初中生数学学习选择能力研究
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摘要
初中生数学学习选择能力研究是数学教育研究领域一个既有理论意义又有实践意义的研究课题。但是目前数学能力研究对“选择”关注不足,关于初中生数学学习中“选择”的系统理论梳理与实证研究也不多见。
本研究是在阅读大量与数学学习选择能力相关文献的基础上,结合数学学科特点和初中数学教学实践而进行的理论和实践相结合的综合研究。论文的研究思路是:在分析相关理论的基础上,本文对初中生数学学习选择能力的概念作以界定,并丰富其内涵;在此基础上,本文建构初中生数学学习选择能力的结构;分析影响初中生数学学习选择能力的因素;研究初中生数学学习选择能力的现状以及发展特点、规律;最后,总结本研究的主要结论,并依据上述的调查、测试、访谈等研究,探讨培养初中生数学学习选择能力的主要途径,并为数学教学中培养初中生的数学学习选择能力提供策略和建议。全文共分为六个部分:导论主要分析研究的背景,确定论文的研究框架、所研究的具体内容及研究思路和研究方法,对相关的文献进行梳理与分析,然后提出本研究的意义和价值。
第一章主要对初中生数学学习选择能力的概念进行分析。在相关的理论前提和基础上,论文提出初中生数学学习选择能力的概念。初中生数学学习选择能力是指为了保证数学学习的高质量和高效率,初中生能对数学学习中的信息积极、主动、有意识地做出正确、合理的筛选、吸收和加工,能监控自己在数学学习中的选择对数学学习产生的影响,并能调节自己选择行为的一种个性心理特征。初中生数学学习选择能力既包含对数学学习中的信息进行吸收、加工等认知成分,又包含对自己的选择进行监控、调节等元认知成分。在概念界定的基础上,论文提出初中生数学学习选择能力结构的理论构想。
第二章主要通过实证研究建构初中生数学学习选择能力的结构。在对数学学习理论分析并征求相关专家、数学一线教师和初中数学教研员意见的基础上,初步形成数学学习选择能力的调查问卷。我们挑选济南市两所初中的三个年级的846名学生进行测试,有效被试752名。我们采用交叉证实的方法,将被试随机分为两组,对其中的399名被试进行探索性因素分析,对其余的353名被试进行验证性因素分析,并确定初中生数学学习选择能力结构由反思、计划、算法优化、数学自我判断能力四个因素组成。在上述研究的基础上,论文形成初中生数学学习选择能力的正式问卷,并且正式问卷的信度和效度符合心理学标准。
第三章主要是通过实证研究分析影响初中生数学学习选择能力的因素。笔者运用正式的初中生数学学习选择能力问卷,以及数学自我效能、数学学习动机、数学学习归因、数学观念和态度的问卷,对济南市两所初中的三个年级的441名学生进行调查和测试,其中有效被试379名。实证分析的结果以及对结果的分析如下:第一,分析数学教学水平对初中生数学学习选择能力的影响,结果表明数学教学水平是影响初中生数学学习选择能力及反思、计划、算法优化与数学自我判断能力的一个重要因素。第二,以初中生数学学习选择能力为因变量,以数学自我效能、数学学习动机、数学学习归因、数学观念和态度这四个因素中,每个因素所包含的维度为自变量,进行多元回归分析。结果表明,内源性动机、对数学学习过程的看法、困难应对感、内归因对初中生数学学习选择能力构成显著回归效应。第三,先后分别以反思、计划、算法优化、数学自我判断能力为因变量,以数学自我效能、数学学习动机、数学学习归因、数学观念和态度这几个因素中,每个因素所包含的维度为自变量,先后进行四个多元回归分析,分别得出对反思、计划、算法优化、数学自我判断能力构成显著回归效应的变量。上述研究为数学教学实践中培养初中生的数学学习选择能力提供重要的参考和依据。
第四章主要研究初中生数学学习选择能力的现状和发展特点、规律。笔者根据编制的《初中数学学习测试题(开放式问卷)》对济南市两所初中的三个年级的441名学生进行测试,其中有效被试374名,并对其中的36名被试进行追述性口语报告测试和访谈。初中数学学习测试题是一份开放式问卷,我们针对每个测试题,从反思、计划、算法优化、数学自我判断能力方面设计了相关的问题,要求学生在解决数学问题的同时,回答体现初中生数学学习选择能力水平的提问。我们在选取测试题目时尽可能削弱学生已有的知识、经验对解题的影响。保证测试题目无偏题、怪题,难度适中,能体现数学教学重点,题目新颖,开放型和探索型问题占一定的比重。每个年级的数学学习测试题有六个题目,在总体上可以分为两个部分。各年级测试题的第1题至第3题的设计和编排,考虑到各年级学生的知识背景、各年级的数学教学进度、教学重点,目的是考察各年级初中生的数学学习选择能力的现状。各年级的第4题至第6题是相同的,是各年级共用的,各年级学生均具备解这三个题目所需要的知识。它们主要用以考察不同年级初中生数学学习选择能力的发展特点和规律。总体而言,目前初中生数学学习选择能力的水平不高,论文发现并指出各年级初中生在反思、计划、算法优化、数学自我判断能力四个因素上存在不同程度的问题和缺陷。如:缺乏主动反思的意识,反思的层次水平不高;解题的计划性及对所选解题策略有效性的预见能力较差;算法优化程度不高;缺乏对自己问题解决的分析、判断能力等。论文在研究初中生数学学习选择能力的发展特点、规律时,首先根据数学学习选择能力的内涵、数学学习选择能力结构的四因素模型,建构初中生数学学习选择能力评价指标体系,分别给出反思、计划、算法优化、数学自我判断能力的四级发展水平,并运用层次分析法确定四个因素的权重,以对初中生数学学习选择能力进行评价。研究表明:初中生数学学习选择能力及反思、计划、算法优化、数学自我判断能力均在三个年级间存在显著性差异,并且随着年级的升高而上升。我们还从初中生对解题策略类型选择的角度考察初中生数学学习选择能力的发展特点和规律。
