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高中生数学建模素养测评指标体系构建研究

【作者】 张瀚兮

【导师】 李忠如;

【作者基本信息】 西南大学, 数学教育, 2019, 硕士

【摘要】 《普通高中数学课程标准(2017年版)》中指出数学建模素养是对现实问题数学抽象,用数学语言表达问题、用数学方法构建模型解决问题的素养。中学生对数学建模接触有助于培养他们分析实际问题、解决实际问题、将学到的数学知识用于生活实际中的能力。中学生的数学建模教学与研究对于我国培养综合性人才有一定的意义。《普通高中数学课程标准(2017年版)》将高中生数学建模素养分为三个水平,三个水平之间层层递进,但更多是文字性描述,中学一线教师用《普通高中数学课程标准(2017年版)》中对数学建模素养三个水平划分来评价学生数学建模素养水平不好操作。同时我国基础教育研究中也暂时没有一套科学完善的数学建模素养测评体系,中学一线教师如何能更好的测评学生的数学建模素养?所以建立一个科学的量化了的高中生数学建模素养测评指标体系非常有必要,有助于中学一线教师数学建模教学与研究,以及为我国数学建模素养测评研究做出一点理论上的贡献。本研究的旨在建立科学的高中生数学建模素养测评指标体系。为构建科学的高中生数学建模素养测评指标评价体系,本研究以高中生为研究对象,以高校教师、教研员、对数学建模熟知的一线教师作为调查对象。采用文献分析法初拟出高中生数学建模素养测评指标体系中的一级指标与二级指标,并形成《高中生数学建模素养测评指标体系指标认同度调查问卷(第一轮)》,再对专家进行专家咨询,请专家对各个指标进行认同度判断,并给出建议,最后运用统计方法分析专家意见,并结合专家建议对初拟的测评指标进行修改,得到修改后的高中生数学建模素养测评指标体系的测评指标,并形成《高中生数学建模素养测评指标体系指标认同度调查问卷(第二轮)》,再一次请专家对修改后的测评指标进行认同度判断,并给出意见,再采用统计方法分析专家意见,最后综合专家意见,得到高中生数学建模素养测评指标体系中的一级指标与二级指标。根据修改后确定的高中生数学建模素养测评指标体系的一级指标与二级指标形成《高中生数学建模素养测评指标相对重要性判断表》,请专家对各个指标的重要程度进行判断。再运用层次分析法,最后得出各个评价指标的权重系数。最终形成高中生数学建模素养测评指标体系。为验证所构建的指标体系的科学性,选取《普通高中数学课程标准(2017年版)》中的两道数学建模案例,用构建的测评指标体系与《普通高中数学课程标准(2017年版)》中的数学建模素养水平评价标准分别测评,0——0.6分与水平一对应,0.6分——0.9分与水平二对应,0.9分——1分与水平三对应。本研究结论如下:(1)拟定高中生数学建模素养测评指标体系的5个一级指标和17个二级指标,其中一级指标包括:数学化、建立数学模型、求解数学问题、数学表达、处理数学结果。其中数学化包含:处理信息或实验数据、确定代数表达式、确定变量和参数,建立数学模型包含:在数据中确认模式、建立模型表征信息,求解数学问题包含:用数学工具找方案、用数学知识得出方案、用数学知识处理信息、论证方案并推广、反思过程,数学表达包含:表征及解释数据、信息图表化、语言表达,处理数学结果包含:解释数学结果、评估数学结果、调整模型、解释意义。(2)确定高中生数学建模素养测评指标体系中的指标权重,其中5个一级指标数学化、建立数学模型、求解数学问题、数学表达、处理数学结果的权重系数分别为:0.36、0.25、0.16、0.15、0.08。二级指标的权重系数具体见表5-7,数学化三个二级指标的权重系数分别为:0.33、0.39、0.28,建立数学模型两个二级指标的权重系数分别为:0.42、0.58,求解数学问题五个二级指标的权重系数分别为:0.14、0.32、0.23、0.16、0.14,数学表达三个二级指标权重系数分别为:0.41、0.30、0.29,处理数学结果四个二级指标的权重系数分别为:0.28、0.19、0.32、0.21。(3)采用《普通高中数学课程标准(2017年版)》与构建的高中生数学建模素养测评指标体系分别测评30位高中生。结合学生的测试结果发现,只有1位学生的答卷,用两种方式测评结果有一点不一样,其余29位学生的答卷用两种方式测评结果均一致,满足0——0.6分与水平一对应,0.6分——0.9分与水平二对应,0.9分——1分与水平三对应。所以认为构建的高中生数学建模素养测评指标体系具备一定的科学性。本研究对高中生数学建模素养测评指标体系构建进行研究,但由于本人学术能力有限,对于一些指标表述不够精炼,且仅仅依靠文献分析初步拟定一二级指标,未采用因子分析等统计手段,对于如何构建可靠的测评工具等也没有进一步探究。在今后的数学教育研究中本人将会对数学建模素养进行更深一步的研究探索。

