Question

谁能帮我翻译成英文非常感谢？

数学是一门逻辑性极强的学科。加强对学生的思维训练是改革数学教学，提高质量的最根本途径，而逆向思维是思维转换能力的一种重要形式。事实上，正向思维定势经常制约思维空间的拓展，有时若是按照顺向思维方式则是比较困难，而且常常伴随着较大的运算量，有时甚至无法解决，这时不妨改变思维方向，用逆向思维的方法去探求新的解题途径，往往能得到突破性的进展，达到柳暗花明的效果。在中学数学课本中的公式逆用、逆运算、反证法、分析法、逆否命题等都涉及思维的逆向性。因此，教师在教学中自觉地、有目的地加强对学生逆向思维的训练，有利于培养思维的灵活性、广阔性、深刻性，克服正向思维所造成的思维定势，突破旧有思想框架产生新思想，发现新知识、开拓解题思路。本文就着重从概念和公式的逆用、反证法、倒序思考问题等方面来研究逆向思维的培
养。

Answer 1

Mathematics is an extremely logical subjects. Enhance training for students thinking of reform and mathematics teaching, improve the quality of the most fundamental way of thinking and reverse thinking is the ability to convert an important form. In fact, positive thinking often set the expansion of space constraints of thinking, if sometimes under-the way of thinking is more difficult, and often accompanied by a larger computing capacity, and sometimes can not be resolved, at this time may wish to change the direction of thinking, Reverse thinking with the approach of problem solving Qutan Innovation way, can often be a breakthrough progress, to turn for the better results. In middle school mathematics textbooks used in the formula reverse, inverse operation, reduction to absurdity, analysis, whether the reverse proposition all involved thinking of the reverse. Therefore, teachers in teaching consciously, a destination for students to strengthen the training of reverse thinking, thinking to cultivate flexibility, broad and profound, positive thinking to overcome caused by the fixed pattern of thinking, breaking the old ideological framework Generate new ideas, discover new knowledge, develop problem-solving ideas. In this paper, focusing on the concept and the formula used reverse, reduction to absurdity, reverse thinking on the areas to reverse thinking on the pui
Custody.

Answer 2

. Mathematics is a logical greatly strengthened discipline. Strengthens reforms mathematics teaching to student's thought training, improves the quality the most basic way, but the negative thinking is the thought transformation ability one important form. In fact, the forward thought einstellung restricts the thought space frequently the development, if sometimes according to is suitable to the thinking mode is quite difficult, moreover is following the big operand frequently, sometimes even the inextricability, by now might as well changed the thought direction, seeks the new problem solving way with negative thinking's method, often can obtain the unprecedented progress, achieves the joy after sorrow the effect. Goes against in the middle school mathematics textbook's formula with, the inverse operation, the reduction to absurdity, the analytic method, the counter otherwise proposition and so on involves the thought the reversion. Therefore, the teacher in the teaching on own initiative, has the destination to strengthen to the student negative thinking training, is advantageous in the raise thought flexibility, the extensity, thorough, the gram clothing forward thought creates the thought einstellung, has the thought frame to have the new thought worn-out suddenly, discovers the new knowledge, the development problem solving mentality. This article emphatically from the concept and formula going against with, the reduction to absurdity, the inverted order pondered that aspects and so on question study the negative thinking to cultivate to raise.