从三角形面积看数学思维的培养

The Development of Mathematical Thinking from the Area of Triangles

摘要: 三角形面积，既有代数意义，又有几何意义，从数与形的角度，可以很好的把握数学思维。本文根据不同年龄学生的认知水平和不同年级的实际教学情况，从培养学生数学思维的角度，分析并讨论三角形面积的求解方法，深入研究三角形面积在不同学段的教学重点与求解方法的发展过程。小学阶段主要以培养计算能力为主，用基本公式求解三角形面积；中学阶段逐步量化，解析几何成为学习重点，常与其它知识相结合求解三角形面积；大学阶段的数学是高维度的数学，从定积分与空间解析几何角度求解三角形面积。在研究中得到三角形面积的学习过程，适应学生发展需要，对学生的逻辑思维、抽象思维、创新思维等数学思维起到促进作用，在解决实际问题、学生未来从业等方面具有重要意义。

Abstract: The area of triangle, which has both algebraic and geometric meanings, can be well grasped from the perspective of number and shape for mathematical thinking. In this paper, according to the cognitive level of students of different ages and the actual teaching situation of different grades, we analyze and discuss the solution methods of triangle area from the perspective of cultivating students’ mathematical thinking, and study in depth the development process of teaching focus and solution methods of triangle area in different grades. At the elementary school level, the main focus is on cultivating computational ability and using basic formulas to solve triangle area; at the secondary school level, the analytic geometry becomes the focus of learning gradually and is often combined with other knowledge to solve triangle area; at the university level, the mathematics is a high-dimensional mathematics and triangle area is solved from the perspective of definite integral and spatial analytic geometry. The learning process of getting triangle area in the study, adapting to the development needs of students, plays a role in promoting students’ logical thinking, abstract thinking, innovative thinking and other mathematical thinking, and is of great significance in solving practical problems and students’ future practice.