认知工具与劣构问题解决探析

基于计算机的认知工具多维度地支持了人类的认知和思维发展。日常生活中,人们在不断地解决各种问题,其中多数是劣构问题,这些问题不同于学校教育中的良构问题。解决劣构问题能够发展人类的高级思维技能,形成专业技能和智慧。"工欲善其事,必先利其器",认知工具作为人类思维的工具,促进了人类解决问题的效力。     

Effects of Cognitive Strategy Interventions and Cognitive Moderators on Word Problem Solving in Children at Risk for Problem Solving Difficulties

This study investigated the role of strategy instruction and cognitive abilities on word problem solving accuracy in children with math difficulties (MD). Elementary school children (N = 120) with and without MD were randomly assigned to 1 of 4 conditions: general‐heuristic (e.g., underline question sentence), visual‐schematic presentation (diagrams), general‐heuristic + visual‐schematic, and an untreated control. When compared to the control condition that included children with MD, an advantage at posttest was found for children with MD for the visual‐schematic‐alone condition on measures of problem solving and calculation accuracy, whereas all strategy conditions facilitated posttest performance in correctly identifying problem solving components. The results also suggested that strategy conditions drew upon different cognitive resources. The General‐heuristic condition drew primarily upon the executive component of working memory (WM), Visual‐schematic condition drew upon the visual component of WM and the combined strategies condition drew upon number processing skills.     

Achieving Optimal Best: Instructional Efficiency and the Use of Cognitive Load Theory in Mathematical Problem Solving

We recently developed the Framework of Achievement Bests to explain the importance of effective functioning, personal growth, and enrichment of well-being experiences. This framework postulates a concept known as optimal achievement best, which stipulates the idea that individuals may, in general, strive to achieve personal outcomes, reflecting their maximum capabilities. Realistic achievement best, in contrast, indicates personal functioning that may show moderate capability without any aspiration, motivation, and/or effort expenditure. Furthermore, our conceptualization indicates the process of optimization, which involves the optimization of achievement of optimal best from realistic best.In this article, we explore the Framework of Achievement Bests by situating it within the context of student motivation. In our discussion of this theoretical orientation, we explore in detail the impact of instructional designs for effective mathematics learning as an optimizer of optimal achievement best. Our focus of examination of instructional designs is based, to a large extent, on cognitive load paradigm, theorized by Sweller and his colleagues. We contend that, in this case, cognitive load imposition plays a central role in the structure of instructional designs for effective learning, which could in turn influence individuals’ achievements of optimal best. This article, conceptual in nature, explores varying efficiencies of different instructional approaches, taking into consideration the potency of cognitive load imposition. Focusing on mathematical problem solving, we discuss the potentials for instructional approaches to influence individuals’ striving of optimal best from realistic best.     

以解决问题为目标导向的自主学习研究

自主学习能力是学生综合素质的重要体现,高职学生自主学习能力还有待提高。本文通过对自主学习课程教学设计中的学习目标编写,设计具有层次性、系统性和学生感兴趣的问题和创设问题学习情境等关键性因素的研究,给高职学生自主学习能力的研究提升带来新的思路,可以丰富自主学习能力教育教学理论;将这种教学模式应用于具体的专业课程教学实践中,可以弥补讲授式教学方法的不足,转变学生学习方式,提高学生自主学习能力。     

小学数学中以“解决问题”教学模式培养学生思维品质

随着新课程改革的不断推进,要求教师能够强化教学改革,加强对学生的思维引导,有效培养学生的思维品质。现阶段需要教师能够及时转换教学模式,以全面加强对学生的思维引导,本文就小学数学教学中如何提高学生的思维品质进行探讨研究,并提出相应的教学建议。     

运用法向量巧解立几题

向量作为一种数学工具引入新教材,为立几教学注入了新的活力．原来对空间想象能力要求较高的作二面角的平面角和作异面直线的公垂线等问题,现在已弱化为法向量与其它向量之间简单的代数运算,从而大大提高了学生学习立几的兴趣和效果．本文就如何用法向量求空间角和距离问题作一归纳,供读者参考．     

