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初中二年级学生解决数学情境问题能力研究

【作者】 吴妍翎

【导师】 喻平;

【作者基本信息】 南京师范大学, 数学教育, 2019, 硕士

【摘要】 随着数学课程教育改革的逐步深入,数学教育越来越关注学生在真实情境中运用数学知识解决现实生活问题的能力。因此,教师需要了解当前学生的数学情境问题解决能力的现状及影响因素。本研究对814名初二学生进行测量,研究初中二年级学生的数学情境问题解决水平及影响数学情境问题的影响因素,并探究数学学业成绩与数学情境问题解决成绩的关系。通过本研究得出以下结论:(1)初中二年级学生数学情境问题解决能力属于中等水平,其中在“知识理解”方面水平较高,而“知识迁移”处中等水平,“知识创新”处低等水平。(2)初中二年级学生数学情境问题解决能力在性别上存在边缘性显著性差异,在地区、学校方面都存在显著性差异。关于知识理解的数学情境问题初二学生在性别、地区、学校存在显著性差异,关于知识迁移的数学情境问题初二学生在性别上没有显著性差异,在地区、学校均有显著性差异:关于知识创新的数学情境问题解决初二学生在性别、地区、学校存在显著性差异。(3)学习兴趣、解题策略、自我监控、对情境问题的认识与初二学生数学情境问题解决成绩呈显著正相关,四者均能有效地预测学生的数学情境问题成绩。(4)数学学习兴趣程度不同的学生其数学情境问题解决成绩有显著性差异;解题策略方面,高策略组和中策略组学生其数学情境问题解决成绩无显著性差异,而高策略组与低策略组、中策略组与低策略组均有显著性差异;自我监控方面,高监控组和中监控组无显著性差异,而高监控组与低监控组、中监控组与低监控组均有显著性差异;对数学情境问题不同认识的初二学生其数学情境问题解决能力有显著性差异。(5)学习兴趣、自我监控、解题策略、对情境问题的认识四个因素中对数学情境问题解决成绩最具有预测力的因素为学习兴趣、解题策略、对情境问题的认识。(6)数学学业成绩与数学情境问题解决成绩呈显著的高度相关;不同数学情境问题解决成绩的初二学生其数学学业成绩有显著性差异。(7)为提高学生的数学情境问题解决能力,提出以下教学建议:在数学课堂教学中教师可创设操作体验性情境,注重过程教学,教会学生提问;在布置数学作业中教师可以教材习题基础上融入数学情境进行变式,布置“大作业”。

【Abstract】 With the gradual deepening of the reform of mathematics curriculum education,mathematics education pays more and more attention to students’ ability to use mathematical knowledge to solve real life problems in real situations.Therefore,teachers need to understand the current situation and influencing factors of students’ability to solve mathematical situational problems.In this study,814 second-year junior high school students were surveyed to study the level of mathematics situational problem-solving and the influencing factors of mathematics situational problem-solving,and to explore the relationship between mathematics academic achievement and mathematics situational problem-solving achievement.The result indicates that:(1)The second-year junior middle school students’ ability to solve mathematical situational problems is of medium level,in which the level of "knowledge understanding" is higher,while the level of "knowledge transfer" is of medium level,and the level of "knowledge innovation" is of low level.(2)There are significant marginal differences in gender and regional and school differences in mathematics situational problem-solving ability of junior high school sophomores.There are significant differences in gender,region and school for junior two students on the problem of mathematical situation of knowledge understanding.There are no significant differences in gender for junior two students on the problem of mathematical situation of knowledge transfer,but there are significant differences in regions and schools.There are significant differences in gender,region and school for junior two students on the problem of mathematical situation of knowledge innovation.(3)Interest in learning,problem solving strategies,self-monitoring,and awareness of situational problems are positively correlated with students’ performance in solving math situational problems in junior two.All four can effectively predict students’performance in solving math situational problems.(4)Students with different interest in mathematics learning have significant differences in their math situational problem-solving performance.In problem-solving strategies,there is no significant difference between the high-strategy group and the middle-strategy group in their math situational problem-solving performance,while there are significant differences between the high-strategy group and the low-strategy group,the middle-strategy group and the low-strategy group.In self-monitoring,there is no significant difference between the high-strategy group and the middle-strategy group.There are significant differences between the high-level and low-level monitoring groups,the middle-level monitoring group and the low-level monitoring group.There are significant differences in the ability of solving mathematical situational problems among the second-year junior high school students who have different understanding of mathematical situational problems.(5)Among the four factors of interest in learning,self-monitoring,problem-solving strategies,and understanding of situation problems,the most predictive factors are interest in learning,problem-solving strategies and understanding of situation problems.(6)Mathematics academic achievement is highly correlated with mathematics situational problem-solving achievement,and there are significant differences in mathematics academic achievement among junior two students with different mathematics situational problem-solving achievement.(7)In order to improve students’ability to solve mathematical situation problems,the following teaching suggestions are put forward:in mathematical lesson teaching,teachers can create operational experience situations,pay attention to process teaching,teach students to ask questions;in the layout of mathematical homework,teachers can incorporate mathematical situation into variants and arrange "big assignments".

  • 【网络出版投稿人】 南京师范大学
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