| Chinese General High School Mathematics Curriculum Standards(2017 Edition Revised2020)require that the characteristics of students’ thinking activities and problems in teaching can only be found by observing students’ learning behaviors and thinking processes.Researches on errors of induction formulas not only help students to master the overall content of trigonometric functions,but also help teachers to find the differences in the causes of problem solving errors of different students,as well as the existing problems in teaching related to induction formulas,which has positive significance for the practice improvement of teaching and learning.Based on a large amount of relevant literature,this paper investigates the problem-solving errors in induction formulas.Firstly,by reading the related literature on errors in problem-solving,the current related researches were summarized in three aspects: error types,error causes,error resource management and teaching of error correction.Secondly,the students’ errors in induction formulas problem-solving were collected using text analysis and test,and the errors were classified and counted according to Newman’s Error Analysis.Thirdly,the oral report method combined with in-class observation,interviews and questionnaires survey were used to analyze the error causes from a psychological perspective based on the current situation of daily teaching of induction formulas and the current situation on the daily teaching of errors in problem-solving.Finally,corresponding teaching suggestions were proposed for the main problem-solving errors of induction formulas for reference of school instruction.The results of the survey show that the main problem-solving error of induction formulas among senior one students is Process skills error,followed by Encoding error and Comprehension error.In different types of problems,the proportion of Comprehension error is around 12%.The most significant errors were found in derivation of induction formulas and then the incorrect placement of parentheses,missing parentheses or unnecessary addition of parentheses.The main causes of students’ errors are:(1)Lack of intuitive imagination ability;(2)Improper use of pithy formula;(3)Improper problem-solving strategies;(4)Poor learning attitude and motivation;(5)Lack of metacognitive ability to solve problems;(6)Inappropriate learning methods.Based on the above survey results and analysis,six suggestions are given from the perspective of teaching and learning:(1)Pay attention to the connection of knowledge points;(2)Teaching design highlights the derivation process of induction formulas;(3)Give instruction on the related problem-solving strategies of induction formulas;(4)Set up the mastery goal in the learning of mathematical problem-solving;(5)Focus on self-monitoring training on problem-solving metacognition;(6)Fully explore and utilize problem solving resources. |
