基于表征重述的机器文本理解

传统机器翻译系统缺乏联系上下文形成认知的能力,仅根据对应单词的默认含义进行翻译,容易导致语义错误等问题。通过模拟人的表征重述认知过程,提出一种新的机器文本理解与翻译方法。该方法可通过较少的实例对文本进行理解和翻译,避免出现语义理解错误问题,且无需进行繁杂的语法标注。实验表明,该方法可通过引入习得的常识,使翻译出现歧义错误的概率降低到 1%以下,并可标注出不符合常理而又无法找到更好解释的句子。     

浅谈幼儿数学表征能力的培养

文章论述了当前幼儿园数学教育中培养幼儿数学表征能力的可能性和必要性,对幼儿在数学表征中所接触到的符号进行了分类与概括,具体阐述了培养幼儿数学表征能力的策略:一是让幼儿通过充分感知积累表象,二是让幼儿识别数字、掌握符号技能.三是让幼儿在操作探索中建立匹配和对应关系,四是让幼儿在特设的问题情境中用符号自由表达,五是让幼儿通过交流评价学会符号转换.     

Affect and Meta-Affect in Mathematical Problem Solving: a Representational Perspective

We discuss a research-based theoretical framework based on affect as an internal representational system. Key ideas include the concepts of meta-affect and affective structures, and the constructs of mathematical intimacy and mathematical integrity. We understand these as fundamental to powerful mathematical problem solving, and deserving of closer attention by educators. In a study of elementary school children we characterize some features of emotional states inferred from individual problem solving behavior, including interactions between affect and cognition. We describe our methodology, illustrating theoretical ideas with brief qualitative examples from a longitudinal series of task-based interviews.     

数学符号与数学理解的关系

对数学符号、数学语言及数学理解之间的关系进行探讨，给出了用符号思想理解学习数学新概念(续创概念、新创概念)的方法。     

元认知开发与数学问题解决

元认知包括元认知知识、元认知检验和元认知监控三个成分。元认知的实质是主体对认知活动的自我意识和自我调节。根据学习的认知理论，数学学习过程是一个数学认知过程，教学教育的根本任务是发展学生的数学认知结构。数学问题解决是创造性的教学思维活动，创造心理活动本身就是人类心智活动的最高形式。因此，与其它较为低级的心理活动相比，数学问题解决更需要元认知的统摄、调节和监控。     

Aspects of Mathematical Understanding

“Teaching for understanding” is often considered to be an important educational objective. For instance, the Singapore Elementary Mathematics Syllabus (1981) states that “… pupils should know and understand mathematical ideas and principles, including the techniques and skills in mathematical computation” (p.2). As the computer is used more frequently in education and society, the aim of education should shift from training for specific skills to understanding. However, “understanding” may mean different things to different people. This paper provides an analysis of the concept of understanding and reports on a survey about mathematical understanding.     

数学理解水平评定方法及其数学模型构建研究

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。     

Preschoolers' Understanding of Plan and Oblique Maps: The Role of Geometric and Representational Correspondence

To study conditions that affect preschoolers' understanding of maps, we asked 4-and 5-year-olds to place stickers on classroom maps to show locations of objects currently in view. Varied were vantage point (eye level vs. raised oblique), map form (plan vs. oblique), and item type (floor vs. furniture locations). Even though they were working with maps of a familiar referent space, preschoolers evidenced difficulty. While an oblique vantage point did not enhance performance, using the oblique map first aided subsequent performance on the plan map. As predicted, performance on floor locations was worse than on furniture locations. Findings are discussed in relation to performance by adults given the mapping task and preschoolers given a nonreferential sticker placement task. Data suggest the importance of ( a ) iconicity and ( b ) studying geometric as well as representational correspondences in map research.     

数学问题错解的感悟

深刻剖析了数学问题错解的根源,指出预防错误的具体对策是深化数学基本概念和基本方法．     

温度梯度的数学理解

借助数学中的梯度概念,指出了热学教材中温度梯度的定义实质上只是温度梯度的模,而不是温度梯度。     

Representational Tools in Computer-Supported Collaborative Argumentation-Based Learning: How Dyads Work With Constructed and Inspected Argumentative Diagrams

This article investigates the conditions under which diagrammatic representations support collaborative argumentation-based learning in a computer environment. Thirty dyads of 15- to 18-year-old students participated in a writing task consisting of 3 phases. Students prepared by constructing a representation (text or diagram) individually. Then they discussed the topic and wrote a text in dyads. They consolidated their knowledge by revising their individual representation. There were 3 conditions: Students could use either (a) the individual texts they wrote, (b) the individual diagrams they constructed, or (c) a diagram that was constructed for them based on the text they wrote. Results showed that students who constructed a diagram themselves explored the topic more than students in the other conditions. We also found differences in the way collaborating dyads used their representations. Dyads who engaged in deep discussion used their representations as a basis for knowledge construction. In contrast, dyads who engaged in only shallow discussion used their representations solely to copy information to their collaborative text. We conclude that diagrammatic representations can improve collaborative learning, but only when they are used in a co-constructive way.     

