Mathematical Manipulatives For Children:Current Situation And Reflections On Their Application

With the deepening of China’s preschool curriculum reform,the goal of mathematics education has shifted from knowledge acquisition to literacy improvement.To achieve this new goal,promoting the renewal of mathematics education concepts and the reform of mathematics education has become a important proposition of concern for many researchers.As an important object to stimulate children’s construction of mathematical thinking and develop mathematical abilities,the improvement and enhancement of mathematical materials is essential to solving this problem.The researchers’ observation found that the understanding and application of mathematical materials tend to be utilitarian,directing learning towards specific mathematical knowledge.This study argues that one of the reasons for this issue is the way in which teachers use mathematical materials in kindergartens.The formation of concepts is a historical and cultural process,and some mathematical materials’ concept representations are rooted in historical concepts,which unconsciously influence the users’ understanding of mathematical materials and subsequently affect their application.Among them,the concept of "mathematical manipulatives" is a representative way of expression that deserves further exploration in this study.Therefore,this study takes the concept of "mathematical manipulatives" as the starting point and advances layer by layer.First,through interviews and surveys of teachers’ understanding of the concept of "mathematical manipulatives" and their current applications,the problem is clarified.Through analysis,this study found that there is a split between the knowledge orientation and the experiential orientation in the value orientation of "mathematical manipulatives" in current kindergarten practices.Mathematical manipulatives can be divided into three categories: teaching aids,learning tools,and toys,and their connotations have five different expressions.The differentiation and oscillation in the recognition and application of mathematical manipulatives in early childhood mathematics education practices are rooted in a particular historical process.Therefore,this study aims to clarify the problem and trace the historical origins of the concept of "mathematical manipulatives" through historical review,presenting a knowledge-oriented perspective.Investigations of relevant educational policies,ideas,and practices from the end of the Qing Dynasty to the end of the last century show the process of the formation of the concept of "mathematical manipulatives".It was found that China has a traditional functional cognition that focuses heavily on "calculations" in mathematics.Additionally,influenced by the Soviet Union’s theoretical and practical knowledge system in the 1950 s and the "traditional three centers" education ideology,China’s education system formed a knowledge orientation characteristic that has continued to this day.Finally,by integrating the causal performances of the first two parts,reflecting on the connotations of "mathematical manipulatives",and breaking the current educational practice’s cognitive bias towards mathematical materials caused by the existence of the concept of "mathematical manipulatives," this study proposes using "mathematical toys" or "mathematical game materials" to replace the original way of expression in a game-based learning context to reshape the connotation and promote changes in practice.