The Leaning Progression For Distributive Law In Primary Mathematics

In recent years,learning progression has become a popular topic in western education circles.The term "learning progression" originated from the field of science education research in the United States.Two reports submitted by the NRC in 2005 and 2007 proposed that learning progression is an important channel of dialogue among theoretical researchers,test writers,curriculum makers and educational decision makers as well as the most potential tool to link curriculum standards,teaching and evaluation and promote consistency.However,the related research in China is still in its infancy.This study takes multiplication and distribution law,an important operation law in primary school,as the core concept and adopts a top-down approach to construct the hierarchy of learning progression.Based on the APOS theory proposed by Ed Dubinsky et al.,a hypothetical learning progression model of multiplication and distributive law is constructed by studying the curriculum standards of primary school mathematics,textbooks published in Shanghai and related literatures of multiplication and distributive law teaching.Based on the characteristics of each advanced level,the semi-open interview questionnaire was designed from two aspects,which are ‘Knowledge of structures that support the distributive property of multiplication' and ‘Flexible use of concepts'.Through the discussion of the single task and the analysis of the summary,this paper studies the actual progression of students in the process of learning the distributive property of multiplication,and tests and adjusts the assumption of progression of the distributive property of multiplication.Finally,a learning progression model of the distributive property is constructed to describe the learning stage,conceptual understanding level and specific academic performance of students about the learning content of the distributive property.Through literature review,interview implementation and result analysis,the following three conclusions can be drawn from this study.Firstly,the actual learning progression of students is basically consistent with the textbook based assumption.Secondly,the learning progression of the distributive property includes 5 learning stages and 6 learning stages.Finally,structure identification and concept application interact with each other in the development of multiplicative distributive property.The study puts forward some Suggestions on classroom teaching,academic evaluation and teachers' quality.And it provides a reference for the follow-up study of learning progression.