湘教版与人教A版高中数学选择性必修教科书数学建模内容比较研究

A Comparative Study on the Contents of MathematicalModeling in HEP and PEP High School MathematicsSelective Compulsory Textbooks

采用内容分析法和比较法,对湘教版和人教A版普通高中数学选择性必修教科书数学建模内容从内容分布与呈现、情境—问题、建模过程、信息技术使用四个方面进行比较分析。研究发现:两版教科书都以专题形式呈现数学建模内容,问题背景比较复杂、问题类型均为开放式,建模过程注重问题分析和模型建立、关注模型检验,信息技术主要应用在模型建立与求解和模型检验环节。湘教版4个建模专题与三大主线相融合,突出数学建模过程的一般性和案例的示范性,问题情境较为丰富,问题表述形式多样,信息技术软件选择具有开放性;人教A版1个建模专题与统计相联系,突出统计建模案例的示范性和对建模选题做题的指引性,问题情境与科学问题相联系,信息技术软件操作具有示范性。基于此,提出教科书使用建议:一是用好教科书中数学建模专题,发挥示范引领作用;二是组织好课题研究活动,发挥师生能动性。

This paper adopts content analysis and comparative analysis methods to study the contents of mathematical modeling in high school mathematics selective compulsory textbooks published by HEP(Hunan Education Press)and PEP(People's Education Press).The analysis was made from four aspects:the distribution and presentation of contents,situation-problem,modeling process and the use of information technology.The results show that both textbooks the matically present the contents of mathematical modeling;the problem backgrounds are complex;the problems are open type problems;the modeling processes pay attention to problem analysis and model building,and model testing;information technology is mainly applied in model building,solution seeking and model testing.The four topics of modeling in HEP textbook are integrated in the three main lines,highlighting the generality of mathematical modeling process and demonstration of cases.The problem situation is rich;the expression forms of problems are diverse;and the choice of information technology software is open.The topics of modeling in PEP-A edition are related to statistics,highlighting the demonstration of statistical modeling case and the guidance for modeling topic selection;the problem situation is linked with scientific problems;information technology software operation is exemplary.Based on the analysis,some suggestions on the use of textbooks are put forward as follows:making good use of mathematical modeling in textbooks so that it plays a leading role,organizing research activities and giving play to the initiative of teachers and students.