The Study Of "One-variable Quadratic Inequality" Content And Teaching Based On The Van Hiele Theory

Van Hiele theory is an important theory research of geometry teaching,the research mainly focuses on the geometry,UK researchers in 1980 s after the theory is extended to non geometric field;its application on non geometric field with geometric feature "content and try,much domestic mathematics educators attention.One of the most important contents in the field of geometry is "inequality".Among them,"one-variable quadratic inequality" existing research mainly from the teaching content set form and writing ideas,teaching design,teaching reflection,various methods to solve,and prior knowledge of the relationship of qualitative research,but has not been studied from the perspective of quantity.Therefore,the use of Van Hiele theory of high school "inequality" in the "geometric features" of the key elements of the "one-variable quadratic inequality" content and teaching a series of quantitative research.The study was based on analysis of one-variable quadratic inequality of preliminary knowledge and teaching contents in the use of Van Hiele thinking on the level of students learning the content before and after testing the level of thinking,to provide the basis for the design and evaluation of one-variable quadratic inequality Van Hiele "teaching program,and through teaching one of the two teaching practice to verify the Van Hiele inequality theory can be applied to non geometric field.The main work of this research is: first,through literature analysis,summarizes the core content of Van Hiele theory and the theory of characteristics,and from the Van Hiele and Van Hiele geometry thinking level geometry teaching stage combing of Van Hiele theory research literature;secondly,according to the Van Hiele thinking level,"the construction scale two times a dollar inequality" the preliminary knowledge level(table 3.2),quantitative analysis of the "one-variable quadratic inequality" curriculum standards,teaching content,and thus the design of the "scale of one-variable quadratic inequality of VanHiele thinking level" level(table 3.4);then,according to the "knowledge" scale,preparation of preliminary knowledge "Van Hiele thinking test"(Appendix 2),the T test a 4 high school class of 194 students "prior knowledge" Van Hiele level of thinking,and that "no difference between all departments,with the The level of analysis " conclusion;then,according to student’s "prior knowledge " Van Hiele level of thinking and learning " one-variable quadratic inequality " target level of thinking,the use of Van Hiele geometry teaching stage design " one-variable quadratic inequality " teaching plan(Appendix 6),and according to the " one of the two inequalities of Van Hiele thinking the level of scale,making the teaching effect assessment tool(Appendix 4);finally,choose to have tested 4 class level Van Hiele thinking as the research object,the " two inequality " Van Hiele scheme on teaching than practice,evaluation tools and test the research object after thinking level.Through the analysis of the level of thinking,compared and concluded:preschool Van Hiele theory can be extended to " one-variable quadratic inequality "teaching;and using the Van Hiele theory of " one-variable quadratic inequality analysis of the content of the second inequality and the corresponding level of the students are more conducive to the design and evaluation of the teaching plan.