The Influence Of HPM On A Primary Mathematics Teacher’s Teaching Design Competency

As an important part of mathematics culture and an academic field,HPM is good for implementation of morality constitution and talent cultivation,cultivation of mathematical core competencies,teachers’ professional growth.However,there are many problems when trying to integrate history into mathematics teaching,for instance,although teachers have strong willingness to use history of mathematics(HM),they are not able to use it well,teacher education curriculum are not effective on cultivating teachers’ competency to use HM well.The field of HPM research also needs to be extended in teacher education and primary school.Therefore,we focused on the primary school,took HPM Lesson Study(LS),with the characteristics of“Action Education”(Gu & Wang,2003),as a research intervention to study primary mathematics teachers’ teaching design competency from an HPM perspective,to solve the following research questions:(1)Can HPM LS promote the development of teachers’ teaching design competency from an HPM perspective?① If so,what aspects have been promoted?② If not,what are the reasons?(2)Under the premise of ①,how HPM LS promote the development of teachers’ teaching design competency from an HPM perspective?(3)What challenges have emerged in practice when HPM was introduced into teaching?In order to solve the above research questions,basing on complex theory,deliberate practice,HPM theory,and referring to "action education",we improved HPM LS,and integrated HPM LS into the Interconnected Model of Professional Growth(Clarke & Hollingsworth,2002),basing on literature,existing lesson and experts argumentation,we constructed a teaching design competency evaluation framework.Firstly,we used a pre-study to explore the answer of the research question(1),finding HPM LS can promote the development of the teachers’ teachingdesign competency from an HPM perspective,but it is a process from scratch,which brought enlightenment to the following study,to prolong the time span of the study,and to go deep into the process of HPM LS.And using the Interconnected Model to comb case teacher’s growth networks in 11 HPM LS,building links among Personal Domain,Domain of Practice,Domain of Consequence and External Domain with Enactment and Reflection(these elements are component of the Interconnected Model),using the teaching design competency evaluation framework to analyse teaching design texts which designed by the teacher independently,using mini narrative to present tensions during HPM lessons study.Through a longitudinal comparison of the teacher’s teaching design competency changes in each lesson,we found that the teacher’s teaching design competency from an HPM perspective can be developed,especially in the dimensions of classroom introduction,class excises,activity inquiry,class summary,and the appropriateness of historical materials.Through a horizontal analysis of the Interconnection Model of each lesson study,we found that design discussion,trial teaching,after-school discussion,teacher reflection,and post-class questionnaire analysis are the key factors affecting the development of teachers’ teaching design competency from an HPM perspective.Summing up mini narrative in each LS,we found the introduction of the HPM perspective into teaching brought many challenges to the teacher,and complexity and diversity of the challenges were beyond our imagination.Finally,we provided inspirations from perspectives of construction of an education-oriented history of mathematics database and an HPM lessons database,an HPM community with multiple identity,targeted strategies to design important teaching links,an unit design development based HM,an teacher education system with HPM,reflected on research limitations and looked forward to further research.