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数学语言学习的心理偏差研究

【作者】 郝兴文

【导师】 傅海伦;

【作者基本信息】 山东师范大学 , 学科教学, 2003, 硕士

【摘要】 数学语言是数学活动的工具,是数学思维的载体,是记录数学知识的符号,是表达数学思想的媒体。科学发展的历史证实数学语言对科学的发展起到了至关重要的作用,是科学的语言。今天,数学在社会各个领域中的应用越来越广泛,社会的数学化程度越来越高,准确掌握与灵活使用数学语言,已是现代社会成员必须具备的基本素质。但是,学生在学习数学语言的过程中,对他往往存在许多片面的、甚至是错误的认识——心理偏差。仔细研究数学语言学习的心理偏差,了解其形成的过程,认清造成数学语言学习的心理偏差的因素,从而有效地纠正这些心理偏差,这具有积极的现实意义。纠正数学语言学习的心理偏差,可以完善学生的数学认知结构,培养学生的数学思维能力,激发学生的数学学习兴趣,落实数学的思想品德教育功能,实施数学素质教育。 通过对信息加工过程与有意义学习理论的研究,我们认为数学语言学习的心理偏差有它的形成机制: 1.感知的不全面是形成数学语言学习的心理偏差的开端。感知是学习的起点,对数学语言不全面的感知不可能实现对它的全面认识。 2.信息加工过程中的错误是造成数学语言学习的心理偏差的根源。数学语言的最终表征形式决定学生对它的认识,而数学语言在内部加工的每一阶段出现的失误,都将导致表征的不全面,从而形成数学语言学习的心理偏差。 3.已有的错误知识经验是数学语言学习的心理偏差的形成因素。学生的学习要受到已有知识经验的影响,已有知识中的错误信息、消极经验影响到数学语言的正确建构。 数学语言学习的心理偏差有它表现的形式,在对数学语言含义分析的基础上,分别讨论了学习数学文字语言、符号语言、图形语言时心理偏差的表现形式。文字语言学习中的常见心理偏差主要表现在忽视某些字、词造成概念内涵与外延的变化;对文字语言的理解不够深入,仅仅停留在表面;用特例来代替整个概念。符号语言学习的常见心理偏差主要表现存不能理解数学符号代表的对象,缺乏对数学符号所表示的数学对象的广泛性的认识;不明白符号语言表达的含义,如果将符号语言与所表达的数学含义相脱离,学生所掌握的数学语言就是毫无意义的符号游戏;掌握不了符号语言的各种变化形式,符号语言有许多的等价形式,如果只是掌握其中的一种或几种形式,对它的认识将不够充分。图形语言学习的常见心理偏差主要表现在概括不全面、直观识图,把握不准图形所反映的数学信息。 为了研究的方便,我们将数学语言学习的心理偏差分为定势性心理偏差与过程性心理偏差。在文献研究的基础上,我们分析了造成定势性心理偏差的有关因素,包括:停留性心理,就是概念或语一言的符号扩展了,但学生的思维产生惰性,停留在原来的地方;典型命题效应,一个命题一旦成为典型命题,它将成为最易提取的对象,从而影响到数货语言的学习,造成认识匕的不均等:规律性心理,这种心理是指学产川等光前学到的知法呀!!方法等做了不恰当的推J一,形成了一定的J自理准备状态:滞后性J心理,是指学生的思维发展水平滞后,造成学生在学习中的认知障碍。通过调查研究,我们分析了造成过程性心理偏差的因素。在感知过程中,造成心理偏差的因素主要有视觉、感知经验、数学语言细节、数学语言差异、数学语一言的变式;在信息加工的过程中造成心理偏差的因素主要有概念表象、数学语一言的形式化程度、缩句、日常概念、元语言、数学语言的形成过程。通过这些调查与分析,我们提出了至Ll正数学语言学习的心理偏差的教学建议- ,研究学生的实际认知水平,在研究学生的实际认知水平的基础上制定出具体的教学策略;诊断其头脑中对数学语言存在的片面认识,通过将数学语言的合理内涵告诉学什,使学才{意识到其在以前认知中的不足。 2应用变式教学,变换数学语言的不卜寸呈现形式,让学生在数学语言的不同变化形;一守1,体会至}j数学语一言的真谛,从而克服数学语言表象不全面的弱点。 污.发掘隐含条件,注重数学语言的等值转化。 4加强数学交流,修正自身认识。在数学交流中,学生用自己的语言表达对一数学语六的理解,并可以及时发现自身认识的不足,在交流中得到纠正。 :).注意辨别新旧数学语言的差异。学生只有对新旧数学语言的差异做到明确区分,才能有效促进学习的正迁移。 6.数学语言的结果与过程并重,利用过程展现数学语言的丰富内涵,帮助学生从情景记忆过渡到语义记忆,从而实现数学语言内容与形式的统一。7应用日常概念的合理因素,形成科学的数学概念。日常概念有它合理的因素,只要发挥好它的实践性、浅显性、通俗性的特长,将为数学概念的形成做好铺垫。