第五章总结本研究的主要结论,并依据前几章的调查、测试、访谈等研究,探讨培养初中生数学学习选择能力的主要途径,笔者提出如下五条策略:使初中生经历数学活动以获得必备的数学基本活动经验,培养初中生数学学习自我效能感及形成良好的学习归因,将“尝试—错误”作为培养初中生数学学习选择能力的一种有效手段,促进初中生解题策略由旧到新的转变,利用概念图促进初中生数学学习选择能力的发展。
Junior middle school students’selective ability to mathematics learning(SAML)is a valuable research area, which has the theoretical and practical significance in the research field of mathematics education. So far, the research on the students’selective ability hasn’t been paid enough attention in the study of students’mathematical ability. Theoretical and empirical research on students’selection in mathematics learning was not a hot topic in mathematics education.
This paper is conducted on the basis of reviewing a large amount of related materials, combined with characteristics of mathematical science and mathematics teaching practice. As a comprehensive study, the paper is the combination of the theory and practice. Firstly, based on the analysis related theories, the paper defines the concept of junior middle school students’SAML. Secondly, the paper studies the structure of SAML. Thirdly, the paper analyzes the factors affecting junior middle school students’SAML. Fourthly, the paper studies current status and the law of development of junior middle school students’SAML. Finally, based on these investigation and tests, we summarize the conclusions of the study and provide strategies for fostering junior middle school students’SAML. This paper consists of six chapters.
The introduction part mainly analyzes the background of this study and proposes aims and content in the paper. We analyze related literature as well as the significance and value of the paper.
Chapter 1 mainly analyzes the concept of junior middle school students’SAML. The conception of junior middle school students’SAML is proposed. The definition is as follows: to ensure high quality and high efficiency in mathematics learning, junior middle school students can filter, absorb and process correct and reasonable information actively and consciously. They can monitor the selection’s effect on their mathematics learning and regulate their selection. Junior middle school students’SAML consists of both cognitive components and metacognitive components. On these bases, the paper put forward theoretical assumption of the structure of SAML.
