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数学概念
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A comparison of an experimental group which experienced the innovative strategy with a control group supported the efficacy of the innovative teaching methods in terms of learning environment, attitudes and mathematics concept development.
      
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The mathematical concept of frames is utilized in the analysis of the properties of the sequence of sampling functions.
      
The underlying mathematical concept is approved in the steganography of audio signals [3, 4].
      
This new model is simple in mathematical concept and is straightforward to be combined into the existing standard finite element code.
      
To this end one dwells only on the permanence principle of functional equations, which is not a physical but purely mathematical concept.
      
The third class coincides with computational complexity, which basically coincides with the mathematical concept of intractability.
      
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This is a comprehensive report of the findings from studies of 959 7-12yearsold child subjects from 10 districts throught China. The developmentof recognition of numbers (including transfer between figure and number),ordinals and sets of series, composition and decomposition of numbers, operationand application was explored. And on the basis of the findings the authorsdiscussed the relations between knowledge learning and development of arit-hmetical concepts, the process of this development, the environmental...

This is a comprehensive report of the findings from studies of 959 7-12yearsold child subjects from 10 districts throught China. The developmentof recognition of numbers (including transfer between figure and number),ordinals and sets of series, composition and decomposition of numbers, operationand application was explored. And on the basis of the findings the authorsdiscussed the relations between knowledge learning and development of arit-hmetical concepts, the process of this development, the environmental effects,and stages of the development.The cooperative way which they have adoptedfor several years is also remarked.

本文综合了对我国十个地区959名7—12岁儿童的协作研究结果。探讨了儿童在认数、数序和系列、数的组成、运算和应用等四个方面的发展情况,并对儿童数学概念和运算能力发展中知识学习与数概念发展的关系、发展的过程、环境的影响、发展的阶段性等方面进行了讨论,也谈到了协作方法问题。

Four sets each consisting of 3 or 5 test-items of different difficultieswere composed. to examine the stability of children's concepts of number,length, area and volume respectively, under both a screened-operation conditionand an unscreened-operation condition. In each of 13 districts throughout thecountry, 3-6-yr olds, with 30 Ss in each age-group, or 7-1l-yr olds, with20-30 Ss in each age-group, were examined individually with the "clinicalmethod". As the general results preliminarily suggest: The stability...

Four sets each consisting of 3 or 5 test-items of different difficultieswere composed. to examine the stability of children's concepts of number,length, area and volume respectively, under both a screened-operation conditionand an unscreened-operation condition. In each of 13 districts throughout thecountry, 3-6-yr olds, with 30 Ss in each age-group, or 7-1l-yr olds, with20-30 Ss in each age-group, were examined individually with the "clinicalmethod". As the general results preliminarily suggest: The stability of children'sconcepts in mathematics, manifesting both in their performances of the examinationand in their cognitive levels of resolving processes, develops with the increaseof age. The stability of one kind of mathematical concepts may emerge earlieror later, depending on the kind and difficulty of test-problems used. Underthe unscreened-operation condition the stability of concepts is higher than thatunder the screened-operation condition. The performance under the screened-operation con-dition may be promoted by the demonstration or enlightenment ofuncreened-operation. Both these two events are more significant during thedeveloping period of concepts. No nationality-or sex-differences are found betweenchildren on the same culture-background. And the stability of concepts seems todevelop in an order of number, length, area and volume. According to theauthors, there exists a developmental process of the concepts from unstableto stable, and stability per se is not absolute, but conditional, it is by nomeans fixed to occur at a certain year of chronological age.

设计了四组试验项目,每组3或5个难度不同的项目,在掩盖操作和不掩盖操作条件下分别检查儿童数、长度、面积、体积等概念的稳定性。全国13个地区每地区以“临床法”个别试验4—6岁儿童每年龄组30人,或7—11岁儿童每年龄组20—30人。总的结果初步表明:儿童数学概念的稳定性随年龄而发展,表现于解答课题的成绩和解答过程的认知水平两个方面。数学概念稳定性的发展因课题的类型和难易而异其先后。数学稳定性在不掩盖操作条件下表现高于在掩盖操作条件下。在不掩盖操作演示的启发下,掩盖操作条件下的成绩有提高。这两者都是在相应数学概念正处于发展中的阶段比较明显。在文化条件相等的情况下未发现儿童数学概念稳定性的民族差异和性别差异。儿童数学概念稳定性发展的顺序似乎是数、长度、面积、体积。作者认为,数学概念从不稳定到稳定有一个发展过程;稳定性本身不是绝对的,而是有条件的,并非出现于特定的年龄。

Analyses the properties and the characteristics of mathematics recognition structure, raises the transverse structure of mathematics recognition structure: It contains mathematics concepts, theories, formula at the bottom. It also contains mathematics methods, the skills of solving mathematics problem in the middle. It also contains mathematics methodology, the viewpoint of mathematics at the top too. The author also raises the longitudinal structure of mathematics recognition structure: It consists of many...

Analyses the properties and the characteristics of mathematics recognition structure, raises the transverse structure of mathematics recognition structure: It contains mathematics concepts, theories, formula at the bottom. It also contains mathematics methods, the skills of solving mathematics problem in the middle. It also contains mathematics methodology, the viewpoint of mathematics at the top too. The author also raises the longitudinal structure of mathematics recognition structure: It consists of many “lattice” pyramids and it is tridimensional and reticular. The author raises several steps of optimizing the mathematics recognition structure according to the structure of the mathematics recognition structure.

从分析数学认知结构的性质和特点出发,提出了数学认知结构的横结构:数学认知结构既包含处于底层次的数学概念、定理、公式等,又包含处于中间层次的数学方法和解题技巧,还有处于高层次的数学方法论和数学观;还提出了数学认知结构的纵结构:数学认知结构是一个立体网状的、其中包含着许多大大小小的“金字塔”的“格”结构.据此提出了构建良好数学认知结构的几点措施.

 
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