一种问题求解的元理论

问题求解是日常生活和专业工作领域中最重要的知活动，问题求解能力是高阶思维能力的重要构成部分是信息时代最为强调和呼唤的人才素质能力之一。然而不论是理论研究，还是实践探索，尤其是在我们日常的规教学中，问题求解的认知活动和问题求解能力的发展很少受到应有的重视。究其原因，一是目前我们对问题解的过程研究尚不成熟；二是虽然当代学习理论把问题解当作理论与实践探究的核心，但现有的研究尚未透彻析所要解决问题的本质特性。     

从物元分析到可拓学：中国人创立的新学科

物元分析是中国人创立的新学科，它在自然科学和社会科学诸如新产品构思、企业管理与决策等多方面都有着广泛的应用前景。本文从物元分析的学科性质及其发展历程，物元分析的主要研究分支等方面概述了物元分析的创立及若干进展。     

谈一元一次方程解法

求解一元一次方程是求解一元一次不等式、二元一次方程组和不等式组的重要基础，在求解过程中我们需要掌握几点技巧，否则求解的过程比较繁琐。求解是需要观察、分析方程的特点，灵活运用五个步骤及等式的两个基本性质确定适当的解法。下面举例分析如下：     

关于物元分析及其哲学思考

物元分析是80年代在中国诞生的一门新兴学科。本文从它的哲学基础,表阴唯物、辩证数学观的胜利、为数学向辩证法、哲学渗透提供了依据,以及丰富了应用哲学研究的内容等方面作了初步探讨,有助于进一步了解和研究物元分析的有关问题。     

关于物元分析及其哲学思考

物元分析是80年代在中国诞生的一门新兴学科。本文从它的哲学基础,表明唯物、辩证数学观的胜利、为数学向辩证法、哲学渗透提供了依据,以及丰富了应用哲学研究的内容等方面作了初步探讨,有助于进一步了解和研究物元分析的有关问题。     

十字交叉法的巧用、妙用、慎用

在中学化学计算题的解题过程中，经常会遇到类似这样的问题：a mol由H2和CH4组成的混合气体共bg，试求H2和CH4的物质的量之比？初学者一般都通过设立未知数建立二元一次方程组或一元一次方程求解，在求解方程组时有时很烦锁．     

丰富多彩的消元技巧

解二元一次方程组的关键在于消元，化“二元”为“一元”．将“陌生”的二元一次方程组转化为熟悉的一元一次方程．从而求解．同学们在掌握用代入、加减消元方法的同时。还要注意观察和分析方程组中各方程的结构特点，开拓新思路，简捷求解，从而培养自己的创新能力．     

静力学中求解物系平衡问题之对策

本对静定的物系进行了详尽的分析和研究，针对不同类型的物系问题，提出了相应的求解策略。     

旋转双线性非协调元二网格法的MATLAB程序实现

高等数学中特征值问题的求解一直是人们关注的核心问题之一,而Poisson方程特征值的求解更是比较复杂的问题。在求解Poisson方程特征值时,高效率更准确是追求的目标。给出了二维情况下二网格法求特征值的Matlab程序,得到Qrot1元的特征值,并且与非二网格下得到的结果进行了比较,得到了高效的结果,进而展示了Matlab软件在特征值问题求解方面的巨大贡献。     

传导变换与相关性

从物元的基本要素出发，对传导变换及相关性提出了新的划分，并研究了二者的相关关系．     

案例知识与复杂问题解决

人们在日常生活中需要不断地解决各种问题,正如波普尔所说"全部的生活就是问题解决"。问题解决,尤其是复杂问题的解决,已成为认知科学和学习研究中关注的焦点。复杂问题的解决是一个动态的复杂过程,需要综合运用多种认知和非认知成分。先前的研究已经提出了解决复杂问题的多种模型,给人们解决复杂问题提供了可依靠的支架。而案例知识作为一种典型性、叙事性、情境性、实践性、个人性、整体性的经验知识在问题解决中得到了广泛应用,已成为支持复杂问题解决的有效形式,具体表现为:支持问题境脉的阐释、支持问题的多视角认识、支持解决方案的生成、支持解决方案的确定以及支持对问题解决结果的评价。它正作为一种支持人们解决问题的资源,在现实中发挥越来越大的作用。     

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.     

THE EFFECTS OF TEACHING PROBLEM SOLVING ON ACADEMIC PERFORMANCE AND RETENTION

A study of the effects of explicitly teaching a problem‐solving strategy on problem‐solving ability, course average, course success, and student retention is reported. Two classes of microeconomics principles were involved in a quasi‐experiment. The experimental class was explicitly taught the problem‐solving strategy and this strategy was then used to solve microeconomic problems in class. The control class was assigned, solved, and discussed the same problems without being taught the problem‐solving strategy. Multiple regression and analysis of variance show that while teaching problem solving did not significantly affect course average, student success in passing the course or problem solving ability, it did result in significantly higher student retention. Results indicate that teaching problem solving only affects those students with low problem solving abilities who would have dropped out of class, and that teaching this strategy helps them remain in the class and succeed.     

