An Investigation On The Understanding Level Of Representing Numbers By Letters In The Second Grade Of Junior Middle School

The "Compulsory Education Mathematics Curriculum Standards" emphasizes the importance of cultivating students’ symbolic consciousness,the symbolic consciousness in the middle school stage is mainly reflected in the understanding and application of "letters represent numbers"."Numbers represented by letters" is the basic knowledge of algebra learning,and its level of understanding will have a great impact on the learning of algebra content.This paper uses the 3UV model as the theoretical framework,selects a second-year student in Anshan City as the research object and measures students’ understanding level of "numbers represented by letters".First of all,the status of research is understanded on the understanding of "numbers represented by letters" and is determined the theoretical framework by consulting related literatures;Secondly,on the basis of the 3UV model and Ursini and Trigueros questionnaires,combined with the "Mathematics Curriculum Standards for Junior High School Students",the "Junior Two Students Letters Representation Comprehension Level Test Paper" is complied and the reliability and validity of the test paper is analyzed to form the final test paper and conduct the formal test;The following,the data is analyzed and discussed by using SPSS on the following four points: the current situation of students’ understanding level of "numbers represented by letters" as a whole and each level;the correlation of the students’ understanding level of "numbers represented by letters" as a whole and at each level;the specific performance of students’ different understanding levels of "numbers represented by letters" in the test paper;and the reasons for the students’ specific performance at the understanding level of "numbers represented by letters".Finally,the students and teachers are interviewed and are puted forward the following teaching suggestions by conclusions of this paper: 1.To strengthen students’ intuitive thinking of "representing numbers by letters";2.Cultivate students to understand the overall meaning of "representing numbers by letters";3.Train the students to calculate the transformation of "algebraic expression";4.Raise the students’ awareness of the application of "representing numbers by letters".