克服认识障碍培养学生解决实际问题能力的实验报告

通过实验给出了克服认识障碍,构建良好的认识结构,从而提高学生解决实际问题能力的若干途径。     

Exploring the Use of Conceptual Metaphors in Solving Problems on Entropy

A growing body of research has examined the experiential grounding of scientific thought and the role of experiential intuitive knowledge in science learning. Meanwhile, research in cognitive linguistics has identified many conceptual metaphors (CMs), metaphorical mappings between abstract concepts and experiential source domains, implicit in everyday and scientific language. However, the contributions of CMs to scientific understanding and reasoning are still not clear. This study explores the roles that CMs play in scientific problem-solving through a detailed analysis of two physical chemistry PhD students solving problems on entropy. We report evidence in support of three claims: a range of CMs are used in problem-solving enabling flexible, experiential construals of abstract scientific concepts; CMs are coordinated with one another and other resources supporting the alignment of qualitative and quantitative reasoning; use of CMs grounds abstract reasoning in a “narrative” discourse incorporating conceptions of paths, agents, and movement. We conclude that CMs should be added to the set of intuitive resources others have suggested contribute to expertise in science. This proposal is consistent with two assumptions: that cognition is embodied and that internal cognitive structures and processes interact with semiotic systems. The implications of the findings for learning and instruction are discussed.     

The Role of Teacher Training in Cognitive Strategy Instruction to Improve Math Problem Solving

The purpose of this article is to offer teacher training and professional development recommendations in mathematics based on the findings of a federally funded 3‐year intervention study that improved the problem solving of middle school students with a focus on students with learning disabilities. Over the 3‐year project, 29 seventh and eighth grade teachers implemented a problem‐solving intervention based on cognitive strategy instruction. Though the intervention was successful in improving students’ problem‐solving performance, several issues related to teaching effectiveness and teacher training came to light. The article will: (1) describe the intervention and its implementation, (2) present the findings of the study, and (3) discuss the issues of effectiveness and possible solutions via teacher education and professional development.     

Effects of Instruction on Verbal Interactions During Collaborative Problem Solving

During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional activities were based on scaffolding instruction and included modelling problem solving, stimulating reflection, and giving feedback on the process of collaboration. These activities were gradually developed and implemented in collaboration with teachers who participated in the study. The main research question in this study was whether student collaboration while working in small groups creates a learning context where students work on open-ended problems and where instructional activities are aimed at stimulating collaborative problem solving in mathematics.To answer the research question, an experiment was undertaken in two classes in different schools. Two groups of students were videotaped while they tried to solve mathematics problems collaboratively. Observational data were analysed with a schema that was developed as part of this research. Analyses of the data showed that, in both groups, collaboration-oriented patterns increased during the school year. It is argued that the approach of gradual implementation of instructional activities that are designed in cooperation with participating teachers is effective in stimulating collaborative problem solving.     

运用问题解决教学策略促进学生有意义学习的初探

“问题解决”是一个被多学科领域所重视和研究的课题。教学中发现，学生在解遗传题时，习惯于运用数理逻辑推理，却容易忽视减数分裂与遗传规律的联系。根据奥苏伯尔的观点，这有悖于有意义学习的目的。为此，本研究着重探讨：通过问题解决教学策略的实施，能否促进学生对于减数分裂与遗传规律关系的理解，从而实现有意义的学习。研究结果表明，问题解决教学策略可以促进学生的有意义学习，其基本过程可以概括为：创设问题情境→拓宽问题空间→进行合作学习→完成知识迁移。     

Student Management of Web-Based Hypermedia Resources During Open-Ended Problem Solving

Abstract

Twelve middle school students' use of computer tools to manage and manipulate Internet-based hypermedia resources was investigated. Tools were proposed to support higher order thinking about hypermedia resources to help students find, frame, and resolve open-ended science problems. Tools alone were insufficient to help students manage hypermedia information for solving open-ended problems. Students more frequently applied lower order tool functions (e.g., information collection) than higher order tool functions (e.g., reasoning). Students typically resolved problems with original solutions, but tools were used infrequently to develop evidence-based arguments justifying new ideas. Computer tools alone may be insufficient to help students manage extensive hypermedia resources. Together with additional support structures, however, tool potential may be realized.     

