Investigation And Analysis On The Level Of Mathematical Understanding Of Eleventh Grade Students

Mathematical understanding plays an important role in high school mathematics learning,plane vector is a bridge to communicate algebra,geometry and trigonometric functions.But at present there is no special tool to measure the level of mathematical understanding of plane vector.This study divided the understanding level of plane vector into four levels(memory,algorithm,interpretation and exploration)by referring to the classification framework of mathematical understanding level of Gu Ling Yuan team.On this basis,a test tool was developed and the level of mathematics comprehension of eleventh grade students was evaluated.From three aspects of algebraic part,geometric part and comprehensive application of plane vectors,this study compiled test questions according to the classification framework of mathematical understanding level and developed scoring criteria.The quality of test questions was analyzed by using the Rasch model to ensure the reliability and validity of the research.It mainly answered the following two research questions :(1)What levels can mathematical understanding be divided into? What is the level of mathematical understanding of plane vector of eleventh grade students?(2)What problems do students have in understanding vector problems,and why?According to the research problems,the students of a Shanghai high school were tested,and the following conclusions were drawn :(1)Mathematical understanding level of plane vectors can be divided into four levels;(2)Most of the eleventh grade students can achieve the level of memory and algorithm understanding for plane vector;(3)The eleventh grade students have initially reached the level of explanatory understanding for plane vector;(4)The level of exploratory understanding of the eleventh grade students needs to be improved for plane vector;(5)There are certain differences between male and female in explanatory comprehension level,but there is no obvious trend that one part is superior to the other part.Therefore,gender cannot be used to judge students' mathematical comprehension level.Based on the above conclusions and the problems in students' understanding of plane vector mathematics found in the research process,the following teaching suggestions were put forward: First,in the teaching process,we should pay attention to the explanation of basic concepts and corresponding exercises;Second,let the students learn mathematical knowledge with holistic thinking and pay attention to the correlation between mathematical knowledge;Third,cultivate students' creativity and dialectical thinking through teaching and regular exercises;Fourth,design the teaching design of mathematics knowledge module that is beneficial to students' understanding;Fifth,pay attention to the connection between plane vectors and other knowledge,and strengthen practical exercises.