A Study On Professional Development For Middle School Mathematics Teachers Prompted By HPM Teaching Practice From The Perspective Of MKT

History and Pedagogy of Mathematics(HPM)is an important research area in mathematics education.And the relation between HPM and teachers’ professional development is also a key aspect of related study.Mathematics teaching that learns from,makes use of and integrates with history of mathematics is called mathematics teaching from the perspective of HPM,or HPM teaching.As HPM teaching is applied from teaching design into classroom practice,it’s named as HPM teaching practice.Recently,the Theory of Mathematical Knowledge for Teaching(MKT),advanced by an American professor Deborah Ball and her team,is one of the most popular studies in mathematics education.What are the relations between HPM teaching practice and teachers’ professional development? Based upon the study in the past three years,which on professional development for middle school mathematics teachers prompted by HPM teaching practice,the author using the method of qualitative research,demonstrates it from the perspective of MKT.It’s worthwhile to note that the core of HPM is mathematical history.As to MKT,mathematical history is a specialized content knowledge(SCK).Therefore,SCK is critical in author’s research and is demonstrated extensively in both dimensions and levels of contents.To be exact,this study explores the following two questions.1.Question I: What is the flowchart for HPM teaching practice? 2.Question II: In what ways does MKT and Teacher’s belief and Teacher’s aptitude exert influence over teachers’ professional development? And what are those influences?Therefore,this study contains two parts.In the first part,based upon a two-year cooperation project,the author appraises the performance of those middle school teachers who participated in HPM teaching practice.With related data,questionnaire,argumentations and literature reviews,theauthor constructs a flowchart for HPM teaching practice.In the second part,based on the HPM teaching flowchart,the HPM community of practice develops HPM teaching cases with more middle school teachers lasting for over a year.Altogether,in the past three years,there are over 60 HPM cases with 36 participating teachers from 21 schools.The author chooses four different teaching cases carried out by middle school teachers,demonstrates their professional development in terms of MKT.The results are as follows.1.HPM teaching flowchart:The first: Introducing historical materials To learn about the development of specific knowledge point and to understand mathematical ideas and facts related to historical figures and stories,i.e.to know what as well as why.The second: Connecting past and present To illustrate the knowledge point from the position of textbook writers and ancient mathematicians,and to explain it with real life applications according to students’ cognitive characteristics.The third: Setting goals To achieve the teaching goals and the task of moral education by making full use of the educational value of mathematical history in view of students’ academic ability.The fourth: Implementing teaching design To implement the teaching design: reconstructing the history in class of mathematical concepts(the method of reconstruction);comparing the different methods used in the past and present in class of proposition(the method of replication or accommodation),and utilizing or adapting historical materials in class of application(the method of replication or accommodation).The flowchart follows a certain order,which is a preset procedure.In fact,every teaching step serves more or less one another,and interlinks.The analysis and usage of the educational value of mathematical history runs through the whole process,which reveals the core value of HPM teaching.2.The influence of HPM teaching practice on middle school teachers’ professional development:(1)Teacher’s knowledge:The findings show that participating math teachers have made remarkable and consistent gains as to SCK,Knowledge of Content and Students(KCS)and Horizon Content Knowledge(HCK).Of which,improvements in explanation and evaluation of SCK are most obvious.Regarding other categories,teachers’ performance appears more or less unstable due to types of courses,contents of courses,etc.With the growth of SCK,the weak correlations among other factors of MKT turn into stronger ones.According to MKT evaluation table,teachers’ knowledge has got enriched,and HPM teaching helps teachers to boost their knowledge of mathematics for teaching.(2)Teacher’s belief:The analysis of SCK contents shows that big improvements have been achieved as to teachers’ conceptions of mathematics,teaching and learning.(3)Teacher’s aptitude:The results verify that there’s great improvement in teachers’ capabilities in terms of teaching reflection,mathematical communication,teaching design and teaching research.In the end,the author puts forward some proposals as to HPM teaching,middle school teachers’ professional development as well as textbook compilation,and also offers some previews on follow-up study.