Textbook Analysis And Teaching Content Reconstruction Of The "triangular Relationship" In Primary Schools

The triangle is the basic graphic in the geometry lesson and the basis for learning polygons.In triangle,the relationship between the any triangle side lengths is "the sum of any two side lengths of the triangle is longer than the third side lengths".This relationship is taught in junior high school,high school and university mathematics,and it is the necessary foundation for follow-up mathematics learning.Therefore,it is necessary to learn "the relationship between the any triangle side lengths" in elementary schools.In 2000,China's nine-year compulsory education full-time primary school mathematics syllabus(trial revision)had not made a requirement for the "triangular trilateral relationship." It was not until 2001 that the publication of the "Mathematics Curriculum Standards(Experimental Draft)" for compulsory education first appeared.In the standard of 2001,the "graphic awareness" in the second section(Grades 4-6)space and graphics requires that students should figure out "the sum of any two sides is longer than the third side;The sum degrees of interior angles in triangle is 180." by recognition of triangles through observation and manipulation,in the standard of 2011,it is clearly proposed that students must have a good command of that knowledge.Although the content of the "triangular trilateral relationship" has appeared in elementary schools for 17 years,there are still some areas for improvement in textbook design and teaching practice.The one is the definition of triangle is not standardized;the other is that it fails to reflect the thinking process of “why should we compare the sum length of two sides with the third side”,which is closely related to the definition of the triangle.By using the literature method,comparison method,content analysis method and sorting out mathematics curriculum target positioning and theoretical analysis,there is a way to solve those problems.First,the definition of the triangle should be “connecting the head and the tail of three line segments one by one and making sure that there are not on the same line,which we called a triangle.”Second,the proposition of “the line between two points is shortest”should be placed after the position of "triangular trilateral relationship".By this way,it becomes the basis derivation of the "triangular trilateral relationship" in middle schools.Third,classroom teaching should reflect the thinking process of "why should we compare the sum length of the two sides with the third side".In this paper,the current primary mathematics textbooks and classroom instructional designs will be analyzed,and the proposed draft textbook for the triangular trilateral relationship in primary schools was proposed.After that,three corresponding instructional designs were designed.