Teaching Research Of The Numeral System Under The Perspective Of HPM

In recent years,HPM has inspired a great debate in the field of mathematics education and its education value is widely accepted.In addition,the research on specific teaching cases from the perspective of HPM has been increasing.The teaching of the numeral system runs through the whole primary and secondary mathematics curriculum as well plays an important role in fundamental education.However,there are few teaching researches of the numeral system under the perspective of HPM.Therefore,we want to by deepen students’ understanding of the concept for the number by the history of mathematics and to transform their understanding of the number from the concrete to the abstract.Based on historical similarities and teaching theoretical basis,we always adhere to the principle of theory with practice.Because the predecessors’ teaching re searches from the perspective of HPM generally lack of specific data,our study will investigate into the mathematics teachers and students of the primary and secondary schools.Firstly,understand the current students’ mastery for the content of the numeral system and the extent of the combination of the history of mathematics and the numeral system,we put forwards the advice about teaching to teachers based on the difficulties in the combination and the learning process of students.Aiming at the content of mathematics teaching,this paper puts forward the teaching principles and strategies of HPM.According to the condition that previous researches rarely mentioned the concrete steps of HPM perspective based on the specific content of numeral system,we have selected the representative concept of the numeral system to conduct teaching design and comparison experiment.Because negative number sparks controversy in history,Students’ learning need to cross the obstacle of thinking and change the original cognition of number.We select the class ‘positive and negative number’ to conduct experiment teaching from the perspective of HPM,comparing with ordinary teaching.Then we design the questionnaire,which explains the advantages of the teaching from the perspective of HPM from the specific data,alleviating the monotony of the questions of number,promotes students’ understanding and mastery of the content of numeral system.The results of this paper can not only provide references and suggestions for the teaching of HPM in the future,but also provide theoretical support and researching ideas for case development from the perspective of HPM.