张蕊,宋信息

• 1:首都经济贸易大学国际经济管理学院

摘要(Abstract)：

如何实现最优教学一直是教育政策制定者、教育管理者和学生家长关心和争论的话题，但在学术界还缺乏严格的理论分析。本文构建了一个可以在不同教学目标情况下分析两种常用分班教育(混合分班还是分层教学)优劣的模型。该模型在一个简易的框架下充分考虑了影响学生成绩的关键变量，包括老师教学能力、学生学习能力、学生努力程度，以及教育经济学实证文献中强调的同群效应。实证文献中发现的“单交叉”“烂苹果”“分层/分流”等同群效应机制可以在模型中进行灵活设定与分析。该模型可以解释不同分班教育的效果差异，为理解文献中不同的研究发现和为学校管理者选择最优的分班教育模式提供了一个理论分析框架，填补了研究分班教学模式的理论文献空白。

关键词(KeyWords)： 同群效应;混合分班;分层教学;效率与公平

Abstract:

Keywords:

基金项目(Foundation):

作者(Author): 张蕊,宋信息

DOI: 10.16513/j.cnki.cje.20220919.004

参考文献(References)：

• 陈昊，郑捷，钟笑寒.2015.基于竞赛模型的分层教学激励机制研究[J].经济学报，2(4):36-61.Chen H,Zheng J,Zhong X H.2015.Incentive mechanism of ability-based grouping:An economic analysis based on contest game[J].China Journal of Economics,2(4):36-61.(in Chinese)
• 崔静，冯玲.2017.同群效应研究述评与未来展望[J].商业经济研究，(10):101-103.Cui J,Feng L.2017.Peer effects:Survey and future prospect[J].Journal of Commercial Economics,(10):101-103.(in Chinese)
• 杜育红，袁玉芝.2016.教育中的同伴效应研究述评：概念、模型与方法[J].教育经济评论，1(3):77-91.Du Y H,Yuan Y Z.2016.The review of the research on peer effect in education:Concept,model and method[J].China Economics of Education Review,1(3):77-91.(in Chinese)
• 王春超，钟锦鹏.2018.同群效应与非认知能力——基于儿童的随机实地试验研究[J].经济研究，53(12):177-192.Wang C C,Zhong J P.2018.Peer effects and non-cognitive skills:A randomized field experiment based on children[J].Economic Research Journal,53(12):177-192.(in Chinese)
• 王春超，肖艾平.2019.班级内社会网络与学习成绩——一个随机排座的实验研究[J].经济学(季刊),18(3):1123-1152.Wang C C,Xiao A P.2019.Social networking and academic performance within classroom—An experimental study of random seating[J].China Economic Quarterly,18(3):1123-1152.(in Chinese)
• 王骏，彭顺绪，原莹.2017.重点高中、学校投入与学生学业成绩——基于J市普通高中的一个经验研究[J].世界经济文汇，(3):17-45.Wang J,Peng S X,Yuan Y.2017.Key high schools,school input and students' academic performance—An empirical analysis based on high schools in J city[J].World Economic Papers,(3):17-45.(in Chinese)
• 许双成，张立昌.2015.教育公平之殇——分层分班教学[J].西北民族大学学报(哲学社会科学版),(4):184-188.Xu S C,Zhang L C.2015.The destruction of education equality—On ability-based grouping[J].Journal of Northwest Minzu University (Philosophy and Social Science),(4):184-188.(in Chinese)
• 叶星，熊伟.2017.国内外同群效应研究综述[J].江苏高教，(4):83-88.Ye X,Xiong W.2017.A survey on peer effects research in China and abroad[J].Jiangsu Higher Education,(4):83-88.(in Chinese)
• 袁玉芝.2016.教育中的同伴效应分析——基于上海2012年PISA数据[J].上海教育科研，(3):30-34,25.Yuan Y Z.2016.Peer effects in education—An analysis based on 2012 PISA data in Shanghai[J].Shanghai Research on Education,(3):30-34,25.(in Chinese)
• 詹宏毅，陈超群.2017.初中生同伴行为与个体认知能力的结构方程分析[J].中国人民大学教育学刊，(4):166-177.Zhan H Y,Chen C Q.2017.The SEM analysis between middle school students' peer behaviors and individual cognitive ability[J].Renmin University of China Education Journal,(4):166-177.(in Chinese)
• 张学敏，谭俊英.2012.同群投入对初中生学习成绩的影响研究[J].教育与经济，(4):21-25.Zhang X M,Tan J Y.2012.Influence of peer inputs on middle school students' achievement[J].Education & Economy,(4):21-25.(in Chinese)
• 赵颖.2019.同群效应如何影响学生的认知能力[J].财贸经济，40(8):33-49.Zhao Y.2019.How peer effects affect students' cognitive abilities[J].Finance & Trade Economics,40(8):33-49.(in Chinese)
• 郑磊.2015.教育中的社区效应和同伴效应：方法、证据及政策启示[J].教育学报，11(5):99-110.Zheng L.2015.Neighborhood effects and peer effects in education:Methods,evidences,and policy implications[J].Journal of Educational Studies,11(5):99-110.(in Chinese)
• 佐藤学.2010.“分层教学”有效吗?[J].钟启泉，译.全球教育展望，39(5):3-7.
• Sato M.2010.Is ‘ability grouping’ effective?[J].Zhong Q Q,trans.Global Education,39(5):3-7.(in Chinese)
• Ammermueller A,Pischke J S.2009.Peer effects in European primary schools:Evidence from the progress in international reading literacy study[J].Journal of Labor Economics,27(3):315-348.
• Arnott R,Rowse J.1987.Peer group effects and educational attainment[J].Journal of Public Economics,32(3):287-305.
• Ballester C,Calvó-Armengol A,Zenou Y.2006.Who's who in networks.Wanted:The key player[J].Econometrica,74(5):1403-1417.
• Ballester C,Zenou Y,Calvó-Armengol A.2010.Delinquent networks[J].Journal of the European Economic Association,8(1):34-61.
• Benabou R.1993.Workings of a city:Location,education,and production[J].The Quarterly Journal of Economics,108(3):619-652.
• Betts J R,Shkolnik J L.2000.The effects of ability grouping on student achievement and resource allocation in secondary schools[J].Economics of Education Review,19(1):1-15.
