A Study On The Mathematical Tasks Based On The History Of Mathematics In Senior Three Mathematical Review Lessons

As a key element of mathematical culture,the history of mathematics is effective in promoting teachers' professional development.However,teachers often suffer from a lack of the history of mathematics materials,methods,and support in learning and practicing the history of mathematics.Therefore,lesson study based on the history of mathematics is of great value as an approach to teachers' professional development,which can support the sharing of the history of mathematics materials,more teaching methods,and collaboration among teachers.At the same time,teachers' professional development can't be separated from the analysis and examination of classroom teaching.As the basic processing unit of classroom teaching,the empirical research on mathematical tasks is powerful hand to achieve moral education and promote teachers' professional development.Taking the history of mathematics as the perspective of teachers' professional development,this study devised and implemented lesson study activities on conic curve for senior three review lessons,then designed and analyzed corresponding mathematical tasks,to answer the following two research questions:First,what are the changes of mathematical tasks and their characteristics during lesson study for senior three review lessons based on mathematical history?Second,what strategies do teachers adopt to improve mathematical tasks during lesson study for senior three review lessons based on mathematical history? What factors do teachers pay more attention to when using mathematical history to design mathematical tasks?This study first constructed a feature coding framework of mathematical tasks which includes task type,cognitive demand,task feature,and the representation of mathematical history,a coding framework of strategies adopted in mathematical task design based on mathematical history,and a coding framework of concerning factors during mathematical task design.Secondly,this study chose the content analysis method to analyze the characteristics of mathematical tasks designed by 7 teachers before during and after the lesson study.Finally,combining interview and observation,the study explored the strategies used by the teachers and the factors they pay attention to when designing mathematical tasks.The basis results are as follows:(1)the structure of the senior three classes integrating with mathematical history is reasonable,and the cognitive demands of tasks integrating into mathematical history are above average;(2)there are abundant representations and exchanges in senior three classes integrating the history of mathematics,but there is a lack of challenging multi-solution mathematical tasks;(3)cognitive demands of mathematical tasks are mostly improved,and the main forms of mathematical history are changed into snippet and question list;(4)the combination of freestyle,target,and duplicate strategies are the key to update the perspective of mathematical task design in senior three classes;(5)teachers at different stages of development have different main concerning factors in task design;(6)two key factors that teachers at all stages generally concerned are students' ability of thinking and reasoning,concepts connection.Finally,this study suggests that:(1)teachers can improve teaching design through solid theoretical study of mathematical history and scientific methods of infiltration;(2)the relevant departments can improve the professional development path according to the concept of “ faith leading-knowledge and ability growth-role improvement”;(3)the researchers can expand the conic curve mathematical history database,and focus on mathematical challenges and teaching variables.