Metacognition, General Ability, and Mathematical Understanding

The purpose of the present study was threefold: (a) to examine the extent to which kindergarten children acquire metacognitive knowledge related to mathematics; (b) to investigate the relationships between children's metacognitive knowledge and general ability; and (c) to examine the relative roles of general ability and metacognition in facilitating word problem solutions. Participants were 32 kindergarten children. Results showed that preschoolers acquired a substantial metacognitive knowledge about mathematical word problems. That knowledge was highly correlated with mathematics performance, even after general ability was controlled. The study further shows that metacognition explained more of the variance in mathematics performance than general ability. The theoretical and practical implications of the study are discussed.     

Metacognition,General Ability,and Mathematical Understanding

The purpose of the present study was threefold: (a) to examine the extent to which kindergarten children acquire metacognitive knowledge related to mathematics; (b) to investigate the relationships between children's metacognitive knowledge and general ability; and (c) to examine the relative roles of general ability and metacognition in facilitating word problem solutions. Participants were 32 kindergarten children. Results showed that preschoolers acquired a substantial metacognitive knowledge about mathematical word problems. That knowledge was highly correlated with mathematics performance, even after general ability was controlled. The study further shows that metacognition explained more of the variance in mathematics performance than general ability. The theoretical and practical implications of the study are discussed.     

关于数学素养及其培养的若干认识

数学素养是数学教育改革的目标,是提高数学教育质量的关键.在数学课程改革不断深化的今天,准确理解数学素养的概念内涵,认真分析数学素养的培养策略具有十分重要的意义.国外对数学素养研究聚焦的层面并不完全相同,作为一种评价研究,PISA没有涉及数学素养培养的对策研究,对我国数学教育的指导具有一定的局限性.国内关于数学素养的研究主要集中在数学素养内涵讨论、数学素养构成要素探析、数学素养培养策略指导等方面.从数学活动的视角进行分析,应当充分认识不同数学成分所对应数学素养的特殊内涵,并因此做好相关方面的工作.从全球教育的视角进行分析,数学教育应当积极响应并落实科学发展观,积极推进创新培养和实施全球化概念的数学素养教育.     

Masking of Children's Early Understanding of the Representational Mind: Backwards Explanation versus Prediction

3–5-year-olds heard a story involving identical twins, one of whom was absent when their ball was moved from one drawer to another. Children found it easy to infer that the twin who later went to the original location to get the ball was the one who had gone outside. Children in a comparison condition found it relatively difficult to predict where a (nonidentical) twin who was absent when the ball was moved, would search for the ball, and made the usual realist error. In further investigations involving variations on the identical twins task, children were equally successful at making the link between looking in the wrong place and having been absent, whether a backwards inference was required (as above) or a forwards one (inferring that the twin who went outside must now be the one who was at the wrong location). We ruled out one twin's physical association with the correct location as an artifactual explanation for facilitation. Children performed well whether or not the experimenter told them explicitly which twin did not know the ball had been moved. These findings support the view that children's early insight into the representational character of mind is masked in traditional prediction tests of false belief.     

中学生对函数概念的理解——历史相似性初探

高一新生和高三学生用自己的语言对函数的描述涵盖了从17世纪莱布尼兹到20世纪布尔巴基学派诸多数学家的各种定义,他们的理解与历史上数学家的理解有着高度的相似性.在中学,课本上函数的抽象定义不易于理解和记忆,学生也往往不从定义出发来理解函数;函数概念历史发展过程中的认识论障碍也会成为课堂上学生的认知障碍.在函数概念的教学中,应该恰当地借鉴历史,以帮助学生更好地理解该概念.     

数学理解及理解障碍的探究

理解在数学学习中占有重要的地位，因此数学理解障碍是数学学习障碍中的一种重要障碍．如果不注重学生是否具有理解的意向，不了解学生的认知水平，就不能帮助学生克服障碍．在教学上，可以通过创设恰当、有趣的教学情境、帮助学生生成正确的数学表象、注重数学交流等途径来排除理解障碍．     

浅议把数学工具引入本科宏观经济学教育的重要性

文章从本科宏观经济学教育中数学工具的重要性入手,以教材中LM曲线与货币政策的有效性为例,探讨了研究经济问题时单纯使用图像分析的局限性,然后剖析了货币政策乘数相对于图像分析的优势,提出了借助数学工具分析经济问题的必要性。由此提出的建议可以为未来本科宏观经济学课程体系设置提供参考。