Research On The Current Situation Of The Application Of High School Student's Thinking Method Of Combination Of Number And Shape

As one of the most important mathematical thinking methods in high school,the combination of numbers and shapes plays a key role in students' learning mathematics.The good use of the combination of numbers and shapes can not only help students broaden their minds,understand knowledge from a deeper level,but also obtain a variety of ways to solve problems.In this paper,on the basis of previous studies,combined with curriculum requirements and SOLO classification theory,designed the student questionnaire,test,and teacher interviews,through the analysis of the data,the author found that most students will be the number form combining as a problem solving tool,didn't rise to the ideological level,the student body logarithmic form combined with the application of consciousness is not strong,and lack the habit of summary reflection in class.In the application of problem solving,the overall ability of students in the aspect of "solving shape by number" is better than that of "helping number by form".From the perspective of knowledge carrier,students have the best combination ability of numbers and shapes in the part of set,followed by plane vector,inequality and trigonometric function,followed by solid geometry,analytical geometry and sequence,and the worst application is function.From the grade point of view,senior three students are better than senior two in the combination of numbers and shapes.When students solve problems by combining numbers and shapes,the main problems are as follows: inability to transform attribute representation,inaccurate drawing,non-equivalence of numbers and shapes transformation,etc.According to the present situation of the application of the combination of numbers and shapes,the author thinks that in order to strengthen the students' application awareness and ability of the combination of numbers and shapes,teachers should first update their teaching concepts and enhance the awareness of the infiltration of mathematical thought.Secondly,teachers should pay attention to the penetration of the new teaching,mining the available teaching materials of the combination of numbers and shapes in the textbook.Only when students realize that the combination of numbers and shapes has been widely reflected in many aspects of the knowledge content,students can gradually improve the combination of numbers and shapes from problem-solving methods to mathematical thinking.Third,teachers should pay attention to the correspondence and transformation of the three languages of mathematics in teaching,and cultivate students' consciousness of number-shape transformation.Finally,teachers should pay attention to students' ability of drawing and recognizing drawing.Students' ability of drawing is weak,so teachers should be more patient and correct students' problems in time.Also,teachers should make good use of information technology software to assist teaching.