The Development of materials and improvement of teaching method on spatial intuition and logical thinking

(1)关于代数定理（1），约有50%的人同时把实验解释和演绎证明当作“证明”。(2)大约60%的人认为一个预形式化证明就是“证明”。大约20%的人从一般性和演绎性的角度理解预形式化证明。(3)约50%的人受到正式表达的影响。(2)在几何定理上，（1）70-80%的人认为实验解释是“证明”，而Ca是“证明”，85%的人认为形式证明是“证明”;（2）60-70%的人认为预形式证明是“证明”，6%的人认为行动证明具有说服定理的作用。(3)首先，我从社会、心理学、数学教育的角度研究为什么空间直觉是重要的。我将空间直觉定义为8种能力。我提出了“心理几何学”和学习活动的必要性，以培养空间直觉。

(1) On algebraic theorem (1) Ca.50% of them consider an experimental explanation and a deductive proof as "proof" simultaneously. (2) Ca.60% of them consider a preformal proof as "proof". Ca.20% of them understand a preformal proof from a point of generality and deductivity. (3) Ca.50% of them are influenced by a formal expression.(2) On geometric theorem (1) 70-80% of them consoder an experimental explanation as "proof" and Ca.85% of them consider formal proof as "proof" (2) 60-70% of them consider a preformal proof as "proof" and 6% of them consider that action proof has a function of convicing a theorem.(3) First I study why is a spatial intuition important from social, sychologial, mathematics educational points of view. I define a spatial intuition as set of 8 abilities. I propose a necessity of "mental gepmetrie" and learninng activities for fostering a spatial intuition.