A Case Study On The Specialized Content Knowledge Based On The History Of Mathematics Of Tibet's Pre-service Junior Middle School Mathematics Teachers

Specialized content knowledge(SCK)is described as the special mathematical knowledge for mathematics teaching,and the specialized content knowledge of Tibet's pre-service junior middle school mathematics teachers based on the history of mathematics(PT-HSCK)studied in this paper,which belongs to the category of specialized content knowledge.This study mainly focuses on the changes of PT-HSCK from the situation to the intervention of HPM afterwards.At present,there is no research on the theoretical construction of PT-HSCK,but there are some researches on the SCK of senior high school mathematics teachers based on the mathematical history for reference,and there are also researches on the SCK and TCK for reference.There is no existing Connotation framework of the specialized content knowledge based on the history of mathematics of Tibet's pre-service junior middle school mathematics teachers.In order to conclude the elements of the Connotation framework,and the research process of pre-service middle school mathematics teachers in Tibet,after the interview aimed at 15 experts,the author use the fuzzy Delphi method with three steps,and screen the factor index.For the PT-HSCK,the author mainly constructs a nine-side model with nine components,and the composition of nine knowledge dimension,respectively,are the knowledge of selection and Introduction(KSI),comparison and design(KCD),responsing and explaining(KRE),exploring and repeating(KER),representing and connecting(KRC),Problem Posing(KPP),assessing and deciding(KAD),judging and revising(KJR),solving and applying(KSA).At the same time,the level of participants is divided into five different levels according to each knowledge dimensions.In order to conduct a more targeted case study,before the intervention of HPM,the author has investigated the current situation and attitude of mathematics teaching involving mathematics history by primary school students,in-service mathematics teachers and pre-service mathematics teachers in Tibet,as well as the PT-HSCK status.Afterwards,a sample of 12 Tibetan pre-service junior middle school mathematics teachers is selected as the study object.in view of 6 knowledge points,such as the Irrational Numbers,binary system of first order equations,the judgement of parallel lines,plane rectangular coordinate system,the application of congruent triangles and quadratic equation of one variable(method of completing the square),the author has designed a questionnaire with 24 objective problems and six subjective problems for the PT-HSCK model with nine dimensions and five levels.In order to explore the change of PT-HSCK,an HPM intervention framework is established.Within the framework,according to the selected six knowledge points,and according to the screening results of fuzzy Delphi method,12 Tibetan pre-service junior middle school mathematics teachers were selected to conduct three HPM interventions of historical documents,HPM teaching and HPM teaching design.After the HPM intervention,the author analyzed the changes of PT-HSCK based on the questionnaire data,interviews and assignment sheet feedback.From the perspective of the overall results,by the t-test for the 9 dimensions of PT-HSCK before and after the intervention,it is found that Seven knowledge component dimensions,which are KRE,KER,KRC,KPP,KAD,KJR,and KSA,had changes that he post-test level was significantly higher than it in pre-test.There was no significant difference in the two knowledge component dimensions of KSI and KCD,but the mean value of the post-test was still slightly higher than that of the pre-test.For the Tibetan participants' PT-HSCK,it can be seen that Seven dimensions of KRE,KER,KRC,KPP,KAD,KJR,and KSA,had changes,the level of the post-test is significantly higher than that of the pre-test.However,there was no significant difference in the other two dimensions of KSI and KCD.For the Han participants' PT-HSCK,it can be seen that Seven dimensions of KRE,KER,KRC,KPP,KAD,KJR and KSA had changes,the level of the post-test is significantly higher than that of the pre-test.However,there was no significant difference in the other two dimensions of KSI and KCD,but the mean value of the post-test was still slightly higher than that of the pre-test.In a word,HPM intervention can improve the level of PT-HSCK.In the meanwhile,this paper can also provide the implementation theoretical framework and data support for the training of pre-service junior middle school mathematics teachers in Tibet.