Research On Solving Sequence Problems In High School Mathematics Competitions

The development of mathematical competitions has roughly experienced three stages.The first stage was from 1894 to 1959,which was the preparatory stage from spontaneous and accidental mathematical competitions to standardized mathematical competitions;The second stage was from 1959 to 1979,which was a rapid development stage from regional mathematical competitions to international mathematical competitions;The third stage,from 1981 to now,is a highly institutionalized,standardized,and recognized mature stage.Sequence is an important component of algebra in high school math competitions,and its flexible and varied examination forms and brilliant and ingenious problemsolving methods are often favored by contest proponents.Therefore,this article takes sequence as the research object,and conducts research from four aspects: the historical background and research status of sequence problems,theoretical basis and examination types,problem-solving methods and analysis,practical research and suggestions.Based on the conclusions drawn from practice,corresponding suggestions are given to both teachers and students in mathematical competitions.The main content of the full text includes four chapters.The first part is Chapter1,briefly describes the development process of mathematical competitions and the emergence of sequence problems,and makes a comprehensive analysis of the current research results at home and abroad on the sequence problems of mathematical competitions.The second part is Chapter 2,starting from the relevant concepts,properties,and propositional principles of sequence questions in high school math competitions,through a brief statistical analysis of the types,problem solving methods,and score ratios of eight series questions in math competitions over the 11 years from2012 to 2022,nine typical problem solving methods for three sequence types are summarized.The third part is Chapter 3,analyzes the problem solving process,solution ideas,and requirements for students’ mathematical operation ability,logical reasoning ability,and mathematical abstraction ability for three types of sequence problems based on specific competition examples.The fourth part is Chapter 4,conducts practical research in the form of test papers and interviews.The test paper examines the development of students’ mathematical computing ability,logical reasoning ability,and mathematical abstraction ability based on a two-way detailed table of learning content and results.110 students in the gifted classes of Grade 2 and Grade 3 of Guangyuan Senior High School are selected as the research objects,use SPSS software to conduct quality analysis on the reliability,validity,difficulty,and distinguishability of the test paper to ensure the accuracy of the research results;In the interview section,based on Dewey’s viewpoint on the essence of education and Tao Xingzhi’s theory of life education,interview the guiding teachers of participating competition students from three dimensions: teaching methods,thinking abilities,and experience growth to understand the difficulties and solutions in the actual sequence of teaching process.Finally,the questions reflected in the test paper and the results obtained from the interview were combined.Provide teaching and learning suggestions for teachers and students in competition teaching,hoping to provide some assistance to teachers and students participating in mathematics competitions.