向量是近代数学中重要和基本的数学概念之一,它是沟通代数、几何与三角的一种工具,但在实际的教学中,由于课时紧张,老师和学生往往会陷入向量代数化的运算中,忽略向量“形”的一面,从而使学生体会不到向量的简洁和实用,也感受不到几种知识的联系,少了发现与创造的过程。题根不是概念,不是结论,而是一个问题。本文是笔者在教学中利用题根引领学生自主学习的 Vector is one of the important and basic mathematical concepts in modern mathematics. It is a tool to communicate algebra, geometry and triangles. However, in practical teaching, teachers and students tend to fall into vector algebraic operations due to tight class hours. , Ignore the side of the vector “shape”, so that students do not understand the simplicity and utility of the vector, and also do not feel the connection of several kinds of knowledge, and less the process of discovery and creation. The root is not a concept, not a conclusion, but a problem. This article is the author’s use of the root in the teaching to lead students to learn independently