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High School Mathematics Teaching Design Based on Problem Solving—Taking the Standard Equation of a Parabola as an Example
DOI: 10.12677/CES.2023.111023, PDF, HTML, XML, 下载: 22  浏览: 63  科研立项经费支持

Abstract: Problem-solving is the focus of today’s mathematics education circle, is a breakthrough of mathematics reform, is the new trend of mathematics education development. Problem solving ability is the ability of students to put forward and understand problems from the perspective of mathematics, and to comprehensively apply the knowledge and skills they have learned to solve problems. The cultivation of problem solving ability runs through the whole mathematics classroom teaching. Taking the teaching design of “the standard equation of parabola” as an example, this paper expounds on how to cultivate students’ problem-solving ability in the new teaching from three aspects, such as teaching idea, case description and teaching reflection.

1. 引言

2. 高中数学新授课问题解决教学思路

2.1. 创设情境，激发学生学习兴趣

2.2. 师生互动，激活课堂激活问题

2.3. 合作学习，交流分析解决问题

3. 教学设计

3.1. 创设情境，问题提出

3.2. 动手实践，探究新知

Figure 1. Light reflection diagram of inner wall section of flashlight

Figure 2. Light reflection diagram of the cross section of the inner wall of a flashlight illuminated by parallel rays

Figure 3. Specular reflection of light

Figure 4. Specular reflection of light

Figure 5. Light reflection diagram of a cross-section surface of a parabolic inner wall illuminated by parallel rays

Figure 6. The image of a point on a parabola with respect to the focus

Figure 7. A geometric drawing board makes a parabola

3.3. 合作探究，建构概念

Table 1. System resulting data of standard experiment

Table 2. Four standard equations for a parabola

3.4. 典例分析，巩固提高

(2) 二次函数 $y=a{x}^{2}\left(a\ne 0\right)$ 的图象是抛物线吗？求它的焦点坐标与准线方程。

4. 教学反思

4.1. 问题是数学的心脏，也是问题解决教学的切入点

4.2. 合作学习促进学生在问题解决过程中的主动参与

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