The Investigation And Research Of PCK In Probability And Statistics Of High School Mathematics Teachers

Professionalization of teachers is a central topic in educational research.Since Shulman put forward the concept of PCK(Pedagogical Content Knowledge),many scholars have participated in the research of teachers' professional development from the perspective of PCK,and MPCK,which integrates mathematics,has emerged.In recent years,probability and statistics are the core contents of high school mathematics curriculum reform,which play an increasingly critical role in both study and life.In our country,the research on the teaching of probability and statistics started late,teachers' experience was insufficient,and the revision of curriculum standards has adjusted the content of "Probability and Statistics" in high school,so it is urgent to understand the knowledge reserve and teaching status of high school mathematics teachers in probability and statistics.The research on the status and sources of teachers' PCK in probability and statistics is of practical value and far-reaching significance.On the basis of previous studies,based on the background of the new curriculum reform,this paper analyzes the relevant literature of teachers' knowledge,PCK and probability and statistics,selects in-service mathematics teachers in high school as the research object,and takes questionnaire survey as the main research method and afterclass interview as the auxiliary research method to explore the current situation and sources of PCK in probability and statistics of high school mathematics teachers,followed by strategies for development of it.This study considers that the teachers' PCK in probability and statistics contains three components: content knowledge,student knowledge and curricular knowledge.Combined with their connotations and the new requirements in curriculum standards,an analytical framework for the status quo of teachers' PCK is established.From Professor Lianghuo Fan's perspective on the sources of teachers' knowledge,the sources of teachers' PCK in probability and statistics are divided into three dimensions: experience as a learner,pre-service training experience and in-service experience,and is specifically subdivided into 13 different sources for examination.In the analysis of the current situation of PCK,the following four conclusions are drawn:(1)The overall situation of PCK is not ideal and the development of PCK is not balanced.The performance in the dimensions of student knowledge and curricular knowledge is prominent,and of content knowledge is somewhat deficient;(2)In terms of content knowledge,teachers have problems such as errors,vague understanding and inaccurate interpretation,and their performance in the correctness dimension is better than that in the relevance dimension;(3)In terms of student knowledge,teachers have a better understanding of students' cognitive foundation and understanding level,but they are not good at explaining errors and evaluation;(4)In terms of curricular knowledge,teachers have a good understanding of the relevant requirements of curriculum standards,the educational value of probability and statistics,and core competence,but they are not clear about the changes of knowledge arrangement and curriculum setting of curriculum standards,and they are not optimistic about the use of information technology.The analysis of PCK's sources and their factors leads to three conclusions:(1)The actual situation and influence of sources of PCK are inconsistent.Teachers' experience as learners and the pre-service training experience are the main sources of PCK in probability and statistics,but neither of them has the greatest impact on PCK.The most influential one is teachers' in-service experience;(2)In the secondary dimension,"teaching and research activities in high school","self-reflection and experience summary","in-service teacher training" and "books or network resources" contribute the most to the overall development of teachers' PCK in probability and statistics;(3)Different sources have different effects on the improvement of content knowledge,student knowledge and curricular knowledge of PCK.Based on the above findings on the status and sources of PCK in probability and statistics,this paper proposes the following suggestions from the aspects of teachers themselves,high schools,teacher training and the cultivation of normal university students:(1)Raise the awareness of lifelong learning of high school mathematics teachers;(2)Attach importance to and innovate the teaching and research activities in high school;(3)Enhance the effectiveness of in-service training for high school mathematics teachers;(4)Optimize the curriculum content and training mode of normal education.