Research On Cognitive Status Of High School Students’ Concept Of Sequence Limit

Sequence is a core concept in the high school mathematics, and sequence limit is an extension based on sequence. Xiaoming Ruan (2012) carried out a research and showed that, sequence limit was one of ten difficult concepts in high school mathematics; furthermore, limit thought is one of basic mathematics thoughts in advanced mathematics with a wide range of applications.In this paper, the author concentrates on sequence limit, and focuses on the following 3 aspects:what the students’understanding of sequence limit and their cognitive level are before, in and after classroom teaching; what the students’specific cognitive barriers and causes are in the process of teaching the concept of sequence limit; what kinds of teaching strategies teachers should take to promote students a correct concept understanding so as to achieve a good teaching effect.The author has selected 5 Shanghai high school with totally 197 high students. These participants have received following three procedures:questionnaire, paper and pencil test, and interview. In addition, the author has conducted questionnaire survey, classroom video-recording and interview towards 6 frontline teachers.Finally, the research conclusions are as below:Firstly, before classroom teaching students’images of sequence limit of images are divided into’"non-mathematics understanding" and "mathematical understanding" "mathematical understanding" are further divided into "the end", "the extreme value" "bound", "asymptotic" and "limit", "non-mathematics understanding" and "the extreme value" account for the majority, but the correct image that "limit" occupy minimal. The average correct rate of students’understanding of conceptual difficulties is:"infinitely approaching"> "uniqueness"> "accessibility"> "infinite series"> "certainty"Secondly, in classroom teaching students’conceptual representations are divided into the correct representations and the error representations. The correct representations include literal representation, symbolic representation and image representation, in which literal representation accounts for the vast majority followed by symbolic representation and image representation. The error representations includes error image (i.e., "the extreme value" "bound" and "asymptotic") and definition misunderstanding. The average correct rate of students’understanding of conceptual difficulties is:"uniqueness"> "accessibility"’> "certainty"> "infinitely approaching". The average correct rate of students’understanding of different sequences types is:"oscillating divergent sequence"> "constant sequence’"> "unbounded sequence"> "monotone bounded sequence"> "oscillating convergent sequence"Thirdly, after classroom teaching students’understanding of different sequences types is: "oscillating divergent sequence"> "unbounded sequence"> "monotone bounded sequence"> "constant sequence"> "oscillating convergent sequence". According to the SOLO taxonomy theory and the scoring criteria, students’ level of conceptual understanding only reaches the multistructural level, hasn’t reached the relational level even the extended abstract level yet.Fourthly, in the process of classroom teaching students’ cognitive barriers are following four aspects:mathematics intuitive, infinitely approaching, accessibility, certainty.Fifthly, according to the students’cognitive barriers, in classroom teaching teachers should:1. explicitly reduce even eliminate the interference of daily life and everyday language towards the classroom conceptual teaching; 2. through counter-example method or geometric intuitive method breakthrough misconception; 3. provide students a comprehensive and diverse types of sequences in order to promote students forming correct concept; 4. create intuitive teaching conditions or computer intelligent simulation teaching conditions as far as possible.At last, the author combines self-thinking and teacher interviews, and gives 3 points of enlightenment and 3 points of perspective.