A Survey Research Of High School Students’ Application Of Venn Diagram To Solve Math Problems

John Venn,a British logician and philosopher,invented Venn diagram in 1881.Venn diagram was a mathematical diagram that classified objects of study by closed figures to demonstrate the relationship between different categories.Venn diagram has rich mathematical,historical,humanistic,and aesthetic values.It connects abstract set with intuitive figures,embodies the thought of symbolic-graphic combination,and conduces to cultivate intuitive imagination and logical reasoning.In present literatures,mathematics teaching research only focuses on the application of Venn diagram,without considering students’ understanding and cognition of Venn diagram deeply.In addition,the test tools used to study the current status of students’ graphic representation and intuitive imagination in China have focused on functional images and curve equations,and the role of Venn diagram as a visualization tool has not been fully considered.This research focuses on the following questions: 1.How do high school students use Venn diagrams to visualize set expressions? How well is it? What mistakes will students make? 2.How do high school students identify Venn diagrams? How well is it? What mistakes will students make? 3.Is the level of visualization and identification of Venn diagrams relevant to solving set problems?To answer these problems,this research designed a test reflecting the mathematical and visual characteristics of Venn diagrams and conducted the test in five classes of different grade in high school of Shanghai.To further supplement the non-written information and ensure the authenticity and reliability of test data,according to test results,this research conduct interviews with four types of students with high,medium and low levels of using Venn diagrams to solve mathematical problems and those who did not use Venn diagrams to assist in problem solving to explore the real situation of students’ visualization,identification and use of Venn diagrams.The results show that students can present Venn diagrams well.More than 80% of students can use Venn diagrams visualize set expressions correctly and orderly.Error types include incorrect identification of operation types,confusion of set operation,and incorrect execution of operation order.Students can identify Venn diagrams well.More than 60% of the students can identify Venn diagrams and write correct set expressions.Error types include incorrect recognition of operation symbols and confusion operation types.More than 50% of the students used Venn diagrams to reason set relations,and more than 80% of the students used Venn diagrams to solve practical set problems.Students’ presentation and recognition level of Venn diagrams is significantly correlated with their performance in solving set problems.