A Study On The Current Status Of Mathematical Flexibility Among Fourth-grade Students In Jiaqiu Count

With the development of the information society,the cultivation of creative talents with individuality has become the goal of curriculum reform in countries around the world.Flexibility is not only an important quality for creative people,but also an important tool for implementing the core qualities of mathematics.For students,flexibility helps them to consciously choose the most effective way to solve a problem in a given situation.Focusing on students’ ability to flexibly call upon strategies to solve problems when they encounter them is important for the development of innovative talent.In the new curriculum,the multiplication law,which is one of the five laws of operations,is often not taught as effectively as it should be,due to its difficulty,teachers’ unidirectional teaching methods and students’ low level of understanding.It has been found that after learning the multiplicative law for the first time,many students still use the arithmetic methods they have learnt before to solve problems,and often do not think of the flexibility of calling upon the multiplicative law to solve problems.Therefore,this study uses the multiplicative law as a vehicle to investigate students’ level of mathematical flexibility in using the multiplicative law to solve problems in different contexts.This study takes 238 fourth-grade students in Gashi County,Xinjiang as the target population.Based on the combing and analysis of domestic and international studies related to mathematical flexibility,the first stage of the three-stage flexibility assessment framework established by Liu Rude et al.is used as the basis for constructing this paper’s mathematical flexibility assessment framework.This paper examines students’ mathematical flexibility through three different problem contexts:pure mathematical contexts,practical problem contexts,and visual problem contexts.Firstly,students’ solutions in these three contexts are categorised into flexible solutions and other solutions,and these two solutions are further subdivided according to students’ specific performance.Secondly,students’mathematical flexibility was categorised into three levels:high,medium and low,and their performance was coded and statistically analysed,and finally,the reasons for this were analysed in relation to the typical student responses.The main conclusions of this paper are as follows:(1)students’ levels of mathematical flexibility are highest in pure mathematical contexts;(2)students’levels of mathematical flexibility are lowest in visual problem contexts;(3)information conversion errors are the main cause of students’ levels of mathematical flexibility;and(4)there is a correlation between students’ flexibility levels in different contexts.To improve students’ level of mathematical flexibility,this article makes the following recommendations for teachers:(1)create problem situations carefully to facilitate the integration of knowledge;(2)pay attention to the creation of visual problem situations to reduce students’ thinking load;(3)improve students’mathematical reading skills to avoid information conversion errors;and(4)cultivate good problem-solving habits to maximise the value of problems.