小学生数学合情推理能力及其培养策略研究

发布时间：2018-05-23 13:16

本文选题：合情推理能力 + 小学数学　；参考：《华中师范大学》2017年硕士论文

【摘要】：合情推理是最具数学学科特征的内容之一,在小学数学教学中不可或缺。学生的数学合情推理能力是衡量其数学素养的重要指标,它不仅有利于培养创新意识和发散性思维,还能够提高解决问题的能力。然而,由于我国数学教育对合情推理的研究时间不长,当前教学中学生合情推理能力的培养有些迷茫。本文试图从理论上对小学生数学合情推理能力作一些探讨,在实践中探寻小学生数学合情推理能力培养中的问题及改进策略。本文除绪论外,总共包括四个部分。第一部分旨在阐明小学生数学合情推理能力的含义、组成因素及其表现。小学生数学合情推理能力是指小学生在具体的数学问题情境中,根据已有的基础知识和经验(即原有的认知结构),通过观察、归纳、类比、猜想等思维过程,运用估算、画图、列表等数学方法对所学知识推断出某些合乎情理的结果时所表现出来的一种个性心理特征。它由数学观察能力、数学归纳和类比推理的能力、数学猜想能力、清晰表达数学思维的能力、合情推理元认知能力组成。第二部分梳理了小学数学合情推理的课程安排,并结合典型课时内容进行分析。以人教版小学数学教科书为例,从不同学段、不同课程版块两个维度对教科书中适合渗透合情推理教学的课程内容进行梳理,并挑选五个课时分别突出合情推理能力各组成因素的培养特点。第三部分主要分析了小学生数学合情推理能力培养中的问题及其原因。由于数学课标对“合情推理能力”的表述笼统,当前的评价目标导向不明确,加之教师的数学素养水平有限,导致教师对合情推理能力的认知不够深入,对其培养重视不足,合情推理能力的培养过程缺乏严谨性,培养方法单一。第四部分针对小学生数学合情推理能力培养中的问题,提出了三个方面的改进策略。首先,教师要准确理解合情推理能力。不仅要研读课标和教材,把握合情推理的本质;还要更新教学理念,注重合情推理能力的培养。其次,教师要合理把握不同学段学生合情推理能力的培养特点。第一学段重在培养学生的数学观察、猜想能力,第二学段重在培养学生的数学归纳、类比推理能力。最后,教师要多渠道拓宽合情推理能力的培养方法。通过创设数学问题情境、鼓励大胆猜想、出声思维训练来引发、形成和深化合情推理。
[Abstract]:Reasonable reasoning is one of the most characteristic contents of mathematics, which is indispensable in mathematics teaching in primary school. Students' mathematical reasoning ability is an important index to measure their mathematical literacy. It is not only conducive to the cultivation of innovative awareness and divergent thinking, but also to improve the ability to solve problems. However, due to the short time of research on reasonable reasoning in mathematics education in our country, the cultivation of reasonable reasoning ability of middle school students in current teaching is somewhat confused. This paper attempts to make some theoretical discussion on the mathematical reasoning ability of primary school students, and to explore the problems and improvement strategies in the cultivation of pupils' mathematical reasonable reasoning ability in practice. In addition to the introduction, this paper consists of four parts. The first part is to clarify the meaning, composition and expression of pupils'mathematical reasoning ability. Elementary school students' mathematical reasoning ability refers to the basic knowledge and experience (i.e. the original cognitive structure) of elementary school students in the specific mathematical problem situation, through observation, induction, analogy, conjecture and other thinking processes, the use of estimation, drawing, and so on. A psychological characteristic of personality when mathematical methods such as lists infer reasonable results from what they have learned. It consists of the ability of mathematical observation, mathematical induction and analogy reasoning, mathematical conjecture, the ability to express mathematical thinking clearly, and the metacognitive ability of reasonable reasoning. The second part combs the elementary school mathematics reasonable reasoning curriculum arrangement, and unifies the typical class time content carries on the analysis. Taking the primary school mathematics textbook as an example, this paper combs the curriculum content suitable for permeating the reasonable reasoning teaching from two dimensions of different learning stages and different curriculum sections. Five classes were selected to highlight the characteristics of each component of reasonable reasoning ability. The third part mainly analyzes the problems and causes in the cultivation of mathematical reasoning ability of primary school students. Due to the general description of "reasonable reasoning ability" in mathematics class standard, the unclear orientation of evaluation goal and the limited level of teachers' mathematical literacy, the teachers' cognition of reasonable reasoning ability is not deep enough, and the training of reasonable reasoning ability is not paid enough attention to. The training process of reasonable reasoning ability is lack of rigor, and the training method is single. In the fourth part, aiming at the problems in the cultivation of pupils' mathematical reasoning ability, three improvement strategies are put forward. First of all, teachers should accurately understand the ability of reasonable reasoning. We should not only study the curriculum standard and teaching material, grasp the essence of reasonable reasoning, but also renew the teaching concept and pay attention to the cultivation of reasonable reasoning ability. Secondly, teachers should grasp the characteristics of reasonable reasoning ability of students from different learning stages. The first stage focuses on cultivating students' ability of mathematical observation and guess, and the second paragraph focuses on cultivating students' ability of mathematical induction and analogical reasoning. Finally, teachers should broaden the cultivation method of reasonable reasoning ability through multiple channels. By creating mathematical problem situations, encouraging bold conjecture and sound thinking training, the rational reasoning is formed and deepened.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G623.5

【参考文献】