High School Mathematics Teachers’ Professional Development Promoted By HPM:

The Mathematics Education Curriculum Reform highlights the significance and certainty of teachers’ professional development. The capability of HPM teaching design is an essential part of the mathematics teachers’professionalism. How to improve the teachers’ HPM teaching design capability is an important task facing mathematics teacher trainers. Based on the analysis of current approaches and strategies of teachers’ professional development, unique advantages of the mathematics education studio and problems in HPM teaching, a design research of HPM teaching was carried out on a mathematics education studio in order to understand about the influence of the HPM designs and teaching on mathematics teachers in the studio as well as on their students.A mathematics education studio and its members, eight senior high school teachers, were chosen as subjects, six of whom participated the complete process of the three rounds of HPM design research. The research questions include:1. What are the effects of HPM design research on the mathematics education studio?2. In which aspects do the HPM designs and teaching process promote the studio teachers’professional development?3. What are the positive impacts of the HPM teaching on students’mathematics learning?4. What productions can we get from the HPM design research?The main methodology is design research, supplemented by the narrative research and the participatory action research. From the first round of HPM design and teaching, the author participated all activities of the studio. The data are collected from video-taped lessons, interviews with teachers before and after lessons, teachers’ reflective diaries, audio-taped activities of teaching research and the questionnaire developed by the researcher,"Teachers’ Self-rating Scale on Professional Growth Basing on HPM". The research findings were presented in both dimensions of transverse and longitudinal comparison. The longitudinal comparative study aimed at the changes of both the teacher who participated the HPM design and teaching and all other members of the studio during the period of a complete round of three times of designs and teaching. The transverse comparative study aimed at the differences between the teachers inside and outside the studio.With the main task of HPM design of the beginning lessons of six topics in senior high school compulsory and elective textbooks, three patterns of HPM designs are developed:cultural orientation, explorative orientation and genetic orientation, and lesson models and design principles in different topics of the senior high school mathematics are provided.Through the longitudinal comparison, it is found that, in all the three rounds of teaching, teachers’ capabilities of HPM design and teaching are improved. In the first design, they used historical materials with the single complementation approach simply paying attention to the quantity of the historical materials; but in the third design, they tend to ad8pt suitable approaches to meet the need of the teaching objectives, paying attention to the quality as well as the quantity of historical materials.Through the transverse comparison, it is revealed that the teachers inside the studio are significantly better than the outside teachers in the following aspects:(1) the knowledge of history of mathematics;(2) the ability and knowledge of HPM design and teaching;(3) the knowledge of the relation between history and mathematics;(4) the research ability and knowledge;(5) the ability of reflection;(6) the ability of cooperation and communication, and so on. But their mathematics knowledge and pedagogical knowledge are not significantly better than the teachers outside the studio. The basic conclusions of this study are as following:1. The effects of HPM design research on the mathematics education studio are mainly shown in the following three aspects:(1) the design research on HPM contributed to the operation and orientation of activities and objectives of the whole studio;(2) it also contributed to the development and implementation of the studio’s strategies of training teachers;(3) HPM design research makes the studio’s learning activities productive.2. The main roles of the HPM design and implementation cycles for teachers in the studio are:(1) changing teachers’attitudes towards HPM instruction, from rejecting to accepting and at last to desiring;(2) changing teachers’conceptions of mathematics;(3) improving the teachers’conceptions of mathematics teaching learning;(4) enhancing the teachers’abilities of HPM instructional design, self-reflection, teaching research and communication and collaboration with peers and experts, and so on.3. The teaching from the perspective of HPM has positive impacts on students’ learning, including:(1) having promoted the students’in-depth understanding of mathematical knowledge;(2) having established the linkage between mathematics and other disciplines, which makes the students’mathematics conceptions more comprehensive;(3) having cultivated students’positive emotion of mathematics and changed students’conceptions both of mathematics and mathematics learning.4. The significances and productions of the HPM design research mainly include the following two aspects:providing references to the other studio activities; presenting three HPM models and six teaching cases and giving the basic principles and steps of the HPM design.Based on the above conclusions, the following educational implications are obtained:(1) The topic-driven design research is of great significance for teachers training;(2) More attention should be paid to the pre-service teachers’ HPM teaching knowledge and capacity;(3) Importance should be attached to the HPM classroom teaching practice and cases development.As far as the HPM research is concerned, further researches should be carried out on the following areas:(1) the relation between HPM and teachers’ professional development and training approaches;(2) the history of mathematics for mathematics teaching;(3) the theoretical framework and other empirical researches.