摘要
高考改革是教育体制改革中的重点领域和关键环节,但同时会带来学生自主选择与资源配置之间的供需矛盾.本文基于模糊软集和多属性决策理论,建立学科组合对应的选择人数的预测模型.在学生完全自主选择的情况下,根据实际情况将排课问题简化为"类背包"问题,进而分析学校现有资源的缺口.分析结果表明,教室资源与教师资源存在缺口,其中教师资源缺口较大.为此,从两个角度提出资源配置优化建议:从学校的角度,可以依据选课组合的文理特性、专业覆盖率和专业亲和度3个指标,设计"菜单式"的选课方案;从政府的角度,可以提高教师的薪资和福利,并应及时招聘新的教师资源.通过两个案例应用,验证了该模型的可行性、可靠性和可推广性.
The reform of college entrance examination plays a critical role in the reform of education system,which also brings contradiction between students′independent choice and the allocation of educational resources.Thus,this paper firstly established a model to predict the number of students choosing the subjects combination based on the fuzzy soft set and multi-attribute decision theory.Supposing that there is no lack of educational resources,the courses scheduling problem was formalized as a Knapsack-like problem so as to analyze the shortage of teaching resources.The analysis results show that the classrooms and teachers are insufficient,and the latter is in severe shortage.To this end,suggestions for resource allocation optimization are proposed from two perspectives.On one hand,the school can design special courses selection plan based on three indicators--the characteristics,the professional coverage and the professional affinity of the subjects′combination.On the other hand,the government is suggested to improve the teachers′salaries and benefits and to publish recruitment for teachers in time.Finally,two case studies are investigated to verify the feasibility,reliability and generalization of the model.
作者
姜柳
陈培智
沈霄菡
高旻昱
朱婷
臧金惠
尚建辉
JIANG Liu;CHEN Peizhi;SHEN Xiaohan;GAO Minyu;ZHU Ting;ZANG Jinhui;SHANG Jianhui(School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;School of Medicine,Shanghai Jiao Tong University,Shanghai 200025,China;School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China)
出处
《数学建模及其应用》
2020年第2期53-64,共12页
Mathematical Modeling and Its Applications
基金
国家自然科学基金(11971311)。
关键词
高考改革
多属性群决策
模糊软集
“类背包”问题
college entrance examination reform
multi-attribute decision
fuzzy soft set
Knapsack-like problem
作者简介
姜柳(1995-),女,2017级博士研究生,研究方向是土木工程信息化;陈培智(1995-),女,2018级硕士研究生,研究方向是土木工程信息化;沈霄菡(1995-),女,2017级硕士研究生,研究方向是混凝土细微观尺度耐久性;高旻昱(1996-),女,2018级硕士研究生,研究方向是基于深度学习的隧道盾构施工土压预测与调控;朱婷(1996-),女,2018级硕士研究生,研究方向是内填混凝土钢桥墩的超低周疲劳性能;臧金惠(1996-),女,2016级本科生,专业是临床医学;通讯作者:尚建辉(1985-),男,讲师,主要研究方向是数学建模和网络科学,E-mail:jhshang@sjtu.edu.cn。
