A Study On The Analysis Of Elementary School Mathematics Teaching Materials For Multiplying And Dividing Integers In The North Teacher’s Edition

Multiplicative thinking is a higher level of thinking based on additive thinking,and consists of three core elements: "many and one correspondence","nested inclusion",and "unit coordination".The core elements of multiplicative thinking are Research has shown that multiplicative thinking is important for students’ mathematical learning and ability development.Multiplicative thinking is necessary for students to understand functional relationships in contexts,and its associated cognitive structures are the basis for understanding fractions,ratios,rates,percentages,proportional reasoning,and algebraic reasoning.However,the development of students’ multiplicative thinking has not received sufficient attention in the current field of mathematics education in China,and as a result,students consistently show varying degrees of error in problem solving involving multiplicative thinking.Therefore,it is important to pay more attention to the development of students’ multiplicative thinking and to provide adequate learning opportunities for the acquisition and development of multiplicative thinking.Teaching materials are a powerful tool for creating learning opportunities,and they are an important factor in the acquisition and development of multiplicative thinking by influencing teachers’ choices of content and strategies and by influencing students’ access to learning opportunities.Therefore,in order to provide better opportunities for the development of multiplicative thinking,it is necessary to conduct a systematic analysis of teaching materials through the lens of learning opportunities and the selection of appropriate content.In this context,this study takes the North Teacher’s edition of elementary school mathematics textbook,which has a wide coverage and high quality,as the target,and selects "multiplying and dividing integers",which is the most relevant and basic content for the development of students’ multiplication thinking,as the specific content for analysis.The research question was: What are the opportunities for learning multiplication and division of integers provided by the "multiplication and division of integers" content of the North Teacher’s edition of elementary school mathematics textbooks? To address this question,this study firstly reviewed the relevant studies from the perspectives of"multiplication thinking","learning opportunities",and "multiplication and division textbook development".Based on the existing studies,this study constructs a framework for analyzing teaching materials that point to multiplication thinking,divides the selected contents into five learning modules,and uses them as units of analysis in terms of"components," "depth and breadth," and "objects.The content is divided into five learning modules,and the unit of analysis is based on three aspects: "components","depth and breadth","objects","cognitive requirements","types of situations","intuitive models" and other six dimensions.The qualitative and quantitative analyses of the learning tasks related to the content of "multiplying and dividing integers" were conducted to investigate the opportunities for students to learn multiplication thinking in this part of the textbook.Finally,based on the results of the analysis of the materials,the study provides some insights into the opportunities for multiplication and division provided by the"multiplication and division of integers" content of the North Teacher’s edition,and suggests strategies for optimizing the materials in view of the current shortcomings.The results of the study show that,first of all,in terms of attention to the components of multiplicative thinking,each learning module of the North Teacher’s edition of the textbook on multiplication and division of integers focuses on the elements of multiplicative thinking,which requires a high level of multiplicative thinking but does not present enough multiplicative thinking,and there is an imbalance that limits students’ understanding of "many-to-one" and "nested inclusion"."nested inclusion" and "unit coordination".Second,in terms of the depth of multiplicative thinking opportunities(i.e.,cognitive requirements):the North Teacher’s edition of the multiplication and division of integers textbook progressively arranges four different cognitively demanding learning tasks to provoke students to think at different levels.The low cognitive requirement tasks are more frequent than the high cognitive requirement tasks,which is in line with the emphasis on basic knowledge and skills in our mathematics curriculum,but the low number of "doing math" tasks is not conducive to students’ in-depth learning to develop higher-order multiplication thinking.Again,in terms of the breadth of learning opportunities(i.e.,types of contexts)for multiplication and division,the textbook provides learning opportunities for students to develop multiplication thinking through both pure mathematical contexts and realistic contexts,and the models of equal groups,rectangles,multiples,and ratios in realistic contexts are regularly distributed in each learning module,providing students with appropriate opportunities to understand multiplication relationships and develop multiplication thinking.However,the lack of paired models narrows the breadth of multiplicative thinking opportunities provided by the materials to a certain extent and limits the development of students’ multiplicative thinking.Finally,in terms of the manipulative objects(i.e.,visual models)of multiplication and division,the North Teacher’s version of the textbook has seven visual models to present the components of multiplication and division,the meaning of multiplication and division,and arithmetic,providing opportunities for students to develop multiplication thinking.The number of visual models decreases as learning progresses,and the transition from concrete to abstract representations provides opportunities for transferring and developing higher-level thinking.Based on the above results,in order to improve the quality of multiplicative thinking opportunities provided by the teaching materials,this study suggests that the teaching materials should be written with more attention to the elements of multiplicative thinking;set reasonable cognitive requirements to stimulate deep learning;value and bring into play the "prototypical" value of the equal group models;and make full use of the intuitive models to make multiplicative thinking gradually move from concrete to The use of visual models can make the transition from concrete to mathematical thinking.