Investigation And Research On The Concept Teaching Of Quadratic Radical Form In The Second Grade Based On APOS

Mathematical concepts are the basis for solving mathematical problems,but in our traditional teaching process,most teachers ignore the teaching process of mathematical concepts.The APOS theory proposed by American mathematics educator Dubinsky is a mathematical concept teaching theory with constructivism as the core idea.It emphasizes the formation process of concepts and believes that students understand mathematical concepts through "operations","processes" and "objects"."And "Schema" these stages.The four-stage model of APOS theory is a theoretical guide for teachers to carry out conceptual teaching,and it also provides a concrete template for conceptual teaching design.The quadratic radical is an important algebraic concept in junior middle school.Many students find it very difficult to learn the concept of the quadratic radical.This article is guided by the APOS theory.The first part uses literature research to deeply understand the research status of APOS theory and quadratic radicals,and theoretically analyzes the application of APOS theory to quadratic radical teaching.The second part uses the questionnaire survey method to carry out the quadratic radical comprehension level test and the investigation of the learning emotion attitude of the students in the second grade of a junior middle school in Changsha,and investigates the teaching status of the quadratic radical by the first-line teachers through teacher interviews.In the third part,theauthor conducts a quadratic radical teaching design based on the survey results and APOS theory,and gives teaching suggestions.After investigation and research,it is found that: First,The second grade students' understanding of the concept of quadratic radicals can reach the operational and process stages,and a few students can reach the object and schematic stages;Second,there is no obvious difference between male and female students in the concept of quadratic radicals.There are significant differences in the understanding of the concept of quadratic radicals among students of different levels.Students with a solid knowledge base can better understand and apply the concept of quadratic radicals;Third,the second grade students are not very active in learning the concept of quadratic radicals,and there are problems in their learning habits and methods.At the same time,a few teaching suggestions are drawn: Attaching importance to the teaching of quadratic radical concepts;Improving teachers' own teaching theory literacy;Paying attention to the process of concept formation and cultivate students' independent exploration ability;Attaching importance to the connections and differences between concepts to help improve the schema structure of students;Cultivating students' good study habits and paying attention to gender differences between male and female students.