V/A模型及其在数学解题中的指导作用

视觉空间表征与言语分析表征相互作用解题模型(Visualizer/Analyzer模型,下称V/A模型)认为,在解题过程中,存在多层次的、相互作用的视觉化思维与分析性思维,每一层次的分析推理包含了4种类型的活动:从视觉表征中推论出附加性结果,数学精致化,设置一个新目标,监控环节.应用V/A模型进行解题教学时,引导学生直接观察已经画好的图形,或是根据已知条件绘制图形,然后从图形表征中观察或推导出更多的信息.图形信息与数式信息相互补充和交互作用,从中推导出更多结论,不断进行数学的精致化和新信息的再探究.再把从图形表征中推导出来且已精致化的信息和题目中的信息相互结合,设置新的目标,继续开展解题活动,且时时进行解题监控.     

小学生数学问题解决中的"视觉-空间表征"

"视觉-空间表征"是采用视觉表象的表征方式,空间视觉化能力是个体对刺激情境进行"视觉-空间表征"的能力,前者成为小学生解决数学问题的主要心理机制之一,后者则成为影响小学生能否成功解决数学问题的重要主体因素.V/A模型阐述了"视觉-空间表征"与数学问题解决、空间视觉化能力的关系及其在数学问题解决中的作用机制."视觉-空间表征"包括图像表征、图式表征两种,图像表征是图式表征的基础,也是低年级小学生数学问题解决的有效表征方式.     

如何运用图式表征思考数学问题

一、问题的提出 认知心理学家认为,在解答数学问题的时候,学生的头脑中会呈现相应的表象,也可以说是人的内部表征在运作.表征,就是信息在头脑中的呈现方式.在教学中,教师可以通过学生的外在表征优化学生的思维.表征技术是针对数学学困生的教学干预措施之一.事实上,数学学困生有基本算数技能上的缺陷,他们面对的更大的困难是数学解题. 一些认知心理学家把问题表征划分为言语分析表征和视觉空间表征两大类.前者主要借助言语逻辑进行,后者主要通过建立视觉空间图形进行.     

关于数学"问题空间"的研究

问题空间是解决问题过程中的一个重要因素.问题空间有多种表征形式,解题者可以通过理解问题意义和意图,对问题进行另一种表述,设想问题已经解出等途径形成正确合理的问题空间.解题教学要揭示问题空间的形成过程,要给学生充分表征问题的机会.     

试论对物理习题的表征问题

1问题的提出我们在进行物理解题时,首先要对习题进行简约化的描述,在心理上对习题的情景和要素进行表征.解题的心理表征通常有抽象表征和形象表征之分.那么,采取何种形式来表征,这不仅与解题者的思维方式、思维习惯,而且还与解题者的经验、解题策略等因素有关.对习题的情景和要     

基于内外部表征的数学高考应用题分析

在数学应用题的解决过程中,学生对问题表征方式的不同将影响学生对解题策略的选择.表征分为内部表征与外部表征,外部表征对应用题解决的影响因素包括文字表征、符号表征、图表表征、背景表征等;内部表征对应用题解决的影响因素包括概念表征、命题表征、概念图表征以及图式表征等.两种表征具有不同的结构及特征,对应用题的解决具有不同的机制,通过内外部表征两个方面对高考数学应用题的分析,认识内外部表征对应用题解决的具体作用.     

小学生作图分析数学问题的自觉性研究

在小学数学教学中,运用画图和列表分析解决数学问题是图式表征的一种外在表现形式.图式表征对解题有促进作用.本研究采用测试与访谈的方法,利用实验数据分析当前小学生数学解题过程的表征类型,以及影响学生作图分析自觉性的因素,提出具有针对性的教学建议,从而帮助学生学会更好地在多元表征的前提下发挥图式表征思考的作用.     

视觉经验缺失对盲人熟悉环境空间表征的影响

研究盲人对熟悉环境的空间表征对于盲人的空间认知和定向行走具有重要意义.本研究通过摆放模型的方式,探究了盲人对熟悉环境空间表征之特点,结果发现视觉经验缺失对盲人熟悉环境空间表征造成了不利影响,先天盲被试对环境空间表征较弱,不能够对环境形成整体的理解,而后天盲被试对环境空间表征较为精确,表现与明眼人相当.性别和环境熟悉度对盲人熟悉环境空间表征没有影响.     

