Research On The Current Situation And Cultivation Of Mathematical Problem Solving Ability Of Eighth Grade Students From The Perspective Of Polya

Mathematical problem solving ability is an important ability in the process of learning mathematics,and it has an important impact on mathematical learning.In this paper,we use the problem solving theory from the viewpoint of Polya as the basis for our research.We use the four steps in Polya’s "How to Solve a Problem Table" as an important basis to construct a framework of four sub-competencies,namely,problem solving ability,planning ability,plan execution ability,and review and reflection ability,to reflect mathematical problem solving ability.The framework of problem solving ability was constructed based on the four steps in the "How to solve a problem table".The eighth-grade students in an experimental middle school in Taiyuan were selected as the subjects of the study,and the following findings were obtained through selfadministered tests,teacher interviews,and student interviews:(1)The overall average level of mathematical problem solving ability of the eighth graders was "pass" level.(2)The eighth graders were better at understanding problems,had a moderate and balanced performance in planning and execution,with execution being slightly better than planning and review and reflection being weaker.(3)The mean scores of boys were slightly higher than those of girls,indicating that boys performed slightly better than girls in problem solving skills,but the overall difference was not significant.The mean scores of boys were higher than those of girls in the problem solving and review and reflection dimensions,and the mean scores of girls were slightly higher than those of boys in the planning and execution dimensions,but the overall difference was not significant,and the differences between boys and girls in the four sub-dimensions did not reach significant levels.In the three major knowledge domains at the junior high school level,the mean values of the scores of boys in the three major knowledge domains were slightly higher than those of girls in Grade 8,but the overall gap was not significant and the differences did not reach a significant level.(4)Students’ mathematical problem solving ability was reflected by their test scores,and there were significant positive correlations between students’ usual mathematics performance and mathematical problem solving ability and each subcompetence dimension of mathematical problem solving process respectively;among the correlations between each sub-competence dimension and their usual performance,the correlation coefficient between execution planning ability and usual mathematics performance was the largest;the correlation coefficient between formulation planning ability and usual mathematics performance was the second,and the correlation coefficient between understanding The correlation coefficient of problem solving ability with the usual mathematics performance was the next highest,and the correlation coefficient of review and reflection ability with the usual mathematics performance was the lowest.(5)The mean values of problem solving ability and each sub-dimension of ability were higher for the top students than for the middle students and the low students.Based on the results of the analysis of the data from the eighth grade students’ mathematical problem solving ability test,combined with the teacher interviews and student interviews,the reasons behind the current situation were analyzed and the feasibility of cultivation was analyzed.Combining the findings of other scholars,experts,tutors and front-line teachers’ suggestions,a program and strategy for cultivating eighth grade students’ mathematical problem solving ability was developed.The eighth grade(1)class was selected as the experimental class and the eighth grade(2)class was selected as the control class for a two-month control training.The experimental class focused on two aspects of intervention: intensive training and case-tracking training.The experimental class was taught by dozens of typical practice lessons selected by the researcher,and the rest of the lessons were taught by the original mathematics teacher;the control class did not have any intervention.In the case training,two students in the experimental eighth grade(1)class were selected from each of the top,middle,and low achievers,and different training programs and strategies were formulated according to the performance of the students at different levels in the pre-test and the process stages of mathematical problem solving ability and sub-ability.The training was carried out in a phased and step-by-step manner,based on observation and communication,and the strategies were adjusted to the students in the middle and late stages respectively,and the performance of the students was recorded and analyzed in a timely manner,combined with post-tests to obtain qualitative training effects.At the end of the training,an overall comparative analysis of the performance improvement of the two classes was conducted through the post-test paper of the mathematical problem-solving ability of the eight students,and the following conclusions were drawn:(1)In the group development,the implementation of the mathematical problem solving skills development program from the Polya perspective improved the mathematical problem solving skills and all sub-competency dimensions of the eighth graders,indicating that incorporating the mathematical problem solving theory from the Polya perspective into the classroom is a proven teaching method.(2)In the case development,the implementation of the Polya’s view of mathematical problem solving skills development program improved the mathematical problem solving skills of students at different levels to different degrees.The above shows that the development program and strategies are effective and have some practical reference value.