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数学课程标准指出,学生学习应当是一个生动活泼、主动和富有个性的过程,学生应当有足够的时间和空间经历观察、实验、猜想、计算、推理、验证等学习过程。归纳概括得到猜想和规律并加以验证,是创新的重要方法,2016年云南省中考数学压轴题就很好地体现了这一要求。笔者对此题进行重点解析,旨在进一步丰富此压轴题蕴含的数学思想方法。一、题目呈现有一列按一定顺序和规律排列的数:
The mathematics curriculum standards point out that student learning should be a lively, active and individualized process. Students should have sufficient time and space to undergo such learning processes as observation, experimentation, conjecture, calculation, reasoning, and verification. Summarizing and concluding the guesses and laws and verifying them is an important method of innovation. In 2016, the mathematics problem of the middle school entrance exams in Yunnan Province reflected this requirement. The author focused on the analysis of this issue, aimed at further enriching the mathematical thinking and methods contained in this final axis title. First, the title presents a list of numbers arranged in a certain order and regular pattern: