The Research On The Cultivation Of Reflective Ability On Mathematics Problem Solving From The Perspective Of Core Literacy

Reflection after problem solving is an important part in students' mathematical problem solving activities and also an eternal theme in mathematics learning.Although massive strategies have been developed to cultivate students' reflective ability on mathematical problem solving,it is still difficult for students to improve it.The key to solve this problem is to define the connotation and extension of the reflective ability on mathematical problem solving,to determine the evaluation criteria,and to formulate reasonable cultivation strategies on this basis.This research adopts mixed research methods,quantitative methods as the main method while supplemented by qualitative research methods.Through literature analysis,relevant research results of reflection on mathematical problem solving at home and abroad are sorted out to determine the connotation of reflective ability on mathematical problem solving.On this basis,the reflective ability on mathematical problem solving is divided into three dimensions:the evaluation and adjustment on the knowledge of problem resources,the procedural knowledge and the strategic knowledge.Further refining the specific manifestations of three dimensions leads to the level table of reflective ability on mathematical problem solving,providing a reference for evaluating students'reflective ability on mathematical problem solving.Through questionnaires and interviews,the author learned about the current situation of students' reflective ability on mathematical problem solving in the first grade of the high school.According to the results of the current investigation and referring to the level table,the author proposes five strategies for cultivating students' reflective ability on mathematical problem solving and conducts empirical tests.The research draws following conclusions:(1)it reveals the connotation and extension of reflective ability on mathematical problem solving,and it is feasible to analyze this ability with the level table of reflective ability on mathematical problem solving;(2)the participants have willingness to reflect but their reflective ability on mathematical problem solving are relatively poor;(3)the paper proposes five strategies for cultivating students' reflective ability on mathematical problem from the perspective of teacher-led and student-centered respectively.