A Case Study Of Applying Problem Posing Into Seventh Grade Mathematics Teaching

Mathematics curriculum needs to develop students' creative spirit and sense of practice in the compulsory education.Problem posing activity as an open-ended learning can be an excellent way to develop all aspects of students' creative thinking.In addition to this,problem posing activity can be useful in implementing the "moral education" and "mathematics curriculum thinking" tasks because of its cognitive,creative and inquisitive nature.In the face of the current "double reduction" policy of "optimization of homework",mathematical problem-solving tasks can contribute to the development of students' knowledge and abilities.Based on the above considerations,this study integrates problem posing into all aspects of junior high school mathematics classroom teaching by reviewing the topic and its related historical literature and designing theme-related problem posing activities;at the same time,this study conducts mathematical extension activities incorporating problem posing for nearly three months.The purpose of this study is to examine the following two questions.Q1: In what aspects has instruction that incorporates mathematical problem posing influenced the characteristics of mathematical problem posing among seventh grade students?Q2: What aspects of seventh grade students' mathematical problem posing styles have changed over the course of changes in mathematical problem posing characteristics?The following conclusions were obtained from this study.Facing structured and semi-structured contexts,students initially performed relatively well in terms of fluency and flexibility levels of mathematical problem formulation,with relatively smooth changes over the course of the study;facing problem contexts with a higher degree of freedom,students made relatively significant progress.In terms of problem originality,students' progress was mainly reflected in the number of students who were able to formulate original mathematical problems and in the diffusion of problem types.In terms of complexity level,after the students learned the mathematical problems,more problems in each situation changed from the "memorization level" to the "procedures without connections level" or from the "procedures without connections level" to the "procedures with connection level"and "doing mathematics level”.Through the analysis of the four students' mathematical problem posing performance in the five study sheets,the writer observes the following changes in the students' mathematical problem posing during the study:(1)a shift from purely mathematical problems with loose conditions to problems with tight background;(2)the understanding of complex mathematical problems shifted from " complex data " to "complex structure";(3)the focus on problem context shifted to the focus on mathematical knowledge;(4)gradually focus on the solver's experience of solving the problem.