Comparative Study On Cognitive Level Of The Uses Of Letters Of The Yi、Tibetan、Han Middle School Students

Comparison between different ethnic groups is an important part of mathematics education research.In the study of the Mathematical cognitive level of ethnic minorities,comparing to ethnic students’ cognitive level,it focus on probability and geometry,but it rarely involve the algebra content.Numerous studies have demonstrated that one of the important reasons of students who had difficulty in learning algebra is students’ understanding difficulties of “the uses of letters to represent numbers”.Therefore,the thesis is the breakthrough point of “the uses of letters to represent numbers”,compared and studied Bi、Tibetan and Han of the three national middle school students’ differences of cognitive level.This study first through the literature analysis method to collect and collate national comparative study of the relevant literature. Analysis of the content presented to compare different nationalities junior high school students’ mathematics cognitive level;To compile and analyze the literature with letters to represent numbers, the Three Uses of Variable model(3UVmodel) is similar to the historical process of the evolution of the letters,in line with students’ cognitive processes;By analyzing and comparing the level of cognitive theory,solo theory more clearly reflect the hierarchy of students cognitive level of the letter to represent the number.Next,“The Three Uses of Variable model(3UV model)”:the role of an unknown 、a general number 、the role of a variable related to another one, which used as theoretical framework, and author design the forecasting volumes which combined Curriculum standards and mathematics textbooks of middle school Published by People Education Press and Beijing Normal University Press,and forecast.Prediction target is junior high school students in long quan,because of the Ninth grade students face in the exam,the first test is invalid,Conducted a second test.After prediction,The formal test paper which through communication with Middle School Mathematics Teacher of participating countries of training and repeatedly amended,its reliability is 0.747. The test objective of the research are Han students in Long Quan area and Yi students in Xi Chang,and Tibetan Students in Gan Zi Autonomous Prefecture,the number of valid questionnaires was 460.Solo classification theory was as an appraisal tool.the data from the test paper was collected and analyzed by SPSS software.Finally, combined qualitative and ANOVA to Finishing and analyze, Results are as follows:(1)Three national students’ cognitive level of the uses of letters is comparatively better with letters as the role of an unknown and a general number,half of the students achieve Relational Structural Level;but students’ cognitive level of the letters as the role of a variable related to another one is relatively poor,most of students are the level of the Pre-structural and Uni-structural level.(2)The cognitive level of three national students about different grades exists significant difference. It is mainly reflected in the cognitive understanding of the letters as representing a general that can assume any value,there are the significant differences between the grade seven and the grade eight of Yi and Han students; in the cognitive understanding of determining the interval of variation of the parameter when the interval of variation of the other one is given,there are the differences in Yi and Tibetan students of grade nine,Yi and Han students of grade eight,Tibetan and Han students of grade eight and nine.