六年级学生解应用题的认知诊断研究

发布时间：2018-08-26 20:01

【摘要】：问题解决是国际数学教育的一个重要研究方向,而解应用题是小学生问题解决中重点且难点内容。作为新一代的测量理论——认知诊断理论,突破了传统测量仅对宏观水平的评估方式,为此本研究将其作为诊断小学生解应用题的内部心理加工过程的理论工具,研究六年级学生解应用题的知识结构的掌握水平及缺失,为教师补救性教学提供依据。本研究首先运用Mayer命题分析法,结合ShalinBee的符号网络分析法对小学应用题(代数应用题)在情境结构和数量结构上进行划分,建立小学应用题的题库资源;运用认知分析法,析出解应用题的2大成分所对应的7个认知属性,即操作成分中:A1(基本算术运算)、A2(多步运算)、A5(识别隐含条件)、A6(算式表征)、A7(正规代数策略);图式成分中:A3(基本数量关系)、A4(复杂知识图式);并建构7个属性间的层级关系(认知模型);基于认知模型和AHM思想编制测验卷,对5所城市11个班级的531名小六学生实施诊断;最后运用multilog7.0软件和属性不等权重多级评分AHM的matlab程序实现对被试的能力以及属性掌握模式的归类的诊断评估。根据诊断结果得出如下结论:(1)总体属性掌握模式归类上:531名被试共21种属性掌握模式;分布最多为全1模式和部分全1模式,较少的为仅掌握A1或全0模式;属性平均掌握水平上,A1(基本运算)和A3(基本数量关系)属性掌握得较为理想,而A4(复杂知识图式)和A7(正规代数策略)为整体学生的薄弱属性;(2)知识状态掌握上的城乡性别差异:城乡间原始总分差异较为明显,城市高分段的人数相对城市较为集中,超过一半的人集中于64-71分之间;在属性掌握模式占比上,大多数模式的男生占比高于女生;城乡差异在A1-A7属性上均较为显著,而男女性别差异仅在A4属性上显著;(3)知识状态掌握上的优差生差异:高分段被试对于A1-A7个属性的掌握概率较为稳定,均在0.962-0.994之间,低分段被试中,A2、A4、A7属性的平均掌握概率小于0.4,其中A4(复杂知识图式)和A7(正规代数策略)均低于0.3,各属性平均掌握概率上优生明显优于差生;鉴于此,提出补救性教学建议:(1)加强A4和A7属性的补救性教学;(2)加强基础性属性的突破教学演练以缩小城乡差异;(3)分析后进生知识状态,及时调整教学设计;
[Abstract]:Problem solving is an important research direction in international mathematics education. As a new generation of measurement theory, cognitive diagnosis theory has broken through the traditional measurement evaluation method of only macroscopic level. Therefore, this study uses it as a theoretical tool to diagnose the inner mental processing process of elementary school students' application problem solving. In order to provide the basis for remedial teaching, this paper studies the level and deficiency of the knowledge structure of the sixth grade students in solving word problems. This study first uses Mayer propositional analysis method, combined with ShalinBee's symbolic network analysis method to divide primary school word problems (algebraic word problems) into situation structure and quantitative structure, and sets up the question bank resources of primary school word problems, and uses cognitive analysis method. Seven cognitive attributes corresponding to the two major components of the solution to the application problem, That is, in the operation component: A1 (basic arithmetic operation) / A2 (multi-step operation) / A5 (identifying implicit condition) / A6 (arithmetic representation) / A7 (normal algebraic strategy); in the schema component: A3 (basic quantitative relation) / A4 (complex knowledge schema); and the hierarchy of seven attributes is constructed. Department (Cognitive Model); Test papers based on Cognitive Model and AHM thought, 531 primary school six students in 11 classes in 5 cities were diagnosed, and finally, multilog7.0 software and matlab program of attribute unequal weight multilevel score AHM were used to evaluate the ability of the subjects and the classification of attribute mastery model. According to the results of diagnosis, the following conclusions are drawn: (1) the total attribute mastering model is classified into 21 kinds of attribute mastering modes in the total attribute mastery model of: 531 subjects, the distribution is at most all 1 mode and partial all 1 mode, less is only master A1 or all 0 mode; The average mastery level of attributes is better than that of A1 (basic operation) and A3 (basic quantitative relation). While A4 (complex knowledge schema) and A7 (formal algebra strategy) are the weak attributes of the whole students; (2) the sex difference in knowledge status between urban and rural areas: the difference of the original total score between urban and rural areas is obvious, and the number of urban high scores is more concentrated than that of the city. More than half of the people were between 64 and 71; most of them had higher proportion of boys than girls in attribute mastering mode; the difference between urban and rural areas was significant in A1-A7 attributes. The difference between male and female was only significant in A4 attribute. (3) the difference of superior and inferior students in knowledge state: the probability of mastering A1-A7 attributes in the high score group was stable, ranging from 0.962-0.994. The average mastering probability of A2A2A4A7 attribute is less than 0.4, in which A4 (complex knowledge schema) and A7 (normal algebra strategy) are all lower than 0.3, the average mastering probability of each attribute is obviously better than that of poor student. Some suggestions on remedial teaching are put forward: (1) to strengthen remedial teaching of A4 and A7 attributes, (2) to strengthen the breakthrough teaching exercises of basic attributes in order to reduce the differences between urban and rural areas, (3) to analyze the knowledge status of backward students, and to adjust the teaching design in time;
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G623.5

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