A Study On The Difference Of Mathematical Representation Translation Ability Of Students With Different Cognitive Styles And Their Teaching Strategies

The ability to translate mathematical representation is an essential ability to learn mathematics.The ability to translate mathematical representations is the ability to write depictive representations from descriptive representations of mathematical knowledge.Students with different cognitive styles have different representational tendencies.Is there any difference in the ability to translate mathematical representations among students with different cognitive styles?The eligible students were selected from 447 high school students and then tested on their ability to translate mathematical representations.This study adopts the method of combining quantitative and qualitative research.Based on the measurement method,combined with the teacher-student interview and text analysis,the following research results are obtained:(1)The ability of mathematical representation translation of imagery cognitive styles students is significantly higher than that of verbal cognitive styles students.The imagery cognitive styles students' mathematical representation translation ability mainly focuses on the specific coding level and the essential coding level.Verbal cognitive styles students mainly have thinking obstacles in the process of internalization and activation,while imagery cognitive styles students have thinking obstacles in the process of activation and externalization.(2)The characteristics of verbal cognitive styles students' ability to translate mathematical representations include: recognition barrier,confusion barrier and automatic feature.Recognition disorder refers to students' inability to correctly identify descriptive representations.Confusing disorder refers to students' confusion between two kinds of depictive representations.Automated features mean that students can write depictive representations from descriptive representations fluently.(3)The characteristics of imagery cognitive styles students' ability to translate mathematical representations include: absence disorder and flexibility characteristics.Absence disorder refers to the absence of the corresponding language code of the depictive representations.Flexibility is students use the third representation as a transition to write linguistic representations from number line representations.According to the characteristics of the ability to translate mathematical representations of students with different cognitive styles,the following corresponding teaching strategies are proposed in this study:(1)Teaching strategies to improve verbal cognitive styles students' ability to translate mathematical representations: pay attention to the detail of image teaching;pay attention to the rigor of teaching language;enhance descriptive representation training.(2)Teaching strategies to improve imagery cognitive styles students' ability to translate mathematical representations: pay attention to the conciseness of teaching language;enhance the training of depictive representation.