Research On The Cultivation Of High School Mathematics Problem Solving Ability From The Perspective Of Language

Mathematical language is the carrier of mathematical thinking and the tool of mathematical communication.The 2017 edition of mathematics curriculum standard for general senior high school takes the proper use of mathematical language and natural language for expression and communication as an important content of evaluation.Therefore,in the daily teaching,we should pay attention to the mathematical language and give full play to its important role in mathematical learning and thinking exercise.Polya once said,"the main purpose of learning mathematics is to solve problems".Problems are the heart of mathematics,and solving problems is an important part of mathematics learning.Moreover,many problems that students have in solving problems can be attributed to mathematics language.Therefore,how to cultivate high school students' problem-solving ability from the perspective of mathematical language has become an urgent problem to be solved.In order to solve this problem better,this paper first analyzes and expounds the research status of "mathematical problem-solving" and "mathematical language" at home and abroad;secondly,it defines the concepts of mathematical language and mathematical problem-solving ability,and analyzes the relationship between them;then it introduces the main theories used in the research;finally,through the test paper and questionnaire survey,it understands In the process of solving problems,senior high school students show the differences and problems of their abilities of understanding,transformation,construction,operation,expression and reflection in different knowledge modules.Through interviews,they further understand students' habits of solving problems and teachers' understanding of mathematical language,and get the following conclusions:(1)senior high school students' abilities of understanding mathematical language in geometry,algebra and unification In addition,probability is mainly at the level of multiple structure,while in function,it is mainly at the level of single structure;(2)mathematical language conversion ability is mainly at the level of multiple structure in function,geometry and algebra,and it is mainly at the level of single structure in statistics and probability;(3)mathematical language construction and operation ability are mainly at the level of correlation structure in function,geometry and algebra,In statistics and probability,they are mainly at the level of multiple structure;(4)mathematical language expression ability is mainly at the level of correlation structure in geometry and algebra,at the level of multiplestructure in statistics and probability,and at the level of single structure in function module;(5)from the perspective of language,senior high school students have the following problems when solving problems: failure in implicit condition analysis;fuzzy concept Unclear;omitting constraints and confusing quantitative relations;incomplete,not smooth and not refined transformation;incorrect use of mathematical symbols;lack of problem-solving skills;unable to find the relationship between knowledge;unclear examination and thinking set;omitting operation steps;expression of imprecise and irregular;unable to use multiple mathematical languages to express information;poor language organization ability;failure to develop problem-solving skills The good habit of reflection;the depth of reflection is not enough;(6)teachers of different teaching ages are aware of the importance of mathematical language in solving problems,but it is difficult to implement because of the limited classroom time and the uneven level of students' solving problems.Therefore,as a teacher,we should attach importance to the teaching of problem-solving from the perspective of mathematical language;strengthen the training of mathematical language reading comprehension,cultivate the ability of information collection and processing;guide students to use as many mathematical language forms as possible to analyze problems;cultivate students' ability of observation and association;strengthen the attention to the standard of problem-solving;create a relaxed classroom environment,and encourage students to actively participate in it Mathematics language expression activities;construction of reflective mathematics classroom.As a student,we should pay attention to the study of basic knowledge;consciously exercise the ability of mathematical language conversion;pay attention to the accumulation of commonly used construction skills in solving problems;read,speak and write more to improve the ability of mathematical language expression;learn to sort out the wrong problems and form a good habit of problem-solving reflection.In terms of examination evaluation: first,we should use multiple evaluation methods and pay attention to the thinking process of problem-solving;second,we should pay attention to the understanding and transformation of mathematical language and less mechanical memory when preparing test questions.