Predictors of well‐structured and ill‐structured problem solving in an astronomy simulation

This study compared the problem‐solving skills required for solving well‐structured problems and ill‐structured problems in the context of an open‐ended, multimedia problem‐solving environment in astronomy. Two sets of open‐ended questions assessed students' abilities for solving well‐structured and ill‐structured problems. Generalized, rubric scoring systems were developed for assessing problem‐solving skills. Instruments were also developed and administered to assess cognitive and affective predictors of problem‐solving performance. By regressing the scores on the cognitive and affective predictors onto students' scores on the well‐structured and ill‐structured problems, we concluded that solving well‐structured and ill‐structured problems require different component skills. Domain knowledge and justification skills were significant predictors of well‐structured problem‐solving scores, whereas ill‐structured problem‐solving scores were significantly predicted by domain knowledge, justification skills, science attitudes, and regulation of cognition. Implications for problem solving in science education are presented. © 2003 Wiley Periodicals, Inc. J Res Sci Teach 40: 6–33, 2003     

麦克斯韦方程反演的大范围收敛共轭斜量法

针对麦克斯韦方程中的电导率参数反演问题,构造一种具有大范围收敛的正则化共轭斜量反演算法,即将用于求解非线性问题大范围收敛的同伦法、求解大规模优化问题的共轭斜量法与求解不适定问题的Tikhonov正则化方法有机结合,得到解决麦克斯韦方程反演问题大范围收敛的数值方法,以求解电导率参数反演问题,解决了求解过程中局部陷入极小值的困惑。实验结果表明此算法是有效的,可以应用于其他类型的参数识别问题。     

Using Number Lines to Solve Math Word Problems: A Strategy for Students with Learning Disabilities

Students with learning disabilities (LD) consistently struggle with word problem solving in mathematics classes. This difficulty has made curricular, state, and national tests particularly stressful, as word problem solving has become a predominant feature of such student performance assessments. Research suggests that students with LD perform poorly on word problem‐solving items due primarily to deficits in problem representation. Therefore, it is imperative that teachers provide these students with supplemental problem‐solving instruction that specifically targets the development of representational strategies. This article describes how one representational strategy, using number lines, can be used to model word problems as part of a comprehensive problem‐solving intervention to improve the conceptual understanding of math word problems and, subsequently, the problem‐solving performance of students with LD.     

解决良构问题与非良构问题的研究综述

学校情境下的问题大部分是良构问题,而现实生活中面临的问题大多是非良构问题。解决良构问题的程序是激活图式表征问题,搜寻解决方案和执行解决方案。结构性知识与具体领域的知识是解决良构问题的主要成分。解决非良构问题的过程包括了解问题的陈述,确定问题是否存在,确定问题的本质,澄清问题产生的原因,识别与澄清不同的看法,生成与选择可能的解决方案,评估与实施解决方案。认知的调节、认知观和情感态度等非认知因素均是解决非良构问题的关键因素。总之,在问题本质、问题解决过程和问题解决成分三个方面,良构问题与非良构问题存在看较大的差异。     

Problem Solving and Teaching How to Solve Problems in Technology-Rich Contexts

ABSTRACT

Problem solving is perhaps the key characteristic that makes us human. Given the kinds of problems that we face in a competitive economy and society, the new generation of learners is ever more required to have problem-solving abilities. By drawing from the literature on technological pedagogical content knowledge, design thinking, general and specific methods of problem solving, and role of technologies for solving problems, this article highlights the importance of problem solving for future teachers and discusses strategies that can help them become good problem solvers and understand the requirements of teaching their students problem solving in technology-rich contexts. This article consists of two main parts. Part 1 focuses on strategies required to help preservice teachers to be better problem solvers, and Part 2 summarizes approaches to introduce preservice teachers to the methods of teaching problem solving. The strategies reviewed provide a tangible guidance for teacher education programs regarding how to promote future teachers’ problem-solving skills.     

加工水平对具有广义抽象关系数学问题迁移的影响

解题者对靶题与源题之间的共性意识及加工水平对解题迁移的影响已经得到了验证,其中靶题与源题之间存在着广义抽象关系.结果表明:(1)当靶题是低难度或高难度问题时,解题者对靶题与源题之间共性关系的意识及加工水平对解题迁移的影响没有显著差异;(2)当靶题是中难度问题时,解题者对靶题与源题之间共性关系的意识及加工水平对解题迁移的影响有显著差异.