Study On The Teaching Design Of "use Letters To Express Numbers" In Elementary School Mathematics

The "Compulsory Education Mathematics Curriculum Standards(2011Edition)" replaces the "symbolic sense" in the experimental manuscript with "symbolic consciousness"and includes it in one of the ten core concepts of mathematics.The phrase "representing numbers by letters" is an important turning point in cultivating students' symbolic consciousness.It is the beginning of the transition from concrete arithmetic to abstract algebra.This is an important and difficult step,but a lot of research shows that students are"representing numbers with letters"."There are cognitive difficulties.In view of this,the author proposes a new teaching design,hoping to promote the establishment of students' symbolic awareness.The main work of the author is as follows:First,combing the historical development of numbers with letters,have a deeper and more essential understanding of the number of letters,predict students' learning difficulties,and guide the design of teaching strategies and classroom activities.Second,the survey students have just contacted the cognitive level after teaching "using letters to represent numbers".In this study,four classes will be selected from the fifth grade as experimental research objects,and their cognitive development tests will be conducted to understand the cognitive impairment of students.Third,the "designation of the number of letters" teaching design.The author combines the teaching enlightenment obtained from history,the cognitive barriers of students and the analysis of the content of the textbooks.The author has developed a new teaching design.Fourth,the effectiveness of the test teaching design.The teaching design is implemented for the selected class,and the effectiveness of the teaching design is tested from two aspects: qualitative analysis and quantitative analysis.The conclusions of the research obtained in this paper are as follows:First,the history of the number of letters indicates that the number of letters is not simply a number instead of a number,but a quantity.The number represented by letters is divided into two stages.One is to evolve from "specific number" to "unknown number",and the other is to evolve from "unknown number" to "variable".Second,students generally have the following cognitive problems:do not understand the duality of the alphabetic formula;the negative migration effect caused by the inherent arithmetic thinking;the phenomenon of "function fixation" appears in the recognition of letters;Just staying in letters instead of numbers,not really knowing the meaning of numbers in letters.Third,according to the historical development order of the number of letters and the actual situation of the students,the design of the number of letters is designed,including four links:the use of letters to indicate the unknown;the second is to use letters to represent variables;to recognize the duality of concepts;Letters represent the laws of operation and calculation formulas.Fourth,the concrete implementation of teaching practice has reached the expected teaching goals and has good results.For the teaching design formulated by the author,from the teacher's classroom teaching to carry out a qualitative analysis,we can see the following advantages:According to the main line of historical development,the design of teaching steps;Reconstructing the duality containing the alphabet;Set appropriate examples to achieve real improvement in student thinking;Let students experience the necessity and rationality of the corresponding rules through personal experience,and get rid of passive learning;Set all kinds of questions for the students,urge them to seek solutions to the problem.Quantitative analysis is carried out from the student's test volume,and the effectiveness of teaching design is tested by setting control group and experimental group,and its practical effect is evaluated.The results show that only a small number of students in the experimental class will be confused by numbers when comparing letter sizes,and there will be relatively few "functional fixed" States,and they can understand the simple duality of letters,but for a little more complicated The situation begins to chaos.However,it still tends to be written,and short-term training can not significantly enhance students 'use of letters.In addition,there is no significant effect in promoting students to clarify the quantitative relationship between the same letters.