Form "Top In Form" To "Bottom In Form"

Abstraction is the basic feature of mathematics.To paraphrase The Book of Changes,mathematics is the erudition of “Top in Form”.Therefore,based on this,we propose the strategy of “Bottom in Form” in mathematics teaching.This paper first discusses the background,significance and theoretical basis of the research.Then the tasks and methods of the research are presented.Additionally,to investigate how to propose the strategy of “Bottom in Form” in mathematics teaching,we adopt the literature research method,text research method and action research method.Based on the mathematics education theory of Friedenthal,problem-solving theory of Polia,constructivism theory and Zhang Dianzhou's viewpoints,this paper expounds the meaning of “Top in Form” and “Bottom in Form”.There is a saying in The Book of Changes,“Top in Form” is objective laws,while “Bottom in Form” is specific matters.That is to say,concrete things are explained by abstract principles.This paper elaborates that mathematical knowledge is "Top in Form",which is different from "metaphysics" and is opposed to "Bottom in Form".Consequently,we further explore the relationship between "Top in Form" and "Bottom in Form".Moreover,we made proposals for how to propose representing "Top in Form" knowledge by "Bottom in Form" strategy: 1)improving the teachers' mathematics quality;2)bringing forth the new through the old in teaching methods;3)expressing the inherent connection of mathematics and thinking deeply;4)showing the enchantment of mathematics via various means.Particularly,for the multiple means in the fourth strategy,the discussion was carried out.For example,several mathematical examples are attached to each strategy.Then,based on the above suggestions,a concrete lesson example is given in the paper(i.e.,equal difference sequence summation).Finally,we promote that teachers should be brave to learn and innovate,develop more strategies of “Top in Form” to represent the knowledge of “Bottom of Form”.