Chapter 2 mainly studies the structure of SAML. On the basis of analyzing the theory of mathematics learning and consulting experts about the study, the paper shapes the preliminary questionnaire of junior middle school students’SAML. The study investigates 846 junior middle school students in three grades from two middle schools, 752 of which are valid. We adopt research method of cross–validation in the study. Exploratory Factor Analysis is undertaken in 399 subjects who are selected randomly. On the other hand, Confirmatory Factor Analysis is undertaken in 353 subjects. Based on the studies above, we conclude that the structure of junior middle school students’SAML consists of four factors, i.e., reflection, plan, algorithm optimization, self judgement in mathematics. The formal questionnaire is developed based on the study mentioned above. Reliability and validity of the formal questionnaire conforms to the statistical analysis standard.
Chapter 3 mainly analyzes the factors affecting junior middle school students’SAML through empirical study. This study investigates 441 junior middle school students, 379 of which are valid, from three grades in two middle schools. The instruments of this study are formal questionnaire of junior middle school students’SAML, questionnaires of self-efficacy in mathematics, learning motivation in mathematics, learning attribution in mathematics, conception of mathematics. Firstly, we analyze mathematics teaching level’s effect on junior middle school students’SAML. The result shows that mathematics teaching level is a key factor affecting junior middle school students’SAML. Secondly, the multiple regression analysis is carried out, taking junior middle school students’SAML as dependent variable, and sub-elements of mathematics self-efficacy, mathematics learning motivation, mathematics learning attribution, conception of mathematics as independent variable. The result shows that intrinsic motivation, conception of mathematic learning process, positive answer to difficulty, intrinsic attribution have significant regression effect to junior middle school students’SAML. Thirdly, the multiple regression analysis is carried out, taking reflection, plan, algorithm optimization, self judgement in mathematics as dependent variable respectively, and sub-elements of mathematics self-efficacy, mathematics learning motivation, mathematics learning attribution, conception of mathematics as independent variable. The studies mentioned above provide several important references for fostering junior middle school students’SAML in mathematics teaching.
Chapter 4 mainly studies current status and the law of development of junior middle school students’SAML. We choose 441 junior middle school students as example, and test them. There are 374 subjects are valid in three grades from two middle schools. Also, 36 subjects are tested by means of retrospective verbal protocol and interview. The instrument of this study is mathematics learning test (opened questionnaire). Mathematics learning test is open-ended. Subjects must answer questions on junior middle school students’SAML, when they solve mathematics problem in the test. There are six problems for every grade. When we choose the first three problems of different grades, we take into account knowledge that students on different grades have, mathematics teaching emphasis on different grades, mathematics teaching schedule of different grades.The remaining three problems are same for all grades. Influence of students’knowledge and experience on their mathematics problem solving is weakened as far as possible, when we choose the three problems. The three problems are used to explore the characteristics and laws of junior middle school students’SAML. The paper analyzes the first three problems of different grades to explore current status among three grades in junior middle school. As a whole, junior middle school students’SAML is low. For students on different grades, we point out shortcomings and problems of junior middle school students’SAML. Next, according to the concept and the structure of junior middle school students’SAML, we establish index system of junior middle school students’SAML evaluation. The development level of four factors is determined. The weight of four factors is calculated by means of Analytical Hierarchy Process. Based on the above analysis, we can evaluate junior middle school students’SAML. The result shows that for students on the three grades in junior middle school, there is significant difference in SAML and four factors. The level of SAML and four factors move upward with grade.
Chapter 5 mainly summarizes the conclusions of the study and explores ways of cultivating junior middle school students’SAML. On the basis of above-mentioned studies, we provide several strategies. Teachers can cultivate students’fundamental activity experience by means of mathematics activity.Mathematics teachers should attach great importance to cultivating mathematics self-efficacy, mathematics learning attribution of junior middle school students. Trial and error is an effective means in mathematics learning. When students learn new strategy, teachers can improve the application of new strategy. Teachers can promote the development of junior middle school students’SAML by means of concept map.