言语信息激活对中文数字空间表征的影响

为了考察言语信息激活对中文数字空间表征的影响,采用含有中文数字的汉语词(如"二胡")作为实验刺激,让被试对其中的中文数字分别做奇偶判断和大小判断.实验结果发现:(1)在奇偶判断任务下,激活中文数字的言语信息,没有产生空间-数字反应编码联合效应(SNARC效应):(2)在大小判断任务下,激活中文数字的言语信息,产生了显著的SNARC效应.实验结果表明,在奇偶判断任务下,如果激活中文数字的言语信息,中文数字不会进行空间表征,而在大小判断任务下,如果激活中文数字的言语信息,则不会对中文数字的空间表征产生影响.     

知识可视化视觉表征的形式分析

在教育技术领域,知识可视化指视觉表征形式,与此相对应的是承载知识的图解手段。知识可视化的视觉表征并非孤立的单位,而是符号的系统。根据视觉形式分为表层形式和深层形式,可以分别阐释知识可视化视觉表征的形式特征。知识可视化视觉表征的表层形式为色彩、线条和大小等材料因素,深层形式为线性结构、循环结构、圆形结构和网状结构和隐喻形式等空间关系。知识可视化视觉表征的形式设计中,需要构建视觉表征的结构关系,展现内容性元素;应用线条、色彩和大小等材料因素,发挥修饰性作用;文字符号与视觉形式结合,明晰所指代的内容。     

图形-背景理论视角下“前”表时间的空间隐喻研究

用汉语方位词"前"表示时间,实际上是一种空间隐喻,它既可以表征过去的时间,又可以表征未来的时间。拟以图形-背景理论为依据,从自我中心表征、地标表征和去自我中心表征层面来研究汉语方位词"前"表时间的空间隐喻。研究表明当观察者从自我中心表征的层面来看,"前"表征过去的时间;当观察者从地标表征的层面来看,"前"表征未来的时间;当观察者从去自我中心表征的角度来看,"前"既可以表征过去,又可以表征未来。     

Students’ reported justifications for their representational choices in linear function problems: an interview study

Thirty-six secondary school students aged 14–16 were interviewed while they chose between a table, a graph or a formula to solve three linear function problems. The justifications for their choices were classified as (1) task-related if they explicitly mentioned the to-be-solved problem, (2) subject-related if students mentioned their own characteristics as representational users, (3) context-related if contextual features surrounding the choice were mentioned and (4) representation-related if formal characteristics of the representations were pointed out. Justifications were mostly task- and subject-related, although contextual and representational features also played an important role. Some students (reportedly) tried to reconcile different (task-, subject-, context- and representation-related) factors before selecting a representation, which was interpreted as an attempt to use their meta-representational competence to make appropriate representational choices. The influence of the didactical contract and the experimental contract on students’ representational choices, as well as the tensions between them, are also discussed.     

External and internal representations in the acquisition and use of knowledge: visualization effects on mental model construction

This article investigates whether different formats of visualizing information result in different mental models constructed in learning from pictures, whether the different mental models lead to different patterns of performance in subsequently presented tasks, and how these visualization effects can be modified by further external representations during task performance. A total of 80 university students learned from an illustrated text different day times and different dates exist simultaneously on the earth. One half of the participants received the text combined with pictures visualizing the earth as a kind of carpet (carpet pictures), whereas the other half received the text combined with pictures visualizing the earth surface as a circle (circle pictures). After learning, the participants received a test including different kinds of tasks. In both visualization groups, one half of the participants solved the tasks with an additional external representation, whereas the other half solved the tasks without an external representation. The findings indicate that the form of visualization affects the structure of mental models. Different structures of mental models result in different patterns of performance, when individuals solve tasks based only on their mental representations acquired during their previous learning. However, these effects decrease, when further external representations are made available to the learners. The findings are discussed within a broader framework of learning with multiple external representations.     

