| Mathematical culture is one of the hot spots in mathematics education research and has an important role in mathematics teaching.The General High School Mathematics Curriculum Standards(revised in 2017 and 2020)clearly put forward that "the high school mathematics curriculum should focus on the infiltration of mathematical culture".Conic curves have an important position in high school mathematics,and the integration of mathematical culture into the teaching of conic curves in high school can help students understand knowledge,develop students’ core literacy and realize quality education.The purpose of this study is to integrate mathematical culture into the design of teaching conic curves in high school.The research questions are:(1)What are the attitudes of students and teachers toward the integration of mathematical culture into teaching conic curves in high school?(2)What is the current status of integrating mathematical culture into teaching conic curves in high school?(3)How to integrate mathematical culture into the teaching design of conic curves?This study compares the literature on "mathematical culture" and "teaching conic curves" to find out what has been achieved and what needs to be improved in the current research on the integration of mathematical culture into the design of high school conic curve teaching.The theoretical basis of this study is Freidenthal’s theory of mathematics education,Smith-Reagan’s model of instructional design,Bruner’s view of education and culture,and Orsuline’s theory of meaningful learning,and the problems and possible causes of the integration of mathematical culture into the teaching of conic curves in high schools are investigated.Using the textual analysis method,the feasibility of integrating mathematical culture into the teaching of conic curves in high school is argued through four aspects: textbooks,new standards,students and teachers,and the necessity is elaborated from two perspectives: the college entrance examination and students.On this basis,the teaching strategies of integrating mathematical culture into conic curves in high school are proposed: enriching classroom teaching with mathematical cultural materials;reconstructing the design of examples with mathematical cultural background;expanding mathematical activities with mathematical cultural contents.Next,the teaching design of integrating mathematical culture into conic curves is carried out,with five major elements: teaching objectives,teaching contents,teaching methods,teaching process and teaching evaluation: First,the design of teaching objectives: the design of teaching objectives is led by mathematical culture;the teaching objectives point to the cultivation of students’ core mathematical literacy.Second,the analysis of teaching content: including the content of conic curves and the mathematical culture and meaning of conic curves.Third,the choice of teaching methods: the chosen teaching methods should be conducive to the cultivation of mathematical literacy;the choice of teaching methods should match the characteristics of the course content.Fourth,the design of teaching process: to create a situation with mathematical culture;to explore new knowledge from mathematical culture;to consolidate new knowledge with mathematical culture;to expand new knowledge through mathematical culture.Fifth is the design of teaching evaluation: focus on process evaluation;adopt diversified evaluation methods.Finally,the specific teaching design of "ellipse and its standard equation",hoping to enrich the teaching cases of mathematical culture and provide reference for front-line teachers’ teaching. |
