关于认知风格与数学解题的调查研究

1　问题的提出认知风格 ,也称认知方式 ,一般指个体在加工信息 (包括接受、贮存、转换、提取和使用信息 )时习惯采用的方式 .认知风格有场独立型与场依存型、冲动型与思考型、求同型与求异型等类型 .认知风格与个体的个性、经历、受教育过程等有关 ,对个体的学业成绩有一定影响 .这已为许多学习心理学的实验和理论所证实 .然而 ,在数学解题过程中是否存在明显不同的认知风格 ?认知风格的不同对解题有何影响 ?认识认知风格的不同在教学中有何实际意义 ?目前尚未见到太多报道 .本研究的目的就是对以上三个问题进行调查和探究 .2　研究的设计本…     

基于形态发生系统的建设项目风险场研究初探

动态风险问题本质上属于风险认知问题,可基于风险场来探讨其方法论.引入形态发生系统理论,探讨了如何基于形态发生过程来认识风险场.首先指出风险场问题本质上属于风险的量化与表达问题,风险场为一种形态场,是风险系统形态发生的原因.其次剖析了风险与形态的关联,指出风险为非生命形态.再次,剖析了概率风险的形态发生过程,并构建了建设项目风险场研究的框架.最后,指出风险分析中的函数识别关系可以用基于数据的形态发生过程来进行估计的形态发生估计方法来解决.研究有助于完善建设工程风险分析理论,并有助于从形态角度探索风险系统的发育机制.     

有邻集上的一般状态的整体马氏场

在[1]、[2],[3]中,分别就有邻集上的一般状态的马氏性进行了讨论,引进了马氏场,完全马氏场等基本概念,并且研究了它们的存在性及唯一性,以及它们之间的关系。但在[1]、[2]、[3]中所引进的马氏场只是一种局部马尔可夫性。本文主要是在有邻集上引进整体马尔可夫性的概念,并研究整体马尔可夫性与局部马尔可夫性之间的关系,并指出在树上,整体马氏场与完全马氏场等价。     

从变换场理论研究大块运动下悬浮体的粘滞率

该文把变换场理论中的变换场概念引进稳态悬浮体领域,建立了确定悬浮体的形变张量场的积分方程,在此基础上计算了稳态悬浮体的粘滞率张量,从而为进一步研究悬浮体的流变学性质开辟了一种新方法。     

自旋s=1的半无限无规场伊辛模型的临界行为

该文应用平均场重整化群方法,对s=1的半无限简立方伊辛铁磁体在表面无规场(三峰分布)存在时的表面临界行为进行了研究,得到了系统的表面相图.     

广义平稳高斯场的附属场的大（小）标度极限定理

本文证明了在适当条件下,广义平稳高斯场的附属场的大(小)标度极限存在,主要结果见定理3.1和定理3.2。     

一种颗粒随机分布复合材料弹性位移场均匀化方法的理论分析

针对计算随机颗粒分布复合材料弹性位移/力学场时,采用样本求力学性能期望值需要花费大量时间和内存的问题,给出了一种计算颗粒随机分布复合材料弹性位移场的均匀化方法,并且获得了均匀化位移场与期望位移场之间的一种理论误差.首先由复合材料的特性定义了均匀化理论的随机场和概率空间,然后结合单胞内颗粒随机分布复合材料的特性做了一些合理假设得到了在整个颗粒随机分布复合材料组成区域上的期望位移场与均匀化位移场之间的一种理论估计,最后对此法所具有的优点、适应范围,缺点、以及需要改进的地方做了进一步讨论.     