【Abstract】 Mathematics language (ML) is the tool of mathematics activity, the carrier of mathematics thinking, the signals of recording mathematics knowledge, the media of expressing mathematics thoughts. The history of science development proved that mathematics language plays a very important role in the developing history of science. ML is a kind of science language. Today, mathematics is applied more widely and more widely in various field of science, and the extent of mathematics application in today’s society is higher and higher. To master ML accurately and use ML flexibly is the basic quality modern society members must possess. But, in the process of learning mathematics exists students incomplete, even wrong cognition to ML psychological deviation.To carefully study students psychological deviation to ML, to know the process of forming of PD, to get a clear understanding to the factors that results in PD in ML learning and to correct these PD effectively has positive and realistic meaning. To correct students’ PD can fulfil students cognition structure to mathematics, implement students morality education function of mathematics, carry out quality education in mathematics teaching.By studying the process of information process and meanful theories of leaning, we think the formation of PD in ML learning has its reason.1.Incomplete perception is the starting point of PD occurred in ML. And perception is the beginning of learning, incomplete perception to ML can not realize overall cognition.2. Errors in the information process is the main reason resulting in PD in ML learning. The final forms of mental representation dominate students’ cognition toit. The faults occurred in every period of inner process of ML all will cause incomplete mental representation, and then form PD of ML learning.3. The wrong knowledge and experience gained before are two kinds of factors affecting the formation of PD in ML learning. The students can be affected by their experience and knowledge gained before. The wrong information and passive experience all can affect correct structure of ML.PD in ML learning has its own forms of expression. On the basis of ML analysis, separately discuss the forms of expression of PD in learning Mathematics word language, signal language and graph language. Common PD in learning word language mainly showed in the following aspects: Ignoring some words and phrases, so result in the variety of intension and extension, understanding to word language is just on the surface, not a deep understanding; using special examples to instead the entire conception. Common PD in signal language learning mainly showed in the following: can’t understand the objects the mathematics signals represent; Scare of extensive cognition to the mathematics objects which mathematics signals represent. Don’t understand the meaning expressed by signal language. The same signal forms can express different meanings, and different signal forms can express the same meaning, if student separate signal language from its maths meaning contained in it, the ML they mastered is a kind of signal game without any meaning; not mastering various forms of signal language (signal language has many equal forms) or only mastering one kind or several kinds forms, the cognition to signals are not enough. Common PD in graph language learning mainly showed in complete conclusion direct perception to the graphs through senses and inaccurate mastering to maths information.For the sake of convenience of study, we divide PD in ML learning into PD caused lay conventional thinking and PD produced in process. ON the basis of document researching, we analyse the relevant factors which result in PD caused by conventional thinking, contaning: 1. Standstell mentality. Namely, the conception or language has widened its meaning, but the students thinking produces inertia and stay at the former place, this kind of meality in fact, is to use old attitudes treating new problems; 2. Effect of typical topic: once a topic becomes a model, this top

  • 【分类号】G633.6
  • 【被引频次】6
  • 【下载频次】564
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