Developing a ‘big picture’: Effects of collaborative construction of multimodal representations in history

Many pupils have difficulties with the abstract verbal information in history lessons. In this study we assessed the value of active construction of multimodal representations of historical phenomena. In an experimental study we compared the learning outcomes of pupils who co-constructed textual representations, visual-textual representations, or visual-textual representations integrated in a timeline. 85 pupils in pre-vocational secondary education, aged 12–13, worked in dyads on a series of four history tasks. All pupils took a pre-test, post-test and retention test. Results show that working on visual-textual representations integrated in a timeline leads to higher short-term results than co-constructing textual representations. Dialogue analyses for two dyads working in the condition with visual-textual representations integrated in a timeline indicate that the extent to which pupils verbally integrate textual and visual information differs for the four different tasks.     

On the difficulties to resurrect the beyond. A commentary on the article Learning beyond the body by Juan-Ignacio Pozo / Sobre las dificultades para resucitar el más allá. Un comentario sobre el artículo Aprender más allá del cuerpo de Juan-Ignacio Pozo

This commentary follows Pozo’s critique of psychological theories rooted in the ‘cognitive revolution’ prompted by the emergence of computer technologies in the mid-twentieth century. The core of his criticism is the assumption of the mind/body dualism built in these theories. Pozo makes the case for an approach striving to integrate mind and body while postulating the notion of a basic incarnate mind, which grows beyond the restrictions of the body by mastering the symbolic formal systems of our culture. I argue that this vision smooths the mind/body dualism without overcoming it. I elaborate on four areas in which Pozo’s theory coincides with assumptions characteristic of the mind/body dualism: explicitness, formal notations, animal cognition and representations.     

Beyond the dual mind: the cultural reconstruction of embodied representations. Response to commentaries from the article Learning beyond the body / Más allá de la mente dual: la reconstrucción cultural de las representaciones encarnadas. Respuesta a los comentarios al artículo Aprender más allá del cuerpo

In the responses to the original article, the necessity of adopting an embodied approach in the study of the mind instead of the traditional symbolic approach in classical cognitive psychology is assumed. However, as soon as the nature of that embodied mind and its relationship to explicit representations mediated by semiotic cultural devices is delved into, that consensus gives way to significant criticism and discrepancies. Without wishing to end the debate, but rather open or ignite it, this article seeks to respond to some these observations, grouping them into four sections: (1) the acceptance of the body as a representational device; (2) the risk of incurring a new dualism when differentiating an embodied and implicit mind from a symbolic and explicit one; (3) the transformation processes of mental representations and functions in development as well as in instruction; and (4) the implications of these reflections on the relationships among mind, brain and culture.     

无意识思维或直觉：基于决策机制的探讨

为探讨无意识思维是否等同直觉,本实验研究发现：（1）被试的无意识思维与直觉在表征极化上并无显著差异,且均更关注极端室友;（2）无意识思维和直觉在表征聚合上存在显著差异,前者的聚合分数显著高于后者,且只有无意识思维产生了表征聚合。上述结果表明,无意识思维并非等同直觉,二者属不同思维过程。本研究建议从更细致的角度探讨无意识思维与直觉的机制,以增进对无意识、自动化思维过程的认识。     

The pedagogical potential of drawing and writing in a primary science multimodal unit

In consideration of the potential of drawing and writing as assessment and learning tools, we explored how early primary students used these modes to communicate their science understandings. The context for this study was a curricular unit that incorporated multiple modes of representation in both the presentation of information and production of student understanding with a focus on the structure and function of carnivorous plants (CPs). Two science teacher educators and two first-grade teachers in the United States co-planned and co-taught a multimodal science unit on CP structure and function that included multiple representations of Venus flytraps (VFTs): physical specimens, photographs, videos, text, and discussions. Pre- and post-assessment student drawings and writings were statistically compared to note significant changes, and pre- and post-assessment writings were qualitatively analysed to note themes in student ideas. Results indicate that students increased their knowledge of VFT structure and function and synthesised information from multiple modes. While students included more structures of the VFT in their drawings, they were better able to describe the functions of structures in their writings. These results suggest the benefits for student learning and assessment of having early primary students represent their science understandings in multiple modes.     

Electromagnetic Concepts in Mathematical Representation of Physics

Our paper deals with the use of mathematics when studying the physics of electromagnetism. We have concentrated on common electromagnetic concepts (magnetic field and flux) and their associated mathematical representation and arithmetical tools. Our studies showed that most students do not understand the significant aspects of physical situations. Students have difficulty in using relationships and models specific to magnetic phenomena (the construction of relationships between concepts, and the use of mathematical formalism).