The Cognitive Consequences of Collaborative Problem Solving With and Without Feedback

The goal of this research was to assess the impact of feedback, partner, and shared understanding in the course of problem solving. A sample of 180 6- to 9-year-olds was pretested to discover the children's "rule" for predicting the movement of a mathematical balance beam. For the treatment they either worked alone or with a partner who was equally, less, or more competent, with two-thirds receiving feedback from the materials. They subsequently participated in 2 individual posttests. The results revealed that children receiving feedback improved significantly more than those who did not, but that the presence of a partner was only beneficial when children received no feedback. Irrespective of feedback, those children whose partner exhibited higher-level reasoning were far more likely to benefit from collaboration than those whose partner did not, provided that the pair achieved shared understanding.     

小学分数问题解决的认知模型研究

分数问题解决是小学数学学习中的重点和难点,本研究采取文献综述、专家和教师判断、学生口语报告与测验结果论证相结合的方法,建构小学生在分数问题解决过程中的认知模型。结果表明:(1)小学分数问题解决的认知属性包含分数知识内容和问题解决加工过程两大部分;(2)分数知识内容包含分数基本概念和分数运算,问题解决加工过程包括语义表征、关系表征、选择运算方法、解决问题,各属性之间存在一定的层级关系;(3)学生顺利解决分数问题首先要以分数基本概念为前提,延伸到分数运算和加工过程的各个环节,最后实现问题解决。     

中学数学课程与问题解决探索

问题解决的思想精髓,即强调创造能力和应用意识.本文从几个方面论述了新课程标准理念下中学数学课程设计与编排的基本指导思想.     

基于图式理论的数学问题解决认知过程研究

图式反映的是学习者的认知结构,是内部的;认知过程通过外显行为来刻画,是外部的。基于图式发展阶段理论,数学问题解决者的图式水平可以划分为四个等级,即前图式水平、单一图式水平、多元图式水平和整合图式水平。分析、评价和创造是与数学问题解决密切联系的认知过程。在数学问题解决活动中,多种认知过程共同促进学习者对数学问题的解决,创造在任一图式水平的问题解决中都代表最高层次的认知过程,从低水平图式到高水平图式的过程是多种认知过程并行发展的过程。     

从“应用题”到“解决问题”——小学数学解决问题的教育价值与教学研究

从应用题到解决问题,这绝不仅是名称上的变化.弄清楚这其中变化的实质,有助于我们更好地继承应用题教学宝贵的、成功的经验,也有助于我们更好地开展解决问题的教学.该文立足于应用题和解决问题的内涵,探讨解决问题的教育价值,并结合当今小学数学教学实际,提出了解决问题的教学建议.     

真实情境中地理诊断问题解决的认知模式研究

地理问题解决能力的水平分层是地理核心素养测量的实质基础。本研究在已有研究的基础上,以真实地理情境为研究任务,收集不同教育水平被试解决地理问题的过程信息,采用质性研究方法,探索地理问题解决的不同认知模式。研究发现,真实情境中的地理问题解决认知模式存在三种类型,它们在问题解决步骤、问题分类、问题表征、认知策略等方面存在不同程度的共性和差异。本研究的发现,为进一步研究中学生在真实地理情境中问题解决的学习进阶,构建地理核心素养背景下的地理学业评价框架提供实证研究基础。     

Use of Paper-Based Support Tools to Aid the Acquisition of Cognitive Skills During Unsupervised Practice

This paper describes how graduate students used paper-based support tools to help them acquire a complex cognitive skill during unsupervised practice, and explains why the tools were able to support the practice. The paper also explains how to design such tools and describes a comparable computer-based performance support system. Ohlsson's (1996) theory of learning from performance errors states that people learn a skill by detecting and correcting errors while performing the skill. Learners must have sufficient initial competence and an informative task environment in order to detect and correct errors and make sound decisions. The support tools were successful because they supplied learners with initial competence and an informative task environment. Tools that support learner error-trapping are more likely to help learners eventually perform without support than systems that correct errors for the learners.