Investigation And Research On The Understanding Level Of "Letters Representing Numbers" In Grade 8 Students

The content of "number and algebra" is the core of the mathematics curriculum in primary and secondary school,which has far-reaching educational significance for students' mathematics learning and thinking mode.The content of algebra is arranged in every period of nine-year compulsory education in china.In the first and second learning paragraphs,students are required to understand the "number" in arithmetic.In the third learning paragraph,students begin to contact algebra formally,which needs to experience the translation from arithmetic to algebra."Alphabetical number" is the key of the transformation from arithmetic thinking to algebra thinking.During the internship,the author found that although after the first academic year of grade seven,the eight-grade students still have trouble understanding how letters represent numbers,Which will inevitably affect the subsequent learning of algebraic knowledge such as equation and function.Thus,the author takes the research on the understanding level of"Alphabetical number" of the eight-grade students as the topic of the graduation thesis.In the research process,first of all,the author consulted literature to understand the history of the development of "Alphabetical number" and related research on students' understanding of "Alphabetical number".Then,the test paper was written in the theoretical framework of"The Three Uses of Variable" model proposed by Ursini and Trigueros,and combined with interviews,the understanding of the three uses of "letter denotes number" among eight-grade students was investigated,the causes and gender differences of existing problems were analyzed.Finally,the author gives the relevant teaching suggestions.The respondents of this questionnaire were 269 students from the junior high school affiliated to Taizhou No.2 middle school in Jiangsu province.256 valid questionnaires were collected.The following conclusions are drawn through analysis and research:(1)Students have a good understanding of how letters represent unknown numbers,some students need to improve their understanding of letters represent a class of numbers.It's difficult for students to understand variables in the functional relationship between letters,and most students lack of the awareness of functions;(2)Students are used to assigning values to letters,regardless of their meaning in the problem situation;(3)There is no significant difference boys and girls in their understanding of "Alphabetical number".In view of the above problems found in the survey and research,the author puts forward the following suggestions:(1)Foster students' abundant representation,encourage the imagination,develop imaginal thinking,facilitate the transformation from arithmetic to algebra;(2)Strengthen symbol conscious,develop the algebraic thinking;(3)Pay attention to understanding the meaning of letters represent numbers in specific situations.