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猜想是一种重要的思维活动,它是在已有知识的基础上,对客观事物不断进行观察、试验、类比,对逐渐积累起来的感性材料进行分析,试图找出某种规律的一种大胆的假设描述或推断。而数学猜想正是这种科学推断在数学学科中的具体体现,这种推断既有一定的科学性,又具有某种假定性,是科学性与假定性的辨证统一。虽然这种猜想和推断的结果还有待证明,但是这种思维过程的确是许多发明创造者的成功之路。《数学课程标准》指出“通过义务教育阶段的数学教学,经历观察、实验、猜想、证明等教学活动,发展合理推理能力和初步演绎推理能力。”同时对推理能力的主要表现作了以下阐述“能通过观察、实验、归纳、类比等获得数学猜想,并且进一步寻求证据、给出证明或举出反例。”不难看出,新课改十分重视学生猜想思维能力的培养。几何直观性猜想就是数学猜想能力之一,借助几何直观提出一般性猜想的方法,因此几何直观猜想能力在高中数学的教学中应更加侧重,注重培养。本文通过2013年宁夏高考理科数学的函数题目的求解,展示几何直观猜想在解题中的简洁性和魅力,说明培养学生猜想能力重要性。
Conjecture is an important thinking activity. Based on the existing knowledge, conjecture constantly observes, tests and analogies the objective things, and analyzes the gradually accumulated sensuous materials in an attempt to find a certain bold Assumptions or inferred. The conjecture of mathematics is just a concrete manifestation of this kind of scientific inference in mathematics. This kind of inference has both certain scientific and certain hypotheses, and is the dialectical unity of science and hypothetical. Although the results of this conjecture and inference have yet to be proved, this thinking process is indeed the success of many inventors. The Mathematics Curriculum Standard states that “through the teaching of mathematics in the compulsory education phase, we can develop reasonable reasoning ability and preliminary deductive reasoning ability through teaching activities such as observation, experiment, conjecture and proof.” “In the meantime, Explain ”Obtain mathematical conjecture through observation, experiment, induction, analogy, etc., and further seek evidence, give proof or give counterexample. " It is easy to see that the new curriculum reform attaches great importance to the cultivation of students’ ability to guess thinking. Geometric intuitionistic conjecture is one of the ability of mathematical conjecture, with the help of geometric intuition, a method of general conjecture is proposed. Therefore, the ability of geometric intuitionistic conjecture should be more emphasized in the teaching of mathematics in high school, with emphasis on training. In this paper, we solve the function of mathematics in Ningxia college entrance examination in 2013, and demonstrate the conciseness and charm of geometric intuition conjecture in solving problems, which shows the importance of training students’ conjecture ability.