理想塑性晶体裂纹顶端渐近场

本文从晶体三维塑性流动理论出发,导出了双滑移理想塑性晶体平面应变问题曲基本方程。利用这些方程求得了静止裂纹顶端应力变形场。该场包含有弹性角形区并且整个应力变形场是连续的。进而导出了定常扩展裂纹顶端应力变形场。该场由五个角形区组成:裂纹前方有两个塑性区,它们的边界是速度场间断面。裂纹面附近有一个二次塑性区,中间是两个卸载弹性区,它们交界面也是个速度场间断面。该五个角形区不是唯一的。本文得到了一簇解答。最后本文分析了这些解答在面心立方和体心立方晶体中的应用。     

对基频光与低强高频光形成的双色场的计算与分析

基频光及一弱的辅助高倍频光（9倍 、1３倍甚至120倍频光等）的双色场（该场高频光强度仅为基频光的1/100）作用于氦离子He⁺,发现高次谐波辐射的效率有了很大的提高,尤其是相应于入射高频光频率对应级次及邻近级次的谐波效率有极大提高. 加入不同的低强高频光对双色场高次谐波产生的影响进行计算及讨论,并对其物理机制进行初步阐释.     

马氏场的遍历性及耦合

给定一族具有相同的条件分布的马氏场,本文找出了它们一致弱遍历的充要条件.在此基础上,我们还证明了一类特殊的强马氏场能够一致成功耦合的充要条件是它们一致弱遍历.     

The Effect of Journal Writing on Achievement in and Attitudes Toward Mathematics

A teaching experiment was conducted to investigate the effect of journal writing on achievement in and attitudes toward mathematics. Achievement variables included conceptual understanding, procedural knowledge, problem solving, mathematics school achievement, and mathematical communication. Subjects were selected from first intermediate students (11–13 years) attending the International College, Beirut, Lebanon, where either English or French is the language of mathematics instruction. The journal-writing (JW) group received the same mathematics instruction as the no-journal-writing (NJW) group, except that the JW group engaged in prompted journal writing for 7 to 10 minutes at the end of each class period, three times a week, for 12 weeks. The NJW group engaged in exercises during the same period. The results of ANCOVA suggest that journal writing has a positive impact on conceptual understanding, procedural knowledge, and mathematical communication but not on problem solving, school mathematics achievement, and attitudes toward mathematics. Gender, language of instruction, mathematics achievement level, and writing achievement level failed to interact with journal writing. Student responses to a questionnaire indicated that students found journal writing to have both cognitive and affective benefits.     

Language Influence on Children's Cognitive Number Representation

This study examined the effect of language on children's cognitive representation of number. The sample for the study consisted of 90 Arabic speaking children with a mean age of 80 months. Children were interviewed individually and asked to represent written two‐digit numbers using base‐10 blocks. A new approach for testing the linguistic relativity hypothesis was used. The results of the study revealed that language played an important role in children's cognitive number representation. On the other hand, the results support the argument that the instructions given with the task alter children's performance on it. This study suggests that language may explain the cross‐cultural differences in mathematics achievement. However, the disadvantage that the language might place on children can be overcome with well‐planned instruction.     

Some remarks on an experiment suggesting quantum-like behavior of cognitive entities and formulation of an abstract quantum mechanical formalism to describe cognitive entity and its dynamics

We have executed for the first time an experiment on mental observables concluding that there exists equivalence (that is to say, quantum-like behavior) between quantum and cognitive entities. Such result has enabled us to formulate an abstract quantum mechanical formalism that is able to describe cognitive entities and their time dynamics.     

Cognitive Demands and Second-Language Learners: A Framework for Analyzing Mathematics Instructional Contexts

The issues involved in teaching English language learners mathematics while they are learning English pose many challenges for mathematics teachers and highlight the need to focus on language-processing issues related to teaching mathematical content. Two realistic-type problems from high-stakes tests are used to illustrate the complex interactions between culture, language, and mathematical learning. The analyses focus on aspects of the problems that potentially increase cognitive demands for second-language learners. An analytical framework is presented that is designed to enable mathematics teachers to identify critical elements in problems and the learning environment that contribute to increased cognitive demands for students of English as a second language. The framework is proposed as a cycle of teacher reflection that would extend a constructivist model of teaching to include broader linguistic, cultural, and cognitive processing issues of mathematics teaching, as well as enable teachers to develop more accurate mental models of student learning.     