【Abstract】 It is pointed out in the mathematics curriculum standards for ordinary senior high school(2017 edition) that mathematical modeling literacy is the accomplishment of abstracting the mathematics of real problems,expressing problems with mathematical language and solving problems with mathematical methods.Middle school students’ exposure to mathematical modeling helps them develop the ability to analyze practical problems,solve practical problems,and apply the mathematical knowledge they have learned to real life.The mathematical modeling teaching and research of middle school students is of certain significance to the training of comprehensive talents in China."Ordinary high school mathematics curriculum standards(2017 edition),the high school mathematical modeling literacy is divided into three levels,three levels between layers of progressive,but it is more a textual description,secondary line teachers use the ordinary high school mathematics curriculum standards(2017 edition)" in on three level mathematical modeling to evaluate students’ mathematical modeling literacy level is bad.At the same time,there is not a set of scientific and perfect mathematical modeling literacy evaluation system in the research of basic education in China.How can front-line teachers in middle schools better evaluate students’ mathematical modeling literacy? Therefore,it is very necessary to establish a scientific quantified evaluation index system for the mathematical modeling literacy of high school students,which is helpful for the teaching and research of mathematical modeling literacy of front-line middle school teachers,and makes some theoretical contributions to the research of mathematical modeling literacy in China.The purpose of this study is to establish a scientific mathematical modeling literacy evaluation index system for high school students.In order to build a scientific mathematical modeling literacy evaluation index evaluation system for senior high school students,this study takes senior high school students as the research object,and college teachers,teaching and research staff,and front-line teachers who are familiar with mathematical modeling as the survey object.Up at the beginning of high school students with the method of literature analysis mathematical modeling quality evaluation index system of the primary indicators and secondary indicators,and form the high school mathematical modeling literacy evaluation index system of indicators were questionnaire(first round),and expert consultation with experts,ask an expert on each index for judging esteemed,and give advice,finally used statistical methods to analyze the expert opinion,and combined with expert advice on early of evaluation index is modified,the modified after high school mathematical modeling quality evaluation index system of evaluation indicators,And form the high school mathematical modeling literacy evaluation index system of indicators were questionnaire(second round),and once again,ask an expert to the modified evaluation indexes were judgments,and gives the opinion,and then use statistical methods to analyze expert opinion,the last comprehensive expertise,get high school mathematical modeling quality evaluation index system of the primary indicators and secondary indicators.According to the modified evaluation index system of senior high school students’ mathematical modeling literacy,the first level index and the second level index form the "judgment table of relative importance of the evaluation index of senior high school students’ mathematical modeling literacy",and experts are invited to judge the importance degree of each index.Then using the analytic hierarchy process,finally get the weight coefficient of each evaluation index.Finally,the evaluation index system of high school students’ mathematical modeling literacy is formed.To verify that the construction of index system of scientific,select the "ordinary high school mathematics curriculum standards(2017edition)" in the case,two mathematical modeling with establishment of evaluation index system and the ordinary high school mathematics curriculum standards(2017 edition)"mathematical modeling of the literacy level evaluation standard evaluation respectively,0-0.6 and a corresponding level,0.6points,0.9 points and level 2,0.9 points-three corresponding points and level 1.The conclusions of this study are as follows:(1)To formulate five first-level indicators and 17 second-level indicators for the evaluation index system of senior high school students’ mathematical modeling literacy,among which the first-level indicators include: mathematization,mathematical model establishment,mathematical problem solving,mathematical expression and mathematical result processing.Mathematical include:processing experimental data,determine the algebraic expressions,or information variables and parameters,establish mathematical model includes: confirm the model,model characterization information in the data,solving math problems include: to use mathematical tools to find solutions,with the mathematical knowledge,using mathematical knowledge processing information and demonstration project and promotion,the reflection process,a mathematical expression contains:characterization and interpret data,information of the chart,language expression,processing mathematical results includes: explain mathematical results,evaluate the results of mathematical,adjustment model,explain the meaning.(2)Determine the index weight in the evaluation index system of senior high school students’ mathematical modeling literacy.Among them,the weight coefficients of the five first-level indexes are: 0.36,0.25,0.16,0.15 and 0.08.Secondary index weight coefficient of the concrete are shown in table 5-7,mathematical three secondary index weight coefficient are: 0.33,0.39,0.28,and establish a mathematical model of two secondary indexes weight coefficient are: 0.42,0.58,and solving math problems five secondary index weight coefficient are: 0.14,0.32,0.23,0.16,0.14,mathematical expression three secondary index weight coefficients are: 0.41,0.30,0.29,with mathematics result four secondary indexes weight coefficient are: 0.28,0.19,0.32,0.21.(3)The general high school mathematics curriculum standards(2017 edition)and the mathematical modeling literacy evaluation index system constructed for high school students were used to evaluate 30 high school students.Combined with the test results of the students,it was found that the test results of only one student were slightly different from those of the other 29 students,and the results of the other 29 students were all the same,meeting the requirements that 0--0.6corresponds to level 1,0.6--0.9 corresponds to level 2,and 0.9--1 corresponds to level 3.Therefore,it is considered that the evaluation index system of high school students’ mathematical modeling literacy is scientific to some extent.This study studies the construction of the evaluation index system of high school students’ mathematical modeling literacy.However,due to my limited academic ability,the expression of some indicators is not refined enough,and the students’ test papers are not explored.The primary and secondary indicators are drawn up only by literature analysis,and the rationality of the established evaluation indicators is not verified because of limited time.In the future research of mathematics education,I will make further research and Exploration on mathematical modeling literacy.

  • 【网络出版投稿人】 西南大学
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