Investigation And Study On Understanding Level Of Counting Principle Of Mathematics Gifted Students

Count principle,one of the most vital mathematical carriers on the middle school students' contacting discrete mathematics,is the basis of the combinatorics which is a significant field of discrete mathematics.Also,counting principle is one of the students' mathematics learning difficulties.Therefore,this paper studies top students' understanding to the principle of the count in order to provide the optimized way of teaching and learning practice about counting principle.First of all,how to evaluate the level of understanding of mathematical gifted students on counting principle by qualitative evaluation needs to be solved.The literature review is carried out by focusing on “gifted students”,“the Structure of the Observed Learning Outcomes(SOLO)Taxonomy”,and “the principle of counting”.According to the standards of high school about mathematics(2017)in counting principle,this paper initially set the evaluation scheme about understanding level of count principle by using the theory of SOLO.Based on that,this paper further creates a level test for mathematics gifted student whose understanding level of count principle.Secondly,the test questions prepared were used to test 340 gifted students in sichuan province.According to the test results,the correlation between their overall performance,common solution strategies and preferred solution strategies,as well as various influencing factors(learning status of counting principle,daily math scores,grade,gender,etc.)and understanding level was analyzed.The main conclusions are as follows.1.The main cognitive barriers and error types of the counting principle mainly include incomprehension of the subject,incomprehension of the concept,failure to consider special elements or special positions,repeated counting,and omission counting,etc.2.It is easier for students to understand the counting principle of step by step multiplication than to understand the counting principle of classified addition.3.There is a positive correlation between the level of understanding and the scores of ordinary mathematics.4.When students learn the principles of counting systematically,there is no difference between different grades.5.The understanding level of boys is higher than that of girls.Beyond that,the students who gave representative answers were selected from them for interviews,so as to have an in-depth understanding of their thinking process during the test,and to identify the problem-solving strategies and cognitive barriers after analyzing the students' test results.Furthermore,6 experienced teachers were interviewed to understand their understanding to the teaching significance and course status of counting principle,teaching difficulties,and specific arrangement of teaching.Ultimately,combining with literature review,the data analysis results of investigation,and the result of the interview,the teaching suggestions in the light of counting principle chapter are put forward.Based on that,combining with taught A version of mathematics(take 2-3)to the counting principle,the overall design on a total of 3 section content has been carried on.It hopes to provide reference for subsequent teaching and research.