初中生对不等式的理解

发布时间：2018-03-20 17:08

本文选题：数学理解　切入点：理解水平　出处：《闽南师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：数学理解是数学教育的中心问题,而不等式又是初中数学教学中的重要内容,因此初中生对不等式的理解就是初中数学教学的重要任务之一。为此,本文以“记忆性理解水平、解释性理解水平、探究性理解水平”为研究初中生对不等式的理解的理论框架,以此框架来了解初中生对不等式的理解情况以及初中生在不等式学习中的易错点。为了了解初中生对不等式的理解在以上三个理解水平上的现状,本文将初中阶段有关不等式的知识划分为五个维度(不等关系、不等式的基本性质、不等式的解集、一元一次不等式(组)、一元一次不等式的应用),根据这五个维度设置测试题,运用随机抽样的方法进行调查研究。研究发现:初中生对不等式的理解在三个理解水平上是递减的;对不等式相关概念的理解明显低于对不等式其他知识的理解;对不等式的学习易受等式的影响;综合运用不等式知识的能力不强。研究还发现,初中生在不等式学习中易在以下几个方面出现错误:(1)解不等式时,易出现由等式到不等式的类比过度一般化的错误;(2)表示不等式的解集时,数轴表示和代数表示之间的相互转化容易出现错误;(3)确定实际问题中未知数的取值范围时容易忽略未知数所受实际问题限制等错误。基于以上研究结论,对初中不等式教学提出了一些具体的建议,供教师参考。
[Abstract]:Mathematics understanding is the central problem in mathematics education, and inequality is an important content in junior high school mathematics teaching. Therefore, the understanding of inequality among junior high school students is an important part of junior high school mathematics teaching. The level of explanatory understanding, the level of exploratory understanding "is the theoretical framework for studying junior high school students' understanding of inequalities." In order to understand the current situation of junior high school students' understanding of inequality in the above three levels, we can understand the understanding of inequality and the error-prone points of junior high school students in inequality learning. In this paper, the knowledge of inequality in junior middle school is divided into five dimensions (unequal relation, basic property of inequality, solution set of inequality, etc. The application of the one-dimensional inequality, according to the five dimensions, set the test questions, The results show that junior high school students' understanding of inequality is decreasing at three levels, the understanding of inequality related concepts is obviously lower than that of other knowledge of inequality. The study also found that junior high school students are prone to make mistakes in solving inequalities in the following aspects. It is easy to appear that the analogy from equality to inequality is overgeneralized and the error is 2) when the solution set of the inequality is represented, The transformation between algebraic representation and number axis representation is prone to errors in determining the value range of unknowns in practical problems, and it is easy to ignore errors such as the practical problems limited by unknown numbers, etc. Based on the above conclusions, This paper puts forward some concrete suggestions on inequality teaching in junior high school for teachers' reference.
【学位授予单位】：闽南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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