A Case Study On The High School Teachers’ Specialized Content Knowledge Based On The History Of Mathematics

The specialized content knowledge is one of the important components of the mathematical knowledge for teaching,referring to the teaching of mathematical knowledge and skills,playing a vital role in teachers’ professional development.The study of the history of mathematics can promote the development of the high school mathematics teacher’s mathematical knowledge for teaching,especially for specialized content knowledge.But researchers have not established an effective method of characteriz the development of teachers’ knowledge.History based specialized content knowledge(HSCK)is defined as the knowledge of integrating history of mathematics into the teachers’ original SCK.The research is on the influence of HPM teaching practice on teachers’ HSCK.The following three research questions are focused on :(1)What HSCK related to trigonometry do the high school mathematics teachers have?(2)How does the history-based mathematics teaching of Introduction to trigonometry and its influence on the high school mathematics teachers’ HSCK?(3)What is the approach to the development of the high school mathematics teachers’ HSCK? Among them,the first and second problems are divided into two subquestions driven by HPM practice.This research states the theoretic framework of HSCK based on of HPM and SCK.The framework consists of six components: knowledge of responding and explaining,knowledge of inquiring and applying,knowledge of representing and connecting,knowledge of problem posing,knowledge of assessing and deciding,knowledge of judging and revising,and provides a four-level evaluation standard.According to the theoretical framework of HSCK,the researcher analyzed the current situation of high school mathematics teachers’ HSCK and its influence on the high school mathematics teachers’ HSCK,constructed the model of development of the high school mathematics teachers’ HSCK.This study consists of quantitative research andqualitative research.In quantitative research,the researcher developed the HSCK questionnaire,and tested the 300 high school mathematics teachers,furthermore analyzed the current situation of high school mathematics teachers’ HSCK from the history of mathematics teaching experience,the different degree and different contact different experiences.In qualitative research,the researcher selected 12 high school mathematics teachers to carry on the teaching of Introduction to trigonometry and analyzed the change of high school mathematics teachers’ HSCK.First of all,they were invited to participate in teaching of Introduction to trigonometry,then teaching and reflection after studying trigonometry materials of history teaching.The researchers used a questionnaire,classroom observation,interviews and teaching reflection to collect data and analyzed based on the theoretical framework of HSCK so as to know the changes of high school teachers’ HSCK;On the basis of these studies,the model of the development of teacher’ HSCK driven by HPM practice is constructed.The conclusions of the research are as follows:1.The current situation of high school mathematics teachers’ HSCK related to trigonometry is:(1)To different of school age,high school mathematics teachers have no significant difference at the same level of performance about KRE,KIA,KAD,KPP and KRC.Teaching experienced teachers have formed their own teaching style,handling of teaching materials with their own strategies,so the novice teachers perform better in KJR,the reason is that most novice teachers had learned about the course of the history of mathematics,knowing the historical development of trigonometry clearly.(2)There is no significant difference in HSCK level between teachers with bachelor’s and master’s degrees;(3)The experienced teachers in the history of mathematics are better than the other teachers in KRC and KPP;(4)The six HSCK constructs are the close relationship,restraining each other and promoting each other.2.The history-based mathematics teaching of Introduction to trigonometry and its influence on the high school mathematics teachers’ HSCK is:(1)The reasons for the improvement of HSCK level are:a.The teachers can select the mathematical historical materials materials shared by the researchers.These materials are closely related to the teaching content in accordance with the five principles of historical material appropration;b.The teachers can seriously study the existing HPM cases and have discussed and implemented the teaching design of "the history-based mathematics teaching of Introduction to trigonometry " many times;c.After the practice,teachers can make a summary after class,and reflect on whether the choice of mathematical historical materials is appropriate and the method of historical material integration is appropriate.(2)The reasons for the unchange of HSCK level are:a.The teachers can select the mathematical historical materials materials shared by the researchers.These materials are closely related to the teaching content according to their own understanding of historical materials;b.The teachers can study the existing HPM cases and the ways of integrating mathematical history in HPM cases and the role of the history of mathematics in the teaching process;c.The teachers’ understanding of HPM theory is not profound.In the teaching practice of HPM,the teachers failed to integrate the mathematical historical materials into the teaching process,which can not achieve the organic combination of historical materials and teaching contents.They have too few HPM teaching practices.(3)The reasons for the reduction of HSCK level are:a.The teachers are biased in their understanding of the history of mathematics.They believe that the history of mathematics is the story of a mathematician.b.The teachers are unable to integrate the historical development of the concept and the proof of the historical theorem into the classroom;c.The teachers are lack of understanding of HPM theory;d.The teachers have not experienced the implementation of HPM teaching practice.3.HPM teaching practice promotes the development model of teacher HSCK includs "knowing HPM","understanding HPM","experiencing HPM" and "implementing HPM".Based on the conslusions are proposed for some suggestions HPM teaching practice,textbook author and MKT researches and the researcher puts forward some prospects for future research on the rationality of the follow-up study about HSCK model,the scientific nature of the questionnaire and universality of test range.