Cognitive Demands and Second-Language Learners: A Framework for Analyzing Mathematics Instructional Contexts

The issues involved in teaching English language learners mathematics while they are learning English pose many challenges for mathematics teachers and highlight the need to focus on language-processing issues related to teaching mathematical content. Two realistic-type problems from high-stakes tests are used to illustrate the complex interactions between culture, language, and mathematical learning. The analyses focus on aspects of the problems that potentially increase cognitive demands for second-language learners. An analytical framework is presented that is designed to enable mathematics teachers to identify critical elements in problems and the learning environment that contribute to increased cognitive demands for students of English as a second language. The framework is proposed as a cycle of teacher reflection that would extend a constructivist model of teaching to include broader linguistic, cultural, and cognitive processing issues of mathematics teaching, as well as enable teachers to develop more accurate mental models of student learning.     

Analysing the use of cognitive maps in an experiment on a group decision process

Identifying the practical benefits of theoretical methods is a challenge in several fields. The operational research approach, known as Soft, has achieved a field of study status and, from that, Problem Structuring Methods (PSM) have been consolidated as support tools in the group decision process. Thus, aiming to contribute to the improvement of the group decision process, this paper presents the results of an experiment involving 42 students of the Management Engineering major in a general decision process. Strategic Options Development and Analysis is a PSM that uses cognitive maps to express the group’s understanding of a problem. Some practical implications on the use of cognitive maps are evaluated by establishing hypotheses. Such implications were drawn from the comparison of each participant’s personal evaluation of the decision-making process to the final decision taken by the group along with observations and analysis of the groups that employed, and the ones that did not employ the cognitive mapping technique.     

Problem modification as a tool for detecting cognitive flexibility in school children

This paper presents the results of an experiment in which fourth to sixth graders with above-average mathematical abilities modified a given problem. The experiment found evidence of links between problem posing and cognitive flexibility. Emerging from organizational theory, cognitive flexibility is conceptualized through three primary constructs: cognitive variety, cognitive novelty, and changes in cognitive framing. Among these components, changes in cognitive framing could be effectively detected in problem-posing situations, giving a relevant indication of students’ creative potential. The students’ capacity to generate coherent and consistent problems in the context of problem modification may indicate the existence of a strategy of functional type for generalizations, which seems to be specific to mathematical creativity.     

A theorical point of view of reality,perception, and language

It is possible to view the relations between mathematics and natural language from different aspects. This relation between mathematics and language is not based on just one aspect. In this article, the authors address the role of the Subject facing Reality through language. Perception is defined and a mathematical theory of the perceptual field is proposed. The distinction between purely expressive language and purely informative language is considered false, because the subject is expressed in the communication of a message, and conversely, in purely expressive language, as in an exclamation, there is some information. To study the relation between language and reality, the function of ostensibility is defined and propositions are divided into ostensives and estimatives. © 2013 Wiley Periodicals, Inc. Complexity 20: 27–37, 2014     

Toward a situation model in a cognitive architecture

The ability to coherently represent information that is situationally relevant is vitally important to perform any complex task, especially when that task involves coordinating with team members. This paper introduces an approach to dynamically represent situation information within the ACT-R cognitive architecture in the context of a synthetic teammate project. The situation model represents the synthetic teammate’s mental model of the objects, events, actions, and relationships encountered in a complex task simulation. The situation model grounds textual information from the language analysis component into knowledge usable by the agent-environment interaction component. The situation model is a key component of the synthetic teammate as it provides the primary interface between arguably distinct cognitive processes modeled within the synthetic teammate (e.g., language processing and interactions with the task environment). This work has provided some evidence that reasoning about complex situations requires more than simple mental representations and requires mental processes involving multiple steps. Additionally, the work has revealed an initial method for reasoning across the various dimensions of situations. One purpose of the research is to demonstrate that this approach to implementing a situation model provides a robust capability to handle tasks in which an agent must construct a mental model from textual information, reason about complex relationships between objects, events, and actions in its environment, and appropriately communicate with task participants using natural language. In this paper we describe an approach for modeling situationally relevant information, provide a detailed example, discuss challenges faced, and present research plans for the situation model.