初中数学学习障碍学生一元一次方程应用题解题过程及补救教学的个案研究

发布时间：2017-12-30 22:43

本文关键词：初中数学学习障碍学生一元一次方程应用题解题过程及补救教学的个案研究　出处：《重庆师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：数学学习障碍是学习障碍研究的重要领域,已有研究对初中数学学习障碍学生解题过程和补救教学方面的研究较少。本研究主要以认知心理学家Mayer的解题理论为理论依据,采用测验法和访谈法,探讨了一名初中数学学习障碍学生在解一元一次方程应用题时的解题过程,并实施12课时的补救教学后,学生在解题表现方面有明显进步,研究结果发现如下:在解题过程方面,研究结果发现:(1)语言知识缺乏。数学学习障碍学生对关系句的理解比较困难,对已知条件的提取能力较差,对解题目标的理解困难。(2)语义知识欠缺。在与解题相关的生活常识上比较匮乏,在单位换算转换方面存在困难。(3)图式知识模糊。对问题类型的辨识困难,对等量关系的理解和记忆能力较差,利用等量关系列方程的能力较弱。(4)策略知识单一。使用的解题策略种类极为单一,不习惯使用列一元一次方程的策略解题,缺少回顾检查的监控策略,易出现随意拼凑数字进行列式的不成熟策略。(5)程序知识不熟练。计算速度慢,计算过程呈现反复的情况,一元一次方程移项时运算符号易出错,列竖式计算出错率较高,缺少验算的习惯,常忘记把计算结果和解题目标进行对照。在补救教学方面,研究结果发现:(1)语言知识:对关系句转换技巧的讲解和练习,提醒学生提高读题次数,采取口语读题,多元表征的训练,有助于学生理解已知条件和解题目标。(2)语义知识:不同情景常识的学习、单位换算的练习,能有效提高学生对于题意的理解程度。(3)图式知识:应用题分类教学,能提高学生对问题类型的辨识能力;对公式的理解和记忆,可以有效提高学生寻找等量关系的能力;引导学生利用等量关系或者抓住不变量进行方程的列式,可以增进学生的问题解决能力。(4)策略知识:算术和方程在列式策略方面的对比教学,可以加速学生从算术思维向代数思维的转变。使用列表法、图示法、分段讨论法、间接设元法、回顾检查等解题策略,能有效提高学生对已知条件和解题目标的整合能力。(5)程序知识:逐步计算,算术和方程中“等号”含义的对比讲解,列竖式计算时把进位的数字明确标示出来,把计算结果回代到方程验算,都可以有效提高计算的准确率。
[Abstract]:Mathematics learning disabilities is an important field in the study of learning disorder, existing research study disabled students problem solving process and remedial teaching less on junior high school mathematics. This research is mainly based on cognitive psychologist Mayer's theory as the theoretical basis, the method of test and interviews, to explore a junior high school students with mathematics learning disabilities in solving a the quadratic equation applied problems solving process, remedial teaching and implement 12 hours after the students have obvious progress in problem-solving performance, the research results are as follows: in the process of solving problems, the results showed that: (1) lack of linguistic knowledge. Students with mathematics learning disabilities to understand the relation between sentences difficult to known conditions the extraction ability is poor, on the problem-solving goal understanding difficulties. (2) the lack of semantic knowledge. In knowledge and solving problems related to life is relatively scarce, in the unit conversion difficulty . (3). Fuzzy identification difficulty of schema knowledge type of problem, the equivalent relation of comprehension and memory ability, using a series of equivalent equation is weaker. (4). A single species strategy knowledge problem-solving strategies use is extremely simple, not accustomed to using a column strategy problem solving one equation, the lack of review of monitoring inspection strategy, prone to random numbers together column type is not mature strategy. (5) program knowledge is not skilled. Computing speed and computing process is repeated, one equation when the transpose operation symbols and error prone, vertical form error rate is high, the lack of the habit of checking, often forget the results of calculation and solving target control. In remedial teaching, the results showed that: (1) knowledge of language: Practice on the relationship between sentence explanation and skills, remind students to improve reading times, take oral reading problems, multiple representation training That helps students to understand the known conditions and problem solving goals. (2) semantic knowledge: scenarios of knowledge learning, conversion of practice, can effectively improve the students' understanding of the problem. (3): application of schema knowledge teaching can improve the students' ability of classification, identification of problem types; understanding and memory of the the formula, can effectively improve the students' ability to find equivalent relation; guide the students to use the equivalent relationship or column type hold invariant equation, can improve the students' ability to solve problems. (4): arithmetic and strategy of knowledge in teaching contrast equation strategy, can accelerate students' transition from arithmetic thinking to algebraic thinking use the list method, graphic method, discussed method, indirect design element method, review inspection strategy can effectively improve the students' ability to integrate the known conditions and problem solving goals. (5) program knowledge: step by step calculation The arithmetic and the equation, "equal" meaning contrast explanation, the vertical columns carry the figures clearly marked, and the calculated results back to equation calculation, can effectively improve the calculation accuracy.

【学位授予单位】：重庆师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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