问题支架对高二学生数学问题解决的影响研究

【作者】 赵慧；

【导师】 宁连华；

【作者基本信息】 南京师范大学 ， 学科教学（数学）（专业学位）， 2023， 硕士

【摘要】 数学问题解决能力是评价高中数学教学效果的重要指标之一,也是高中生数学学科核心素养的最直接体现。我国一直以来都比较重视培养学生的问题解决能力,但受传统教学模式中一些弊端的影响,当前中学生数学问题解决能力现状并不乐观。研究表明支架式教学通过搭建支架不仅可以提高学生数学问题解决的兴趣,还可以带学生梳理解题思路、走出思维误区,进而提高学生的数学成绩。问题支架作为支架式教学中使用最广泛的交互式脚手架,其对学生数学问题解决必然存在着深刻的影响。因此研究问题支架对学生数学问题解决的影响具有一定的理论价值与实践意义。本研究首先采用文献分析法梳理有关问题支架与数学问题解决的相关理论,给出核心概念的界定,然后以波利亚的怎样解题表和朱龙、付道明学者的问题支架应用框架为依托编制带有问题支架的测试卷,并以高二年级学生为对象进行测试,测试结束后利用问卷调查不同问题支架对学生的帮助情况,以此探究问题支架对学生数学问题解决的影响。通过对数据进行分析得到以下结论:(1)问题支架对学生数学问题解决具有显著性的积极影响。(2)问题支架对学生数学问题解决的影响在性别上不存在显著性差异,男、女在数学问题解决成绩上不存在显著性差异。(3)问题支架对学生数学问题解决的影响在知识水平上存在显著性差异,其中问题支架对中等能力组的学生帮助最大,高能力组次之,对低能力组的学生无影响。(4)问题方案分析支架对学生数学问题解决的帮助最大,问题表征支架对学生数学问题解决的帮助最小。根据实验结论及支架式教学模式的原则为教师在教学中利用问题支架提高学生的数学问题解决能力提出如下建议:(1)合理构建问题支架:构建有层级的问题支架、构建开放性的问题支架、构建动态性的问题支架。(2)有效呈现问题支架:依据学生的思维进展提供问题支架、依据学生的个性提供问题支架、依据学生的知识水平提供问题支架。(3)逐渐撤销问题支架:培养学生使用问题支架的兴趣、教授学生使用问题支架的策略。更多还原

【Abstract】 Mathematics problem-solving ability is one of the important indicators to evaluate the effect of high school mathematics teaching,and it is also the most direct embodiment of the core literacy of high school students’mathematics.China has always attached great importance to cultivating students’problem-solving ability,but due to some drawbacks in the traditional teaching mode,the current status quo of mathematics problem-solving ability of middle school students is not optimistic.Studies have shown that scaffold teaching can not only improve students’interest in solving mathematical problems by building scaffolds,but also take students to comb out the ideas of understanding problems and get out of thinking misunderstandings,thereby improving students’mathematical performance.As the most widely used interactive scaffolding in scaffold teaching,the problem scaffold must have a profound impact on students’mathematical problem solving.Therefore,the influence of research problem scaffold on students’mathematical problem solving has certain theoretical value and practical significance.In this study,the literature analysis method is first used to sort out the relevant theories of problem scaffolds and mathematical problem solving,and then the test paper with problem scaffolds is compiled based on Polia’s how to solve the problem table and the problem scaffold application framework of scholars Zhu Long and Fu Daoming,and the test is conducted for high school sophomores.In this way,the influence of problem scaffolding on students’mathematical problem solving is explored.Through the analysis of the data,the following conclusions are obtained:(1)The problem scaffold has a significant positive effect on students’mathematical problem solving.(2)There was no significant difference in gender difference in the influence of problem scaffolds on students’mathematical problem solving,and there was no significant difference between male and female mathematical problem solving scores.(3)There was a significant difference in the influence of problem scaffolds on students’mathematical problem solving in terms of knowledge level,among which problem scaffolds helped students in the middle ability group the most,followed by the high ability group,and had no effect on students in the low ability group.(4)The problem scheme analysis scaffold is the most helpful for students’mathematical problem solving,and the problem characterization scaffold is the least helpful for students’mathematical problem solving.According to the experimental conclusion and the principle of scaffold teaching mode,the following suggestions are put forward for teachers to use problem scaffold in teaching to improve students’mathematical problem solving ability:(1)reasonable construction of problem scaffolding:construct hierarchical problem scaffolding,build open problem scaffolding,and construct dynamic problem scaffolding.(2)Effectively present the problem scaffold:provide the problem scaffold according to the student’s thinking progress,provide the problem scaffold according to the student’s personality,and provide the question scaffold according to the student’s knowledge level.(3)Gradually withdraw the problem scaffold:Develop students’interest in using the problem scaffold and teach students strategies for using the problem scaffold.更多还原