本研究是在阅读大量与数学学习选择能力相关文献的基础上,结合数学学科特点和初中数学教学实践而进行的理论和实践相结合的综合研究。论文的研究思路是:在分析相关理论的基础上,本文对初中生数学学习选择能力的概念作以界定,并丰富其内涵;在此基础上,本文建构初中生数学学习选择能力的结构;分析影响初中生数学学习选择能力的因素;研究初中生数学学习选择能力的现状以及发展特点、规律;最后,总结本研究的主要结论,并依据上述的调查、测试、访谈等研究,探讨培养初中生数学学习选择能力的主要途径,并为数学教学中培养初中生的数学学习选择能力提供策略和建议。全文共分为六个部分:导论主要分析研究的背景,确定论文的研究框架、所研究的具体内容及研究思路和研究方法,对相关的文献进行梳理与分析,然后提出本研究的意义和价值。
第一章主要对初中生数学学习选择能力的概念进行分析。在相关的理论前提和基础上,论文提出初中生数学学习选择能力的概念。初中生数学学习选择能力是指为了保证数学学习的高质量和高效率,初中生能对数学学习中的信息积极、主动、有意识地做出正确、合理的筛选、吸收和加工,能监控自己在数学学习中的选择对数学学习产生的影响,并能调节自己选择行为的一种个性心理特征。初中生数学学习选择能力既包含对数学学习中的信息进行吸收、加工等认知成分,又包含对自己的选择进行监控、调节等元认知成分。在概念界定的基础上,论文提出初中生数学学习选择能力结构的理论构想。
第二章主要通过实证研究建构初中生数学学习选择能力的结构。在对数学学习理论分析并征求相关专家、数学一线教师和初中数学教研员意见的基础上,初步形成数学学习选择能力的调查问卷。我们挑选济南市两所初中的三个年级的846名学生进行测试,有效被试752名。我们采用交叉证实的方法,将被试随机分为两组,对其中的399名被试进行探索性因素分析,对其余的353名被试进行验证性因素分析,并确定初中生数学学习选择能力结构由反思、计划、算法优化、数学自我判断能力四个因素组成。在上述研究的基础上,论文形成初中生数学学习选择能力的正式问卷,并且正式问卷的信度和效度符合心理学标准。
第三章主要是通过实证研究分析影响初中生数学学习选择能力的因素。笔者运用正式的初中生数学学习选择能力问卷,以及数学自我效能、数学学习动机、数学学习归因、数学观念和态度的问卷,对济南市两所初中的三个年级的441名学生进行调查和测试,其中有效被试379名。实证分析的结果以及对结果的分析如下:第一,分析数学教学水平对初中生数学学习选择能力的影响,结果表明数学教学水平是影响初中生数学学习选择能力及反思、计划、算法优化与数学自我判断能力的一个重要因素。第二,以初中生数学学习选择能力为因变量,以数学自我效能、数学学习动机、数学学习归因、数学观念和态度这四个因素中,每个因素所包含的维度为自变量,进行多元回归分析。结果表明,内源性动机、对数学学习过程的看法、困难应对感、内归因对初中生数学学习选择能力构成显著回归效应。第三,先后分别以反思、计划、算法优化、数学自我判断能力为因变量,以数学自我效能、数学学习动机、数学学习归因、数学观念和态度这几个因素中,每个因素所包含的维度为自变量,先后进行四个多元回归分析,分别得出对反思、计划、算法优化、数学自我判断能力构成显著回归效应的变量。上述研究为数学教学实践中培养初中生的数学学习选择能力提供重要的参考和依据。
第四章主要研究初中生数学学习选择能力的现状和发展特点、规律。笔者根据编制的《初中数学学习测试题(开放式问卷)》对济南市两所初中的三个年级的441名学生进行测试,其中有效被试374名,并对其中的36名被试进行追述性口语报告测试和访谈。初中数学学习测试题是一份开放式问卷,我们针对每个测试题,从反思、计划、算法优化、数学自我判断能力方面设计了相关的问题,要求学生在解决数学问题的同时,回答体现初中生数学学习选择能力水平的提问。我们在选取测试题目时尽可能削弱学生已有的知识、经验对解题的影响。保证测试题目无偏题、怪题,难度适中,能体现数学教学重点,题目新颖,开放型和探索型问题占一定的比重。每个年级的数学学习测试题有六个题目,在总体上可以分为两个部分。各年级测试题的第1题至第3题的设计和编排,考虑到各年级学生的知识背景、各年级的数学教学进度、教学重点,目的是考察各年级初中生的数学学习选择能力的现状。各年级的第4题至第6题是相同的,是各年级共用的,各年级学生均具备解这三个题目所需要的知识。它们主要用以考察不同年级初中生数学学习选择能力的发展特点和规律。总体而言,目前初中生数学学习选择能力的水平不高,论文发现并指出各年级初中生在反思、计划、算法优化、数学自我判断能力四个因素上存在不同程度的问题和缺陷。如:缺乏主动反思的意识,反思的层次水平不高;解题的计划性及对所选解题策略有效性的预见能力较差;算法优化程度不高;缺乏对自己问题解决的分析、判断能力等。论文在研究初中生数学学习选择能力的发展特点、规律时,首先根据数学学习选择能力的内涵、数学学习选择能力结构的四因素模型,建构初中生数学学习选择能力评价指标体系,分别给出反思、计划、算法优化、数学自我判断能力的四级发展水平,并运用层次分析法确定四个因素的权重,以对初中生数学学习选择能力进行评价。研究表明:初中生数学学习选择能力及反思、计划、算法优化、数学自我判断能力均在三个年级间存在显著性差异,并且随着年级的升高而上升。我们还从初中生对解题策略类型选择的角度考察初中生数学学习选择能力的发展特点和规律。
