A Study On The Teaching Design Of "Decimal" Through The Infiltration Of Mathematical Culture

The times put forward more and more demands on cultivating students' mathematical and cultural accomplishment.Moreover,in the whole knowledge structure system of primary school,the “decimal” part is particularly important and it takes on the task of infiltrating mathematical culture.Teaching design is the basis of teaching.From the cultural point of view,the teaching design of “decimal number” can often make the teaching quality double with half the effort.There is still a lack of guidance on how to permeate mathematical culture in the teaching of “decimal number”.The article takes this as the question to carry on the research,in order to provide the certain reference to the elementary school mathematics teacher teaching “decimal” content when permeates the mathematics culture.It is found that the basic forms of mathematics culture in primary school mathematics textbooks are mathematical history,mathematical beauty,mathematical activities,and mathematical thinking methods by combing the relevant documents of“mathematical culture” and “decimal”.The basic forms of “decimal” mathematical culture in primary school mathematics textbooks are: the origin of decimal number,the mathematical thought method in problem solving,the mathematical game activity in teaching process.However,when teaching “decimal”,most teachers do not integrate mathematical culture well with “decimal” knowledge,which usually results in the following problems:(1)students' thinking is limited to “mathematical culture=history of mathematics”,and mathematical culture in “decimal” is limited to the source of“decimal”.(2)there will be a lot of calculation errors when students finish their homework.For example: the decimal point is not aligned,the full ten do not advance one,the final answer forget the decimal point and so on;(3)when teaching,the infiltration of mathematics culture mostly comes from the teacher's experience summary,lacks the theoretical support;(4)in order to help the students master,the teacher began a lot of mechanical repetition,and let the students do the problems constantly,and in such a dull calculation process,the students gradually lost interest.In view of these problems,based on cognitive theory,Freudenthal's mathematical teaching theory and instructional design model,through text analysis,the conditions of“decimal” teaching design which permeate mathematical culture are put forward:teaching analysis should highlight the content of mathematical culture;attention should be paid to the needs of students for mathematical culture in the analysis of learning situation;teaching objectives should stress the guidance of mathematical culture;teaching methods should pay attention to students' experience of teaching activities;teaching materials should stimulate students' appreciation of beauty.The following principles should be followed in the teaching design of “decimal” which permeates the mathematical culture: the principle of the requirement of mathematical culture should be clearly defined in the teaching goal;the principle of the relationship between situation and life reflected in teaching materials;teaching methods embody the principle of step-by-step and step-by-step inquiry;teaching activities reflect the principles of mathematical thought and method;the purport of the five links in the “decimal”teaching process of the infiltration of the mathematical culture:(1)setting the situation and exploring it by writing;(2)step by step,so as to find out by writing;(3)to consolidate practice,to use it;(4)to sum up and sum up,to memorize by writing;(5)to arrange the work and to expand the knowledge by writing.According to the requirement,principle and aim of “decimal” teaching design which permeates mathematical culture,this paper designs two cases of “comparing the size of two decimal numbers” and “multiplication of decimal numbers-solving problems”,and makes case analysis,and draws a conclusion: This study can provide some reference for teachers to infiltrate mathematical culture in teaching “decimal”content.In practical teaching,teachers should learn to break through the framework when they are familiar with the “decimal” teaching that permeates mathematical culture.And the mathematics culture permeates into the other teaching content,truly achieves the culture and the mathematics teaching fusion.