Teaching Research On Training High School Mathematical Abstraction

The core of mathematics is one of the hot topics in mathematics education.Mathematical abstraction is one of the six core qu.alities of mathematics.There is not enough implementation in the current classroom teaching.Cultivating students’abstract literacy can help students learn to learn and discover and raise questions,and promote students to fully understand knowledge and form a perfect knowledge structure.This research combs the research results on mathematical abstraction,and analyzes the connotation,characteristics and training strategies of mathematical abstraction.Investigating the current state of high school mathematics abstract literacy teaching,it is found that teachers pay attention to the teaching of mathematics knowledge,ignore the background of knowledge generation,pay attention to the cultivation of mathematics skills,and neglect the guidance of thoughts and methods.On the basis of the investigation,the teaching strategies for the cultivation of mathematical abstract literacy have been preliminarily constructed through case studies and action studies:(1)The mathematical abstract thinking should be highlighted in teaching,and through the creation of a reasonable problem context,students should be instructed on what to study;Math activities guide students how to study.Strategies for creating problem situations include providing content background,proposing enlightening questions,and introducing new ideas;strategies for designing mathematics activities include building scaffolding to help students integrate new knowledge.(2)At the macro level,we must grasp the integrity of abstract content,grasp the main lines of teaching content,clarify the inner logic of mathematics and refine its hidden thoughts and methods.(3)At the micro level,we must clarify the level of abstraction of mathematics.The abstract process of the concept is divided into four levels:activity,program,object,and schema;the abstract process of proposition is divided into three levels:special case,general,and schema;The abstract process is divided into real problems,which are transformed into mathematical problems(real prototype abstraction)and complex problems into simple problems(mathematical internal abstractions).