信息技术支持真实情景中的数学建模教学——来自德国的经验

Information Technology Supporting the Teaching of Mathematical Modelling: Experiences from Germany

数学建模近年来成为各国课程的重要发展内容。德国数学城市地图项目利用信息技术支持教师在真实情景中的数学建模教学,同时在任务设计和教学方法等多个方面给予教师系统的支持。本研究基于数学建模的过程定义和一系列关于宏观和微观建模能力研究,结合当前我国中学数学建模教学的诸多挑战,对数学城市地图项目的内容进行深入分析,总结出若干先进经验。这些经验包括:通过移动应用程序中的导航、分级提示和答案验证系统,让学生自主完成户外建模任务,培养学生提炼现实模型和数学化的建模子能力,减轻教师在户外引领和实地教学干预中的工作量;开发门户网站简化户外建模任务的创建流程;以通用型任务"授之以渔",为教师的任务设计提供指引,注重任务内容的开放性、在场性和任务提示的启发性、渐进性;在网站中引入"公开""复制""粘贴"等功能,促进资源交流与共建;在教师培训中设置"教师/学生"双重视角和多轮"设计-反馈-修订"循环,推动学员多方位的实践、交流与反思。项目同时也存在一些不足之处,如任务主题分布不均、教师培训过于注重教师的主体性、难以推动学生对数学模型的反思等。我国在开展数学建模教学的创新改革时,要注意吸取目的先进经验,并对其不足之处加以改进。

Mathematical modeling has recently become an important object of curricular development in various countries.The MathCityMap project in Germany takes advantage of information technology to support the teaching of mathematical modelling in realistic situations,and meanwhile provide teachers systematic support in various aspects such as task design and pedagogical strategies.Based on the procedural definition of mathematical modelling and researches on the related competencies,and combining the current challenges faced by Chinese middle schools in the teaching of mathematical modelling,this paper analyzes in depth the content of the MathCityMap project,and summarizes some advanced experiences of it:(1)allowing students to accomplish the outdoor modelling tasks autonomously with the mobile applications equipped with the navigation,stepped hints and the answer validating system,developing students’competencies of constructing real models and of mathematising and alleviating teacher’s workload in outdoor leading and on-scene pedagogical intervention;(2)inventing a portal website to simplifying the procedures of constructing outdoor mathematical modelling tasks for teachers;(3)"teaching to fish"by providing generic tasks which can only be solved on the scene and allow multiple solutions,with the hints being heuristic and progressive,as a guidance for teachers’task design;(4)introducing the options of"publish""copy""paste"in the website to promote exchange and co-design of resources;(5)setting the dual perspectives of student-teacher and multiple cycles of designing–feedback–revising in teacher training,motivating teachers to practice,exchange and reflect in various aspects.The project also has some shortcomings,such as uneven distribution of task themes,excessive emphasis on teacher’s subjectivity in teacher training,and difficulty in promoting students’reflection on mathematical models.When implementing innovation reforms of mathematical modeling teaching,we should carefully learn from advanced experience of the project and meanwhile overcome its shortcomings.