The Evaluation Index And Its Application Of Pupils' Mathematical Problem Posin Ability

In recent years,mathematical problem solving ability has been mentioned in the mathematics curriculum standards of primary and secondary schools in many countries,and has become an important part of the core mathematics literacy.Therefore,the measurement and evaluation of mathematical problem solving ability has become a hot topic in mathematics teaching research,among which the evaluation tool and its application have become the primary concern of researchers.Research Objectives: On the basis of sorting out the definition of "mathematical problems",existing evaluation contents and methods,the evaluation model of mathematical problems is constructed from the three dimensions of the essential characteristics,mathematical characteristics and language characteristics of the problems,and all levels of indicators in the model are given weight.In study 2,for the multi-nested and complex data structure,considering that the unitary and one-dimensional rater reliability cannot accurately estimate the reliability and error of the measurement,the multivariate generalization theory(MGT)was used to verify the rater consistency reliability of the evaluation index of mathematical problem solving ability.Study 3: Classify students' mathematical problem putting ability through latent profile analysis,verify whether there are differences in mathematical achievements among students with different problem-putting ability levels,and explore the relationship between mathematical problem putting ability and demographic variables.Research process and methods: Study 1:(1)Based on theoretical research,the main factors related to the evaluation of students' mathematical problem putting ability are extracted preliminarily from three levels,the meaning of each evaluation index is clarified,and the element dissection table of the evaluation index system of mathematical problem putting ability is compiled.(2)Collect data from primary school,junior high school,senior high school,university and other front-line teachers as well as current mathematics graduate students and doctoral students,analyze the data through statistical measurement methods,and extract and evaluate the basic elements of mathematical problem solving ability.(3)Confirmatory factor analysis was used to construct structural equation model to verify the representativeness and interpretation degree of evaluation indicators.(4)Prepare the weight matrix judgment table,invite 5 experts to fill in the weight judgment matrix table,and use the analytic hierarchy process(AHP)to calculate the weight of the evaluation indexes of mathematical problem solving ability at all levels.Study 2 :(1)Determine the problem situation of mathematical problems under the guidance of experts;(2)The fifth grade students were tested to collect the math problems raised by the students,and the final test situation was determined;(3)Formal test data results,10 undergraduate students were randomly selected to cross score all questions raised by all students according to the scoring criteria and rules of Study 1;(4)The rater consistency reliability of the evaluation index was verified by MGENOVA software.Study 3 :(1)Classify students' mathematical problem solving ability by using Mplus software and using latent profile analysis;(2)Explore the relationship between mathematical achievement,demographic variables and mathematical problem solving ability.Results and Conclusions: Study 1:(1)The indicators performed well in confirmatory factor analysis,the structural validity of the proposed model performed well,and the internal reliability of each dimension was also high;(2)The consistency index CI and consistency ratio CR of the maximum characteristic root calculation show that the experts' weighting of the evaluation index of mathematical problem solving ability has a high consistency and the weighting results are reasonable and scientific.The determination of evaluation model and index weight provides a more scientific and reasonable way of thinking for how to measure and evaluate students' problem raising ability,but its significance is unclear.Study 2 :(1)The covariance component of students in the three sub-dimensions of the evaluation index of mathematical problem solving ability is large,which indicates that the results of determining the level of students' mathematical problem solving ability by using the scores of the three characteristics of the problem will be relatively consistent;(2)The generalization coefficients of the three variables of the essential feature,mathematical feature and language feature are 0.98,0.97 and 0.97 respectively,and the reliability indexes are 0.97,0.96 and 0.96 respectively.The results are all good.(3)In this study,the synthetic generalization coefficient of the overall score of the mathematical problem making ability assessment tool is 0.99,with a relatively small error and a variance component of only 0.30,indicating that the overall graders in this test have a high degree of consistency.Study 3 :(1)According to the fitting index and classification verification,it is reasonable to divide pupils' mathematical problem solving ability into three categories;(2)Students with different problem-solving abilities have different performance in mathematics;(3)There is no significant difference in mathematical problem solving ability on demographic variables such as gender and children category.