基于GeoGebra的高中数学探究式教学研究

【作者】 李敏；

【导师】 王海平； 陆新生；

【作者基本信息】 上海师范大学 ， 教育硕士（专业学位）， 2022， 硕士

【副题名】以圆锥曲线为例

【摘要】 随着课程改革的不断深入,与传统教学方式相对的探究式教学越来越受到教育者的重视。相关研究表明,探究式教学可以改善学生在数学教学中的表现,提升学生数学能力,对学生的数学学习有积极的影响。随着科学技术的迅速发展,许多软件被开发运用到数学教学之中,Geo Gebra作为一款功能强大、操作简单的免费动态软件,可以有效提高课堂效率。同时,圆锥曲线作为高中数学的重要内容,知识复杂繁多,给许多学生造成困扰。因此,笔者试图以圆锥曲线为载体,将Geo Gebra和数学探究式教学结合起来进行研究。本文研究的问题有三个:(1)高中生的数学探究意识如何?(2)如何将Geo Gebra与高中数学课程融合,进而开展有效的探究式教学活动?(3)基于Geo Gebra的高中数学探究式教学是否可以提高学生的数学学习兴趣、数学探究能力、数学成绩?针对问题1,笔者制作了调查问卷,以四川省成都市某高中高二151名学生为对象进行了调查。针对问题2,笔者通过梳理相关文献,对Geo Gebra软件的特点,数学探究式教学的相关理论、教学原则、教学模式、实施策略,圆锥曲线相关教学内容的要求和特点等方面进行了研究。针对问题3,以四川省成都市某高中高二两个班学生为对象进行了教学实验,实验班开展运用Geo Gebra的数学探究式教学,对照班采用传统式教学。以问卷调查和测试卷的形式进行前测和后测,考察学生的数学学习兴趣、数学探究能力、数学成绩是否发生改变。其中,数学学习兴趣的改变,是通过问卷调查进行考察;数学探究能力,是通过数学探究能力测试卷进行考察;数学成绩的变化,是利用数学月考试卷进行分析。根据实验结果,可以得到以下结论:(1)高中生的数学探究意识普遍不强;(2)结合探究式教学的理论,建立了基于Geo Gebra的高中数学探究式教学设计的一般模式和设计原则(主体性、价值性、适宜性、简单性、过程性),提出了开展基于Geo Gebra的高中数学探究式教学的策略(创设问题情境、引导发现问题、营造探究氛围、避免假性探究、注重循序渐进),并以圆锥曲线为例,分析了该章节作为教学内容载体的可行性和必要性,然后依据上述内容,以圆锥曲线为载体,设计了3个教学案例;(3)基于Geo Gebra的数学探究式教学,可以提高学生的数学学习兴趣,可以提升学生的数学探究能力,但对数学证明能力和数学拓展与推广能力作用不大,对学生数学成绩的提高没有显著性作用。更多还原

【Abstract】 With the deepening of the new curriculum reform,inquiry-based teaching has received more and more attention from educators.Relevant studies have shown that inquiry-based teaching can improve students’ performance in mathematics teaching,enhance students’ mathematical ability,and have a positive impact on students’ mathematical learning.On the other hand,with the rapid development of science and technology,many software has been developed and applied to mathematics teaching,Geo Gebra as a highly interactive,powerful,simple to operate free dynamic software.At the same time,as an important part of high school mathematics,the conic curve has a complex knowledge and causes trouble to many students.Therefore,the author tries to use the conic curve as a carrier to combine Geo Gebra and mathematical inquiry-based teaching for research.There are three research questions in this paper:(1)What is the sense of inquiry of high school students?(2)How to integrate Geo Gebra with the high school math curriculum to carry out effective inquiry-based teaching activities?(3)Can geo Gebra-based high school mathematical inquiry-based teaching improve students’ interest in mathematical learning,mathematical inquiry ability,and mathematical achievement?In response to question 1,the author produced a questionnaire and conducted a survey of 151 students in the second year of high school in Chengdu,Sichuan Province.In view of question 2,by combing through the relevant literature,the author studied the characteristics of Geo Gebra software,the relevant theories,teaching principles,teaching modes,implementation strategies,and requirements and characteristics of the teaching content related to the cone curve by combing through the relevant literature.In response to question 3,two classes of students from a high school in Chengdu,Sichuan Province,were subjected to teaching experiments,and the experimental class carried out mathematical inquiry-based teaching using Geo Gebra,and the control class adopted traditional teaching.The pre-test and post-test are conducted in the form of questionnaires and test papers to examine whether students’ mathematical learning interests,mathematical inquiry ability,and mathematical performance have changed.Among them,the change of interest in mathematical learning is examined through a questionnaire survey,the ability to explore mathematics is examined through the test paper of mathematical inquiry ability,and the change in mathematical score is analyzed by using the monthly examination paper of mathematics.According to the experimental results,the following conclusions can be drawn:(1)the sense of inquiry of high school students is generally not strong;(2)combined with the theory of inquiry-based teaching,the general mode and design principles of high school mathematical inquiry-based teaching design based on Geo Gebra(subjectivity,value,appropriateness,simplicity,process)are established,and the strategy of high school mathematical inquiry-based teaching based on Geo Gebra is proposed(creating problem situations,guiding the discovery of problems,creating an atmosphere of inquiry,avoiding false inquiry,Timely reflection and evaluation),and analyzed the feasibility and necessity of using the conic curve as the carrier of teaching content,and then based on the above content,three teaching cases were designed with the conic curve as the carrier;(3)Geo Gebra-based mathematical inquiry-based teaching can improve students’ interest in mathematical learning and improve students’ mathematical inquiry ability,but it has little effect on mathematical proof ability and mathematical expansion and promotion ability,and has no significant effect on the improvement of students’ mathematical achievements.更多还原