Teaching Case Study Of Quadratic Equation Pointing To Translation Of Representation

Representation conversion is a focus of attention in the field of mathematics education research.Many scholars believe that the development of mathematical core competency is closely related with individual's representation and flexible representation conversion.Relevant researches have showed that problems and methods about history can enable students to understand the nature of mathematics,and the history of mathematics can help students understand various representations.Quadratic equation is the basis for further study of equations and other mathematical knowledge,and plays an important role in solving practical questions.With the historical research of quadratic equations in one variable,it is found that geometric solutions and textual expressions can provide materials for designing representation conversion activities,and help to improve students' representation conversion ability.Therefore,this research explores the combination of the history of quadratic equations and mathematical representational transformations,so as to develop the teaching of quadratic equations in one variable.The research questions are as follows:(1)How does the teaching of quadratic equations in one variable from the perspective of representation conversion influence students' representation conversion ability?(2)What are the reasons for the changes in students' representational conversion ability after the implementation of teaching?This research design five cases about concepts,solutions,and applications.The process is mainly focusing on research questions,constructing instructional designs,implementation of classroom teaching and assessments related to representational transformation.This study adopts three research methods: case study,questionnaire survey and interview,specially,analyzing the teaching cases with the HPM curriculum evaluation framework,compling the questionnaires with refrence to the mathematical representation transformation difficulty level model and analyzing questionnaires with double-digit coding,this research uncovers the changes of students' representation transformation.With the feedback of homework and interview results,the reasons for the change of students' representation conversion ability are analyzed.The research conclusions are as follows:(1)The students' representational conversion ability has improved overall,but there are differences in the changes of different representation conversion methods.The ability of convering between graphical and symbolic representations has improved significantly,but the changes of the conversions related to verbal representations is not obvious.(2)The changes of students' representation conversion ability are influenced by teaching activities related to representation conversion designed with the histoty of the quadratic equation,teachers' emphasis on representation conversion and students' cognitive basis and attitude.The research obtains the following inspirations:(1)Teachers' appropriate teaching activities of representation conversion in the classroom can play a very important role in improving students' representation translation ability;(2)History is irreplaceable for the teaching process integrated with mathematics history.It is vital to find an an entry point related to the students' core mathematical literacy and core competence,and take the history of mathematics as the thread running through a certain knowledge section.In summary,this research is of great significance both in theory and in practice,also provides front-line teachers with new ideas about teaching design.