Research On The Influence Of Thematic Workshop On Mathematics Teachers'Teaching Belief Of "Problem-Posing"

Students' ability to propose mathematical problems is of great significance to the development of their problem-solving ability,mathematical understanding,mathematical emotion and creativity.Therefore,some countries,including China,have put forward the necessity for teachers to cultivate students' ability to propose mathematical problems in educational programmatic documents.In spite of this,the performance in the teaching practice of mathematical problem-posing is not ideal.As teachers play a leading role in the classroom,it is an important way to promote teachers' professional development in order to implement the problem-posing teaching.The professional development of teachers should include the change of teachers' teaching belief and the increase of teaching knowledge.In terms of teacher professional development,teacher educators can implement teacher education or training more effectively on the premise of understanding teachers' teaching beliefs.As for teaching practice,teacher's behavior is to some extent dominated by teaching belief.Therefore,it is theoretically meaningful to improve the practical effect of problem-posing from the perspective of developing teaching beliefs of mathematics teachers.This study tries to focus on this perspective and find a new breakthrough for teachers' professional development in problem teaching.This study relies on a teacher workshop training project with the theme of "problem-posing",selecting 8 teachers as a sample from the group of teachersparticipating in the training,and analyzed the changes in their teaching beliefs about "raising questions" before and after attending the workshop,as well as the correlation between the workshop training experience and these changes.Firstly,based on literature research,it is clear that teachers' teaching beliefs of "problem-posing" should include the belief about problem-posing,the belief about controlling problem-posing teaching,and the belief about students' mathematics learning by problem-posing.Then,based on this dimension division,open questionnaire and semi-structured interview are designed as research tools.With the help of Nvivo software,drawing on the ideas of grounded theory,this paper makes a qualitative analysis of teachers' teaching beliefs,and analyzes the influence of workshops on teachers' teaching beliefs.Finally,based on the research results,suggestions are provided for improving the role of thematic workshops in cultivating teachers' teaching beliefs:(1)The thematic workshop is the foundation for teachers to establish the "belief about problem-posing".In the workshop training,teachers first form the understanding of the value of problem-posing.Later,while the understanding of the value is deeper and broader,they gradually form the understanding of the connotation of problem-posing and the applicable conditions.At present,teachers' understanding of the connotation of problem-posing is limited to use it as a teaching method to promote problem-solving in the classroom,and there are individual differences in the understanding of operation forms;teachers believe that problem-posing is suitable for students with relevant knowledge base or life experience,but there is a difference in the understanding of the applicable teaching content;teachers affirm problem-posing to put forward the value in reducing teachers' teaching burden and promoting students' mathematics learning.Workshops to teachers' problem-posing beliefs influence mainly comes from the lecture and expert teachers' teaching case sharing,expert lectures are teachers form the problem put forward the connotation and the main source of value understanding,the expert teachers' teaching case as teachers imitate and reference model,often affects their judgment of the applicable conditions for problem-posing.(2)The influence of thematic workshops on teachers' "the belief about controlling problem-posing teaching" can be divided into two paths.Teachers' concerns in this dimension can be divided into three aspects: teaching cognition,teaching design and classroom management.Only the understanding of teaching design is influenced by the workshop,and the direct and indirect influences coexist.The direct influence comes from the teaching cases shared by expert teachers in the workshop.Teachers will imitate or use the ideas of these cases for reference in the teaching design.Indirectly,the workshop influences the teachers' understanding of the teaching design of problem-posing by shaping the teachers' "belief about problem-posing".Whether the teachers are satisfied with their ability to put forward instructional design depends on whether they meet the teacher's cognition of problem-posing.Generally speaking,the workshop training has helped some teachers to build confidence in the teaching design of problem-posing.In addition,teachers' belief in personal teaching cognition and classroom management mainly comes from the feedback of teaching practice from problems-posing outside the workshop,which makes teachers' understanding of these two aspects relatively negative.(3)The activity design of the thematic workshop did not have a direct impact on the teachers' belief about "students' mathematics learning by problem-posing".The workshop guides teachers' teaching practice by cultivating teachers' "belief in problem-posing" and "belief in controlling problem-posing teaching,",and the teaching practice in turn reacts on teachers to form their belief in students' mathematics learning by problem-posing.All of the above reflect that thematic workshops have a positive impact on the overall teaching beliefs raised by teachers,but their development effect on the teaching beliefs raised by teachers is limited in terms of dimensions,and the activity design that can have a positive impact on teachers' teaching beliefs is also limited.In order to improve this problem,it is recommended to:(1)strengthen the degree of detail in the practical guidance,so as to help teachers develop a more complete teaching belief from the workshop learning experience;(2)adjust the order of workshop activity design so that more activities in the workshop can bring positiveinfluence to teachers' teaching beliefs;(3)the establishment of a certain influential problem-posing teaching training,seminar,and competition system is a powerful guarantee for steadily advancing the problem-posing teaching reform.