Case Study On Mathematical Modeling Content Knowledge And Pedagogical Knowledge Of High School Mathematics Teachers

As the main link between mathematics and other disciplines,mathematics and real life,mathematical modeling has gradually become the central topic of our mathematical education and the important content of high school mathematical education.Through sorting out the research on mathematical modeling in high school,it is found that the existing research pays more attention to the level of mathematical modeling of students and the teaching strategies of mathematical modeling,but pays less attention to the other subject in teaching except students and the classroom--teachers.The main purpose of this study is to explore the characteristics and differences of mathematical modeling content knowledge and pedagogical knowledge between novice teachers and experienced teachers in high school.Case study method was used and questionnaire survey and interview were conducted on two mathematics teachers in Southwest China.On the one hand,the quantitative analysis of teachers’ mathematical modeling content knowledge is carried out through the questionnaire of mathematical modeling content knowledge in high school.On the other hand,an interview outline is made according to the results of students’ mathematical modeling test,and the teachers’ mathematical modeling pedagogical knowledge is qualitatively analyzed through their interview records.By comparing the content knowledge of mathematical modeling between novice teachers and experienced teachers,it is found that both teachers are familiar with the concept of mathematical modeling,and the differences are mainly reflected in the application and understanding of mathematical modeling.Novice teachers are very good at the application of mathematical modeling and tend to view mathematical modeling from the perspective of university mathematics,while experienced teachers encounter great difficulties in the first step of mathematical modeling--structuring realistic situations,and their understanding of mathematical modeling is only limited to the high school stage.For mathematical modeling pedagogical knowledge,both teachers could accurately judge the difficulty of modeling tasks and predict students’ mistakes,but could not find students’ model building mistakes.In addition to the above points,there are significant differences between novice teachers and experienced teachers in other dimensions.In terms of modeling task knowledge,novice teachers can analyze the difficulty of modeling task from multiple perspectives and give a variety of solutions,while experienced teachers only analyze the difficulty of the task out of their own intuitive feelings and cannot give any solutions.In terms of knowledge about students,experienced teachers show their advantage of rich teaching experience in predicting and analyzing students’ mistakes,while novice teachers show their advantage of rich mathematical modeling experience in finding students’ mistakes,and evaluating students’ solutions.In terms of teaching strategy knowledge,novice teachers can use analogy and penetrate mathematical modeling ideas,while experienced teachers cannot give effective teaching strategies,but they are good at expanding.The research results bring new enlightenment to teacher education: in the education of normal university,students should pay attention to the connection between higher mathematics and high school mathematics;pay attention to the practice of mathematical modeling in teacher education;at the same time,based on the difference between nnovice teachers and experienced teachers,the form of mutual assistance between novice teachers and experienced teachers can be adopted in the process of teacher training.