A Preliminary Construction And Empirical Study Of Mathematical Problem Solving Assessment Framework And Coding System

Mathematical problem solving has always been a hot issue in mathematics education research.With the advancement of the new round of curriculum reform,the Senior High School Mathematical Curriculum Standard(the 2017 version)proposed six mathematical core competencies.This standard also propose the understand of the essence of mathematical content in the problem solving process and facilitate the formation and development of mathematical key competencies.However,the Senior High School Mathematical Curriculum Standard(the 2017 version)does not give a set of solutions for evaluating students' skills in mathematical problem solving,And this is one of the research problems that need to be solved urgently in the current mathematics education research.This study absorbs the assumptions about the relationship between mathematics ability,thinking level and problem solving ability in test items such as PISA and TIMSS.It selectively refers to their division in objective coding and method level,which is based on six mathematical core competencies of the Senior High School Mathematical Curriculum Standard(the 2017 edition),and also retain some of the operations in the traditional scoring method.Based on the concept of two-digit coding system,the method level and type,literacy in the process of understanding the problem separate the three components of horizontal and dual-base capabilities.Based on the above viewpoints,this study constructed a Mathematical Problem Solving Assessment Framework and Coding System.The system is divided into two parts:(1)the coding method of the topic features,(2)the coding method of the students' answers.On this basis,the researchers conducted pre-tests to verify the feasibility of the evaluation scheme and the coding system.Subsequently,two junior high schools and one normal university students(pre-teachers)were selected in Jiangsu and Shanghai for testing and talking.The evaluation program and coding system were used to evaluate the current level of mathematics problem solving forjunior high school students and pre-teachers,as well as the understanding and suggestions of pre-teachers for this system.In the end,this study got the following conclusions:1.This study proposes a Mathematical Problem Solving Assessment Framework and Coding System.It consists of the coding method of the topic features and the coding method of the students' answers.The coding method of the topic features can locate and categorize the questions,the coding method of the students' answers can be used to evaluate the performance of students' solutions and the characteristics of thinking and literacy in the process of students' answers.2.The factors considered in the Mathematical Problem Solving Assessment Framework and Coding System proposed in this study are also the components of the mathematical problem solving ability to a certain extent.Therefore,Mathematical Problem Solving Assessment Framework and Coding System proposed in this study have certain rationality.In the pre-test,by using the Mathematical Problem Solving Assessment Framework and Coding System,the results obtained that the scheme can test the math problem solving ability of different students.According to the Mathematical Problem Solving Assessment Framework and Coding System of this study,the following conclusions can be drawn: the higher the score one gets,the stronger the mathematical problem solving ability he/she has.3.After the selected two samples are tested,it can be seen that the junior high school students are lacking in the unconventional type and rich background mathematics questions,according to the Mathematical Problem Solving Assessment Framework and Coding System of this study.However,students are very interested in such topics,and the topics they are most interested in are often highly consistent with the topics they find most difficult;the third-year college students are lacking in abstract mathematical proofs or rich background mathematics questions,and they provide some suggestions for revision.Both of them do well in the correctness ofmethod and mathematics double-base but get low score at the level of method and mathematical core competencies.Finally,the researcher fully explained the limitations of this study,hoping to be helpful for the subsequent research,and hope that the Mathematical Problem Solving Assessment Framework and Coding System of this study can evaluate the students' mathematical literacy and problems for teachers and further theoretical research.