以一道高考解析几何题为楔子,引领学生学会发现特殊中的一般性,在类比、变式探究中关注运算的算理,看清问题本质,实现深度学习,进而发展逻辑推理、数学运算等核心素养.

本单元设计从整体教学的理念出发,对教材中具有内在关联性的内容进行分析、重组、整合,形成相对完整的单元,为学生深度学习回归模型和发展核心素养创造机会.学生经历数据收集和数学建模的全过程,丰富发现、提出、分析和解决问题的体验,感悟数形结合、类比、函数与方程、化归等思想,为将来开展其他主题的数学建模活动积累经验.

从确定题眼入手,在"将面积之比为定值化归为直线过定点"这一核心思想的引领下,让学生更多关注简化运算的算理,依靠逻辑推理能力的支撑,逐步看清问题本质、突破难点,能"见"椭圆而"思"圆锥曲线,实现深度探究,完成从特殊到一般的数学抽象,"知"数学思想的精妙,达到分析、评价、创造的高阶思维水平.

Cognitive linguists believe that language competence is a part of cognitive ability,and the application of language is closely related to human beings' activities.As a special form of language application,cartoon and humor,a kind of on-line metaphor,have drawn the attention of linguists at home and abroad for its novelty.However,most of Chinese studies are static form the perspective of the relevance theory.Lakoff's mental space theory can not give a satisfactory explanation either.Luckily,Fauconnier's conceptual blending theory interprets the interactive process of metaphor in a detailed and comprehensive way.This paper will interpret the dynamic cognitive mechanism through which people understand the meanings of cartoon and humor.