基于HPM视角的等比数列前n项和教学设计探讨

Discussion on the Teaching Design of the Sum of the First n Terms in the Geometric Progression Based on the HPM Perspective

等比数列求和是高中数学一个基础且重要的知识点,但学生因没有接触过求和方法,产生思维断层,常无法把握其本质。从HPM视角出发,通过合理选取、重构相关史料,融入数学文化,以认知、思维、能力和价值观四个层面为指引,采用“支架式”教学方式,设计一种较新颖的等比数列求和教学策略,能够帮助学生正确认识概念,感悟文化魅力与数学价值,提高其数学思维能力。

The summation of the geometric progression is a basic and important knowledge point in senior high school mathematics.However,students are often unable to grasp its essence because they have not contacted its summaion methods and generated the thinking disconnection.From the perspective of HPM and guided by the four levels of cognition,thought,ability and value,this paper adopts the“scaffolded”instruction method through the reasonable selection,the reconstruction of relevant historical materials,and the integration of mathematical culture.It designs a novel teaching strategy of the summation of the geometric progression,which can help students understand the concept correctly,understand the cultural charm and mathematical value,so as to improve their mathematical thinking ability.