Investigation And Research On The Cognitive Level Of Irrational Numbers Of Junior High School Students Based On SOLO Theory

The content of irrational numbers has an important position in middle school mathematics.It is not only the basis for subsequent learning knowledge of quadratic radicals,quadratic equations in one unknown,and acute-angle trigonometric functions,but also the basis for learning knowledge of functional inequalities in high school mathematics.This article attempts to use SOLO classification evaluation theory explores junior high school students' cognition of learning irrational numbers from four aspects:definition,estimation,number axis representation,and arithmetic.A questionnaire survey was conducted among 163 eighth-grade and ninth-grade students in a middle school in Qingdao.Analyzing cognitive differences between grades and classes,and after the questionnaire survey,interviews with individual students and teachers were conducted to find the factors affecting the cognitive level.On the whole,junior high school students have a low level of knowledge about irrational numbers.They have the best cognition level of the definition of irrational numbers.The level of cognition of multi-concentration and multi-point structure accounts for 60.9%;the error rate of the estimation of irrational numbers is high,with an error rate of 64.6%,and a low level of cognition;the number axis of irrational numbers indicates a high level of cognition,mostly focusing on the level of cognition of association structures and expanding the level of abstract cognition;the level of cognition of the four arithmetic operations is relatively high,focus on multi-point structure rate of 55.4%.From the other level,the difference and correlation analysis of its cognitive level is carried out.From the perspective of gender,independent sample test found that there is no obvious difference in the cognitive level of irrational numbers between boys and girls;from the perspective of grade,the cognition level of irrational number knowledge of the ninth grade is higher than that of eighth grade students,mainly focusing on the estimation on irrational numbers and number axis representation.From the perspective of the class,the experimental class' s cognition level of irrational number estimation,number axis representation and four arithmetic operations is higher than that of the ordinary class.However,only in the definition of irrational number,the students in the experimental class have a greater understanding of irrational numbers than the students in the ordinary class.The essential level of cognition is high,there are significant differences,and the differences in other aspects are not statistically significant.Finally,based on the above research conclusions,some suggestions are put forward for teachers in the teaching of irrational numbers,so as to have certain reference value for the teaching of irrational numbers.