Research On Learning The Concept Of Mathematical Induction Among The High School Students

Mathematical induction is an important proof method in senior high school mathematics, and it is a tool for students to grasp from the finite to the infinite.Teacher Xiaoming Ruan led several Shanghai excellent first-line teachers to do an investigation about "ten difficult concepts in high school mathematics", among whose results is mathematical induction method. Based on the above investigation, this study researched on 196 students from six classes and six teachers, all of whom are in a key middle school in Shanghai.This study mainly inspects the students’mastery of the structural characteristics of mathematics induction method as well as the mistakes and causes when they understand and apply mathematics induction method through ways of paper and pencil test, questionnaire, and interview. Finally this study divides the level of students’ application of mathematical induction method.This study shows that:(1) half of the students know the application scope of mathematical induction, namely that mathematical induction is used in the proof relating to the set of natural numbers or a subset of relevant propositions. (2) the mistakes made by students when they understand the mathematical induction are the following several kinds:not understanding the relationship between the two steps in mathematical induction; not understanding the structural characteristics of mathematical induction method; unable to make assumptions correctly; considering that the first step of mathematical induction step to verify several; when they need to discuss the topic, students are also in accordance with the general practice without discussion; learning in dealing with practical topics relevant to life are also not very good. (3) based on the application of Freudenthal’s level of division theory and APOS theory, the students’ application levels of mathematical induction are divided into the following four levels:summary Level (level 1) and recursive level (Level 2), logic level (Level 3), integrated application level (Level 4). In total sample,57 students (accounting for 29.1% of the total sample) are in four levels (integrated application level), slightly higher than the proportion of the other three levels.40 students are in level 1, the ratio of students in level 2 and level 3 are 26.0% and 24.5%.