Problem-driven High School Mathematics Classroom Instruction Design Theory And Practice

For decades,several reformations had carried out in national high school education in order to fit education in the new era.From replacing teaching syllabus with the standard curriculum,the new standard curriculum released in 2017,reformers made improvements by cutting contents after new teaching doctrines.However,improving teaching style and methods unfortunately became the concern of the majority of teachers."Freudenthal"and"Re-creation"fill up theses.But what are the real re-creation to mathematics?At the time we do not have a clear interpretation and its code of conduct.As this study shows,"problem-driven"mentioned here is an extent of Freudenthal's concept of education.In other words,it actualizes the "re-creation".The concept,"problem-driven",induces teachers to touch the core of mathematics via history.Thus,they are able to know the situation,the process,and its value.Then by combing pedagogy and psychology principles,teachers can design consistent application of the content according to student's differed level of cognition.Thus,the class is driven by the student's curiosity on the problem.This study includes the following five parts:1.Briefly explains reformations on high school mathematical education through PRC,as well as mathematical education reformations around the world,the United States and Japan for example.2.Elaborates the guiding doctrine of designing "problem-driven"high school teaching and proposes that humanistic values in mathematical education should be present along with its scientific value,since mathematics help students improve their creativity.3.Elaborates the concept of"problem-driven",approaches to achieve re-creation in mathematics driven by problems,and criteria for high school problem-driven mathematics education.4.Demonstrates how to design problem circumstance for teaching by evaluating 5 classic situations on three class formation out of nearly a hundred of examples studied.5.Summarizes the achievements and potential shortcomings of the 4-year-long research and decided the direction for future studiesInnovations of this study are the following1.Establishes the theory and implements of Problem-driven Mathematics Teaching with Prof.Cao2.Establishes a simple criterion which resembles the essence of mathematics class environment with Prof.Cao3.Proposes that mathematics education is a limited re-creation of mathematics and furnished Freudenthal'rs theory of re-creation4.Via a brand-new teaching model of combining theories and practices,educators and education researchers can keep theories feasible and pleasant to conduct.Meanwhile,teachers'teach and research capability experienced significant improvement in this processThrough action research,this study has formed a set of effective and feasible theories to realize mathematical recreation.On one hand,it implements the"4 JIs"and"4 NENGs",on the other hand,it explores a way to find a balance between exam-oriented education and quality education.This study has achieved great impact in high school teaching in China.