Research On Cultivating High School Students' Core Mathematical Literacy Through Mathematical Problem Solvin

From the 1980 s to the present,the hot issue of mathematical problem solving has received widespread attention both at home and abroad,with most scholars conducting research on the theoretical aspects of mathematical problem solving,such as its connotations,influencing factors and countermeasures for improvement,lacking the integration of theory and practice.Today’s education reform is constantly improving.The new curriculum reform focuses on students’ basic knowledge and fundamental skills,but also has higher requirements for students’ core literacy in mathematics,advocating students’ independent exploration,encouraging learners to cooperate and communicate,and strengthening the cultivation of core literacy in mathematics in teaching and learning.Problem solving and core literacy in mathematics are closely linked.Therefore,this article combines the two,defines the types of problems that effectively develop students’ six core literacies,and elaborates on the development of each core literacy in the process of concrete problem solving with the help of examples,which is very important for effectively developing students’ core literacy.In this article,the ultimate aim is to effectively develop students’ core literacies in mathematics,and to define the types of problems that are conducive to the development of literacies by using mathematical problem solving as a means of cultivation.The types of problems are first classified as conventional and non-conventional,and based on the elemental analysis method,rule-based and application-based problems are classified as conventional,and exploration-based and research-based problems are classified as nonconventional.The core mathematical literacies of students,which include a variety of characteristics such as contextualisation,innovation,variation,compounding and reflection,are defined,and specific pedagogical suggestions are given for developing each of these literacies at the Polya problem-solving stage from the perspective of developing students’ core mathematical literacies.Firstly,the research direction of this paper is determined by collating and analysing the current situation of problem solving in mathematics,core literacies in mathematics and the links between them at home and abroad,and elaborating the theoretical definition of each element.Then,six classes of students in a high school in Q city are chosen as the subjects of investigation,and classroom observation is made on the teaching of problem solving in one of the classes,and through analysing the types of problems solved in the classroom and the ways in which they are solved,it is possible to understand the teachers’ classroom development of students’ The questionnaires and test papers were analysed to find out students’ problem solving skills and core literacy levels and their understanding of them at the four stages of Polya’s problem solving;the teachers were interviewed to find out their understanding of problem solving and core literacy in mathematics and the development of core literacy.Based on the problems and the mutually reinforcing relationship between the two,the six aspects of students’ core mathematical literacy are used as the target for the development of students’ core mathematical literacy,and suggestions are made for the development of teaching and learning in each of the main stages of Polya’s problem solving in conjunction with non-conventional types of problems:(1)presenting problem scaffolding to penetrate the essence of the problem;conducting experimental mathematics teaching to develop abstract mathematical literacy.(2)Set up problems to stimulate the sense of reasoning;consolidate the foundation;focus on the divergent thinking patterns in students’ problem solving to cultivate logical reasoning literacy.(3)Strengthen basic knowledge and strengthen variation training;develop the habit of arithmetic testing;improve the management of errors and cultivate attribution of errors to develop mathematical operational literacy.(4)Use the combination of numbers and shapes to cultivate intuitive imagination;use information software to develop spatial concepts to cultivate intuitive imagination literacy.(5)Create problem contexts to lay the foundation for modelling;teach in a variety of forms to expand modelling ideas to develop mathematical modelling literacy.(6)Cultivate diverse data analysis strategies;organise students to design statistical investigation activities to cultivate data analysis literacy.Finally,a lesson on principles is selected,using The Fundamental Theorem of Plane Vectors as a case study,and problem solving teaching design is combined with teaching suggestions conducive to developing core mathematical literacy as a teaching practice,aiming to serve as a reference for teachers’ teaching implementation.