在图形与几何教学中培养初中生几何直观的教学研究

【作者】 刘畅；

【导师】 朱鸿玲；

【作者基本信息】 天津师范大学 ， 教育硕士（专业学位）， 2019， 硕士

【摘要】 在数学学习中几何和代数的地位是相当的,在生活的方方面面都需要几何知识的辅助,学生们对几何学习的兴趣和方式,对他们未来的发展有着极大的影响。几何直观和空间观念是数学学科核心素养中直观想象的体现和基础。如何培养学生们的几何直观,进而培养他们的创造性思维,是教师们值得思考的问题。义务教育新课标指出,学生应可以通过一系列的探究操作等学习活动建立空间观念,发展几何直观。在小学阶段,学生们已经对几何方面有了初步的了解和学习,但小学阶段的学生智力和思维的发展还没有足够成熟,对于抽象事物的接受能力还存在困难。因此初中阶段培养初中生几何直观与创造性思维就显得至关重要,这个阶段的思维会形成基本的定式,与未来学生的学习以及工作都息息相关。培养初中生的几何直观,也是为今后深入学习立体几何和大学相关知识的学习打下良好的基础。研究对象选取的是实习所在学校初二年级的学生,这个阶段的学生既经历了小学到初中的过渡期,基本适应了初中的学习方式,又不存在中考升学的压力。论文采用文献法,访谈法和案例分析法,在皮亚杰的建构主义学习理论和奥苏贝尔的有意义学习理论的支持下,分析访谈结果,得到几何直观的培养方法和影响因素,分析“对称轴图形”和“勾股定理”两个案例,进而提出几何直观的培养策略。研究表明:对学生识图,作图和用图能力的培养是学生几何直观得以发展的关键。识图是培养几何直观的基础,也是开始思维的第一步;作图是在识图的基础之上进行的,同时也是培养几何直观的中心环节;用图是在识图和作图的基础上进行,用图也是培养几何直观的目标,包括几何直观素养的提升,发散性思维的锻炼以及创造性思维的形成。通过和学生以及教师关于几何直观培养中存在的问题和教学方法进行访谈并进行分析,得到培养初中生几何直观的三个策略,包括:(1)构建丰富直观表象:利用直观模型构建数学表象,熟悉情景导入重塑数学表象(2)提升数学模型意识:鼓励大胆联想,直观表征问题,利用基础模型的归纳,锻炼作图意识(3)培养直观想象能力:结合空间观念培养学生的几何直观,设置因果问题串,培养学生的发散思维。最后通过观摩,教研和一线教师学习,进一步提出建议和不足。更多还原

【Abstract】 The status of geometry and algebra in mathematics learning is comparative.Geometry is required in many aspects of life.Interest and the way of geometry,has a great impact on their future.Geometric intuition and spatial concept are the embodiment and foundation of intuitive imagination in the core accomplishment of mathematics discipline.How to cultivate their geometric intuition and then cultivate their creative thinking is a problem worth thinking about for teachers.The new curriculum standard of compulsory education points out that student should be able to establish the concept of space and develop geometric directness through a series of learning activities such as inquiry operation.In the primary school stage,students have a preliminary understanding and study of geometry,but the development of their intelligence and thinking in the primary school stage is not mature enough,and there are still difficulties in the ability to accept abstract things.Therefore,it is very important to cultivate the ability and thinking of the students in junior high school.The thinking of this stage will form the basic pattern,which is closely related to the future study and work.Cultivating the geometric intuitive ability of junior high school students is also to lay a good foundation for the further study of three-dimensional geometry and university related knowledge in the future.The subjects selected were the eighth grade students in the internship school.In this stage students go through the transition period from primary school to junior high school.They fit in the learning style of junior high school,and there is no high school entrance pressure.The paper adopts literature method,interview method and case analysis method.Based on Piaget constructivism learning theory and Osobel meaningful learning theory,this paper analyzes the interview results,obtains the training methods and influencing factors of geometry intuitionism,analyzes two cases of Axial symmetry and The Pythagorean theorem.And then the training strategy of geometric intuition is proposed.The research shows that the cultivation of their ability to understand,draw and use is the key to the development of geometric intuition ability.Drawing is not only the basis of cultivating geometric intuition,but also the first step of starting thinking.Drawing is carried out on the basis of understanding drawing,but also the central link of cultivating geometric intuitionism;thinking of drawing is carried out on the basis of recognition and drawing,and thinking of drawing is also the goal of cultivating geometric intuition,including the improvement of geometric intuitionistic literacy,the exercise of divergent thinking and the formation of creative thinking.Through interviews and analysis with students and teachers on the existing problems and teaching methods in geometric intuitionistic training,three strategies for cultivating junior high school their geometric intuitionistic ability are obtained.Including:(1)constructing rich intuitive representation:The visual model is used to construct the mathematical representation,and familiar with the scene into the reconstruction of mathematical representation(2)improving mathematical model consciousness:Encourage bold associations,intuitive representation problem,using the induction of the basic model to exercise the drawing consciousness(3)Cultivate visual imagination:combined with the concept of space to cultivate their geometric intuition,setting up a series of causal questions to train their divergent thinking.Finally,through observation,teaching and research and front-line teachers learning,further suggestions and shortcomings are put forward.更多还原