根与系数关系证明图式的研究

Studying on Students’ Proof Schemes about the Relations of Root and Coefficient of Quadratic Equation

证明图式是个体对命题正确性产生疑惑和消除疑惑的心理对应物.学完一元二次方程根与系数关系证明之后的大多数学生同时具有一般式证明和举例证明图式;面对不同的问题情境时,他们会使用不同的图式.在进行一元二次方程根与系数关系的证明教学时,应引导学生观察、归纳得出猜想,然后进行证明,把证明作为探索活动的自然的延续和必要的发展.

Proof schemes is the psychological counterparts which remove own and others＇ doubts about the truth of proposition. In this paper, 9 students were interviewed after learning proof about the relations of root and coefficient of quadratic equation, the conclusion which proof by example and analytical proof all existed in most of students＇ mind and students used either of them when they faces different problem situations a was found. In the basis of that, reflecting the teaching about proving the relations of root and coefficient of quadratic equation was presented.