These explanations are expressed in terms of the mental mechanisms of interiorization and encapsulation. Our purpose for providing a cognitive perspective is that issues involving the infinite have been and continue to be a source of interest, of controversy, and of student difficulty. We provide a cognitive analysis of these issues as a contribution to the discussion. In this paper, Part 1, we focus on dichotomies and paradoxes and, in Part 2, we will discuss the notion of an infinite process and certain mathematical issues related to the concept of infinity. 相似文献
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Two important aspects of transfer in mathematics learning are the application of mathematical knowledge to problem solving and the acquisition of more advanced concepts, both in mathematics and in other domains. This paper discusses general assumptions and themes of current cognitive research on mathematics learning, focusing on issues of the understanding thought to facilitate transfer of mathematical knowledge. Two studies illustrating these themes are presented, one concerning students' understanding of numerical relationships involved in basic addition and subtraction combinations, the other dealing with students' understanding of algebraic expressions and transformations. Implications of these cognitive perspectives for instruction are discussed. 相似文献