A Study On The Process Object Of Mathematics And Its Presentation In The Textbooks And Teaching In The Primary School

The Mathematics Curriculum Standards on Compulsory Education(2011 edition)stipulates that “The object of mathematics curriculum includes both process and resultant objects”,and proposed three behavioral verbs sketching process objects:experience(feel,try),immerse(taste),and explore.Under the background of the development of the curriculum objects from “knowledge-based” to “ability-oriented”and further to “accomplishment-oriented”,the adjustment and renewal of mathematics curriculum and teaching have became a new challenge in the deepening stage of curriculum reform.Until now,although resultant object has already been well presented and implemented during the mathematics curriculum and the corresponding teaching,it is pivotal to conduct an in-depth research of process object in terms of its application and realization in mathematical curriculum and teaching.This study focused on the process object embedded in the subject of mathematics in primary school.And accordingly,the specific theme of the current study is: A Study on the Process Object of Mathematics and Its Presentation in Textbooks and Teaching.Literature analysis,expert consultation,content analysis and video analysis were carried out to study the process object of primary mathematics from four aspects:connotation interpretation,curriculum standards presentation,textbook presentation and teaching presentation.First,literature analysis was done to define basic concepts and relevant connotations of process object of mathematics curriculum.Second,the same approach was utilized to analyze the presentation of the process objects in the Mathematics Curriculum Standards on Compulsory Education(2011 edition),and to tap into the basic requirements within process objects.Third,expert consultation was used to negotiate and confirm “the Analysis Framework for Presentation of Process Objects in the Primary Mathematics Textbook(Official Edition)”,and content analysis was used to design customized analysis tools to delineate the process objects in 12 primary mathematics textbooks that published by Beijing Normal University Press,and to learn the present situation about the presentation of process objects in primary mathematics textbooks.Lastly,the same approach was utilized to gain “the Analysis Framework for Presentation of Process Objects in the Primary Mathematics Teaching(Official Edition)”,and to analyze the process objects in 34 teaching videos totaling 1,360 hours of school D,J,and Z,and to retrieve the present situation about the presentation of process objects during primary mathematics teaching.Direct conclusions of the study are as follows:1.In Mathematics Curriculum Standards on Compulsory Education(2011editions),74 times of “process objects” presentation,with the hierarchical distribution that in the state of “overall decline,partial decentralization”.Specifically speaking,in general,the numbers of “experience”,“immersion”,and “exploration” are decreasing step by step,but in the curriculum object and curriculum content,the presentation of“experience”,“immersion”,and “exploration” has different emphases.2.In the primary mathematics textbook that published by Beijing Normal University Press,the implementation of process objects stay at the level of “sensory perception”(accounting for 80.9% of the total),while less attention is paid to“experience”,“immersion”,and “exploration”(among which,the attention on“exploration” stood the most,accounting for 12.0%).The distribution of the process objects in the grade and content is consistent with the overall distribution.3.In the practical teaching activities,the implementation of process objects was polarized between “not implemented at all” or “implemented excessively on‘exploration’”.This differentiation is more distinct in different types of courses(i.e.,regular or public courses),different content areas(i.e.,number and algebra,and graphics and geometry),and different grades(i.e.,third and fourth,fifth and sixth grades).4.In the primary mathematics textbook that published by Beijing Normal University Press,to a great degree,the requirements of the process objects(54.67%)are stricter than those stipulated by the curriculum standards,and some of the requirements(38.67%)are consistent with those in the curriculum standards.Especially in Statistics and Probability Field,and Synthesis and Practice Field,more consistencies of the process objects presentation could be found.5.In the practical teaching activities,the requirements of the process objects are largely consistent with the stipulation of the curriculum standards(25 classes),and to a large extent,also consistent with the requirements of the mathematic textbooks(22classes).In addition,the case in which “the presentation rate of process objects is higher than that in the curriculum standards or textbooks” also exist,but more in public courses,especially in Number and Algebra Field.Other relevant conclusions are:1.Within the perspective of accomplishment object,one of the important missions of current and future curriculum reform lies in the reconstruction of curriculum and teaching with process objects.Mathematics curriculum should be reconstructed based on the “result-based,process-oriented” principle,which is a feasible way to face the implementation of accomplishment rationally and efficiently.2.The mathematics textbooks of primary school still need to be developed and perfected from the perspective of process object,which should be put on the priority list.The process-oriented textbooks are the ones which could help realize the curriculum objects of knowledge,skills,process,methods,emotions,attitudes and values and even the effective implementation of accomplishment object.3.Two guidelines ought to be adhered to in textbook presentation of process objects,that is,to give full play to the strengthening value of process to result objects and to the formation of core mathematical literacy;also,two targets must be hit,that is,to consolidate mathematical foundation and to accumulate mathematics experience;moreover,three basic principles should be followed,namely,the principle of“standardization”,of “orderliness” and of “the ease of teaching”.The textbook presentation rate of process objects shall be higher than the curriculum standards,or at least,be consistent with it.Meanwhile,the textbook presentation of process objects must ensure the appropriateness of contents,base itself upon its own prescriptive nature,and balance between the content attributes of mathematics;also,the presentation of process objects should conform to the stages of development,and embody students’ sequential development stages and the sequence of learning.4.Textbooks,teachers,together with teaching environment are factors influencing process object implementation,and are also keys to strengthening its implementation effects.Hence,joint efforts must be made to enhance the teaching effect of process objects.Firstly,current textbooks need to be further improved and designed as to highlight process object.Additionally,teachers’ professionalism and quality must be sharpened to internalize both teaching theories and practices of process object.Thirdly,the school’s basic environment of practice need to be upgraded,so that curriculums,teaching,classrooms,the school,the principal,and even parents are able to take process object seriously.Lastly,continuous efforts could be made to optimize social environment for education to achieve the leading role of the development and spiritual culture.