高中学生运用FDI认知方式解决数学应用问题的表征及策略关系研究

国内外关于问题解决中表征和策略的研究成果不少，但涉及高中数学应用题解决中的问题表征及其与解题策略关系的研究不多。高中学生运用FDI认知方式解决数学应用问题有5个表征层次--文字表征、具体表征、抽象表征、形象表征和数学表征，4种解决策略--盲目搜索策略、情景推理策略、原理统率策略和数学模型策略。高中解决数学应用问题时的表征程度决定了其问题解决策略的选取，表征程度的学生倾向于选择相对优化的策略。     

浅谈数学符号在解题中的作用

从暗示信息、约简思维、刺激联想、诱发灵感等方面探讨了数学符号在解题中的重要作用.     

小学生应用题表征类型及其对问题解决的影响

为考察小学生算术应用题的表征类型及其对问题解决的影响,选择60名四年级小学生为被试,以4种应用题为实验材料进行了实验研究。实验表明:小学生的应用题表征有4种基本类型:关系表征、语词表征、图式表征和图画表征。表征类型与应用题主导特征有密切的对应关系,即不同类型的应用题有与之对应的适宜表征;适宜表征对应用题解决有促进作用,表现为解题正确率高,在解题速度上,语词表征和关系表征普遍快于图画表征和图式表征。     

Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students

In this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. Analyses indicated a repeating cycle in which students typically exploited abilities relating to the ways they orientated themselves with respect to a problem, recalled mathematical facts, executed mathematical procedures, and regulated their activity. Also, while the nature of this cyclic sequence varied little across problems and students, the proportions of time afforded the different components varied across both, indicating that problem solving approaches are informed by previous experiences of the mathematics underlying the problem. Finally, students’ whose initial problem formulations were numerical typically failed to completed the problem, while those whose initial formulations were algebraic always succeeded.     

Focus on the Representation of Problem Types in Intended Curriculum: A Comparison of Selected Mathematics Textbooks from Mainland China and the United States

This study compared how selected mathematics textbooks from Mainland China and the United States at the lower secondary grade level represent various types of problems for classroom teaching and learning. The examination of problems was carried out based on the classifications of problem types established in the study, including routine problems versus non-routine problems, open-ended problems versus close-ended problems, traditional problems versus non-traditional problems, and application problems versus non-application problems, among others. Both the similarities and differences in the representation of problems in the selected textbooks were analyzed. The results were used to explore the possible influences of those textbooks on students’ different performances in mathematics, as revealed in cross-national comparisons. Discussions about how to improve the representation of problems in mathematics textbooks were provided at the end of the study.     

马克思主义在中国早期传播的落地实践(1918-1921)——基于知识社会学视野的考察

将“五四”前后马克思主义在中国的传播作为一种知识传播的社会活动进行考察,可以看到知识建构为现实的过程落实为三重层面：一是以学会、研究会等“组织”为中心,接触、学习、理解并运用马克思主义理论的知识分子凝聚为意识形态共同体;二是以报纸杂志所构建的“语言”为中心,知识群体借助文本载体介绍、阐释马克思主义,以建构知识正当性;三是以学校等“空间”为中心,在传播过程中联合社会各阶层并作“实际运动”,扩大革命影响力。回溯马克思主义在中国早期传播的落地实践,对于推进新时代党的宣传思想工作具有启示意义。