Mathematics Curriculum Research On Orientation Of Big Ideas In California,USA

China's 2017 version of the mathematics curriculum standards for ordinary senior high schools point out: “attach importance to the Big Ideas of discipline as the core,make the curriculum content structured,themed,contextualized,and promote the implementation of the core quality of the discipline”.The curriculum standards for the first time use Big Ideas to unify the mathematics curriculum content,emphasizing the important role of Big Ideas in implementing the core quality of mathematics.However,the curriculum standards do not clarify the basic connotation of Big Ideas in mathematics,and the vision of developing the core quality of mathematics with Big Ideas has a long way to go.For a long time,mathematics teaching under the baton of "only scores" in the college entrance examination evaluation has fragmented mathematical content into knowledge points,which is not conducive to the development of core quality of mathematics.Big Ideas in mathematics can make mathematical knowledge structured,which is the key to eliminating the drawbacks of mathematical knowledge fragmentation and implementing the core quality of mathematics.Since the 21 st century,developed countries such as the United States,Canada,Australia and Singapore have successively promulgated and implemented mathematics curriculum standards around Big Ideas,and the exploration of teaching practice is also in the ascendant,with fruitful research results,but there are few translations and introductions in China.The theoretical construction and practical exploration of Big Ideas in mathematics have just started,making it necessary to translate and introduce foreign achievements.In 2021,California's newly revised Mathematics Framework becomes the most detailed document on Big Ideas in mathematics in the world.Therefore,this research uses text analysis method and case study method to sort out the theoretical basis of Big Ideas in mathematics;Analyze how California uses Big Ideas in mathematics to design curriculum,organize teaching and evaluation,and extracts the characteristics of Big Ideas in mathematics in the California mathematics curriculum;and designs the "proportional" Big Ideas in mathematics teaching case based on the textbook of People's Education Press.This research draws the following conclusions.1.This research constructs the theoretical basis of Big Ideas in mathematics.Big Ideas in mathematics is an abstract mathematical ideas that has the function of connection and integration and can be widely transferred,and its essential feature is "connection",mainly "classification" and "enumeration" two models.2.Based on the analysis of the 2022 mathematical framework of California,the following conclusions are drawn.(1)The Framework adopts Charles' s definition,defining Big Ideas in mathematics as "Big ideas in math are central to the learning of mathematics,link numerous math understandings into a coherent whole,and provide focal points for students' investigations",reflecting the "connection" characteristics of Big Ideas in mathematics and its importance in focusing on mathematical investigations.(2)The Framework changes the previous model of organizing courses around a single content standard,and puts forward the three-dimensional model of designing mathematics courses as a whole by taking Big Ideas in mathematics as the starting point,connecting mathematics content knowledge,process method and application as a whole.This model reflects that Big Ideas in mathematics adopts the "classification" model,which is divided into three categories: content Big Ideas,process Big Ideas and transfer Big Ideas.(3)The Framework distills Big Ideas in mathematics of number sense,data science,and Mathematics: Investigating and Connecting curriculum,realizes the vertical and horizontal connection between mathematical knowledge content,and constructs a consistent mathematical curriculum.Among them,Mathematics: Investigating and Connecting curriculum is a new path of high school mathematics curriculum.It is different from the previous traditional curriculum and integrated curriculum.It provides a way to integrate the curriculum from the concept,and reflects the characteristics of cross grade,cross topic and cross disciplinary connection of Big Ideas in mathematics.(4)Teaching practice and evaluation echo the emphasis of the Framework on Big Ideas in mathematics,and realize the unity of teaching,learning and evaluation.3.The research on the teaching of Big Idea of "proportionality" has the following conclusions.(1)The textbook of People's Education Press regards "ratio" and "division" as an equivalent relationship,and is not prepared for learning of proportion;the learning of proportion lacks attention to proportional reasoning,does not place enough emphasis on invariance in change,and learning lacks integrity.(2)Big Idea of "proportionality" means that if two quantities change in proportion,this relationship can be expressed by linear function,which can connect various mathematical understandings related to it into a coherent whole.(3)By distinguishing between "ratio" and "rate",identifying the characteristics of "proportionality",and applied to practical problem-solving,which reflects the characteristics of cross grade,cross theme,cross disciplinary connection content,process method and application of Big Idea of "proportionality",which can pave the way for learning relevant concepts in the futurethe.In summary,the Framework represents California's vision to advance the Big Ideas mathematics curriculum and thereby improve the quality of mathematics education,and has important reference significance for the theoretical and practical research of Big Ideas mathematics.