第五章总结本研究的主要结论,并依据前几章的调查、测试、访谈等研究,探讨培养初中生数学学习选择能力的主要途径,笔者提出如下五条策略:使初中生经历数学活动以获得必备的数学基本活动经验,培养初中生数学学习自我效能感及形成良好的学习归因,将“尝试—错误”作为培养初中生数学学习选择能力的一种有效手段,促进初中生解题策略由旧到新的转变,利用概念图促进初中生数学学习选择能力的发展。
Junior middle school students’selective ability to mathematics learning(SAML)is a valuable research area, which has the theoretical and practical significance in the research field of mathematics education. So far, the research on the students’selective ability hasn’t been paid enough attention in the study of students’mathematical ability. Theoretical and empirical research on students’selection in mathematics learning was not a hot topic in mathematics education.
This paper is conducted on the basis of reviewing a large amount of related materials, combined with characteristics of mathematical science and mathematics teaching practice. As a comprehensive study, the paper is the combination of the theory and practice. Firstly, based on the analysis related theories, the paper defines the concept of junior middle school students’SAML. Secondly, the paper studies the structure of SAML. Thirdly, the paper analyzes the factors affecting junior middle school students’SAML. Fourthly, the paper studies current status and the law of development of junior middle school students’SAML. Finally, based on these investigation and tests, we summarize the conclusions of the study and provide strategies for fostering junior middle school students’SAML. This paper consists of six chapters.
The introduction part mainly analyzes the background of this study and proposes aims and content in the paper. We analyze related literature as well as the significance and value of the paper.
Chapter 1 mainly analyzes the concept of junior middle school students’SAML. The conception of junior middle school students’SAML is proposed. The definition is as follows: to ensure high quality and high efficiency in mathematics learning, junior middle school students can filter, absorb and process correct and reasonable information actively and consciously. They can monitor the selection’s effect on their mathematics learning and regulate their selection. Junior middle school students’SAML consists of both cognitive components and metacognitive components. On these bases, the paper put forward theoretical assumption of the structure of SAML.
Chapter 2 mainly studies the structure of SAML. On the basis of analyzing the theory of mathematics learning and consulting experts about the study, the paper shapes the preliminary questionnaire of junior middle school students’SAML. The study investigates 846 junior middle school students in three grades from two middle schools, 752 of which are valid. We adopt research method of cross–validation in the study. Exploratory Factor Analysis is undertaken in 399 subjects who are selected randomly. On the other hand, Confirmatory Factor Analysis is undertaken in 353 subjects. Based on the studies above, we conclude that the structure of junior middle school students’SAML consists of four factors, i.e., reflection, plan, algorithm optimization, self judgement in mathematics. The formal questionnaire is developed based on the study mentioned above. Reliability and validity of the formal questionnaire conforms to the statistical analysis standard.
Chapter 3 mainly analyzes the factors affecting junior middle school students’SAML through empirical study. This study investigates 441 junior middle school students, 379 of which are valid, from three grades in two middle schools. The instruments of this study are formal questionnaire of junior middle school students’SAML, questionnaires of self-efficacy in mathematics, learning motivation in mathematics, learning attribution in mathematics, conception of mathematics. Firstly, we analyze mathematics teaching level’s effect on junior middle school students’SAML. The result shows that mathematics teaching level is a key factor affecting junior middle school students’SAML. Secondly, the multiple regression analysis is carried out, taking junior middle school students’SAML as dependent variable, and sub-elements of mathematics self-efficacy, mathematics learning motivation, mathematics learning attribution, conception of mathematics as independent variable. The result shows that intrinsic motivation, conception of mathematic learning process, positive answer to difficulty, intrinsic attribution have significant regression effect to junior middle school students’SAML. Thirdly, the multiple regression analysis is carried out, taking reflection, plan, algorithm optimization, self judgement in mathematics as dependent variable respectively, and sub-elements of mathematics self-efficacy, mathematics learning motivation, mathematics learning attribution, conception of mathematics as independent variable. The studies mentioned above provide several important references for fostering junior middle school students’SAML in mathematics teaching.
Chapter 4 mainly studies current status and the law of development of junior middle school students’SAML. We choose 441 junior middle school students as example, and test them. There are 374 subjects are valid in three grades from two middle schools. Also, 36 subjects are tested by means of retrospective verbal protocol and interview. The instrument of this study is mathematics learning test (opened questionnaire). Mathematics learning test is open-ended. Subjects must answer questions on junior middle school students’SAML, when they solve mathematics problem in the test. There are six problems for every grade. When we choose the first three problems of different grades, we take into account knowledge that students on different grades have, mathematics teaching emphasis on different grades, mathematics teaching schedule of different grades.The remaining three problems are same for all grades. Influence of students’knowledge and experience on their mathematics problem solving is weakened as far as possible, when we choose the three problems. The three problems are used to explore the characteristics and laws of junior middle school students’SAML. The paper analyzes the first three problems of different grades to explore current status among three grades in junior middle school. As a whole, junior middle school students’SAML is low. For students on different grades, we point out shortcomings and problems of junior middle school students’SAML. Next, according to the concept and the structure of junior middle school students’SAML, we establish index system of junior middle school students’SAML evaluation. The development level of four factors is determined. The weight of four factors is calculated by means of Analytical Hierarchy Process. Based on the above analysis, we can evaluate junior middle school students’SAML. The result shows that for students on the three grades in junior middle school, there is significant difference in SAML and four factors. The level of SAML and four factors move upward with grade.
Chapter 5 mainly summarizes the conclusions of the study and explores ways of cultivating junior middle school students’SAML. On the basis of above-mentioned studies, we provide several strategies. Teachers can cultivate students’fundamental activity experience by means of mathematics activity.Mathematics teachers should attach great importance to cultivating mathematics self-efficacy, mathematics learning attribution of junior middle school students. Trial and error is an effective means in mathematics learning. When students learn new strategy, teachers can improve the application of new strategy. Teachers can promote the development of junior middle school students’SAML by means of concept map.
引文
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