• Boozer M A,Cacciola S E.2001.Inside the ‘Black Box’ of Project STAR:Estimation of peer effects using experimental data,Discussion Papers.840[R].Yale University.
• Burke M A,Sass T R.2013.Classroom peer effects and student achievement[J].Journal of Labor Economics,31(1):51-82.
• Byrne B M.1996.Academic self-concept:Its structure,measurement,and relation to academic achievement[M]//Bracken B A.Handbook of Self-concept:Development,Social,Clinical Considerations.New York:John Wiley and Sons,287-316.
• Calvó-Armengol A,Zenou Y.2004.Social networks and crime decisions:The role of social structure in facilitating delinquent behavior[J].International Economic Review,45(3):939-958.
• Calvó-Armengol A,Patacchini E,Zenou Y.2009.Peer effects and social networks in education[J].The Review of Economic Studies,76(4):1239-1267.
• Carrell S E,Sacerdote B I,West J E.2013.From natural variation to optimal policy?The importance of endogenous peer group formation[J].Econometrica,81(3):855-882.
• Cooley J.2010.Desegregation and the achievement gap:Do diverse peers help?WCER Working Paper No.2010-3[R].Madison:University of Wisconsin-Madison.
• Duflo E,Dupas P,Kremer M.2011.Peer effects,teacher incentives,and the impact of tracking:Evidence from a randomized evaluation in Kenya[J].American Economic Review,101(5):1739-1774.
• Elsner B,Isphording I E.2017.A big fish in a small pond:Ability rank and human capital investment[J].Journal of Labor Economics,35(3):787-828.
• Elsner B,Isphording I E,Z?litz U.2021.Achievement rank affects performance and major choices in college,CEPR Discussion Paper No.DP16066[R].
• Epple D,Romano R E.2011.Peer effects in education:A survey of the theory and evidence[M]//Benhabib J,Bisin A,Jackson M O.Handbook of Social Economics1A,1B.Amsterdam:Elsevier,1053-1163.
• Figlio D N,Page M E.2002.School choice and the distributional effects of ability tracking:Does separation increase inequality?[J].Journal of Urban Economics,51(3):497-514.
• Gamoran A.1987.The stratification of high school learning opportunities[J].Sociology of Education,60(3):135-155.
• Hanushek E A,Kain J F,Markman J M,et al.2003.Does peer ability affect student achievement?[J] Journal of Applied Econometrics,18(5):527-544.
• Hanushek E A,W??mann L.2006.Does educational tracking affect performance and inequality?Differences-in-differences evidence across countries[J].The Economic Journal,116(510):C63-C76.
• Hoxby C M.2000.The effects of class size on student achievement:New evidence from population variation[J].The Quarterly Journal of Economics,115(4):1239-1285.
• Hoxby C M,Weingarth G.2005.Taking race out of the equation:School reassignment and the structure of peer effects[R].Cambridge:Department of Economics,Harvard University.
• Huang B,Zhu R.2020.Peer effects of low-ability students in the classroom:Evidence from China's middle schools[J].Journal of Population Economics,33(4):1343-1380.
• Lavy V,Paserman M D,Schlosser A.2012.Inside the black box of ability peer effects:Evidence from variation in the proportion of low achievers in the classroom[J].The Economic Journal,122(559):208-237.
• Lazear E P.2001.Educational production[J].The Quarterly Journal of Economics,116(3):777-803.
• Lu F W,Anderson M L.2015.Peer effects in microenvironments:The benefits of homogeneous classroom groups[J].Journal of Labor Economics,33(1):91-122.
• McEwan P J.2003.Peer effects on student achievement:Evidence from Chile[J].Economics of Education Review,22(2):131-141.
• McMillan R.2005.Erratum to “Competition,incentives,and public school productivity[J].Journal of Public Economics,89(5/6):1133-1154.
• Murphy R,Weinhardt F.2020.Top of the class:The importance of ordinal rank[J].The Review of Economic Studies,87(6):2777-2826.
• Sacerdote B.2011.Peer effects in education:How might they work,how big are they and how much do we know thus far?[M]//Hanushek E A,Machin S J,Woessmann L.Handbook of the Economics of Education.Amsterdam:Elsevier,249-277.
• Vandenberge V.2006.Achievement effectiveness and equity:The role of tracking,grade repetition and inter-school segregation[J].Applied Economics Letters,13(11):685-693.
• Wennberg K,Norgren A.2021.Models of peer effects in education,Working Papers 21/3[R].Stockholm School of Economics.
• (1)《北京市第一〇一中学初一数学和英语学科分层教学实施方案(试行)》,2014年。
• (2)中文文献中,同群效应也译作同伴效应或同辈效应。
• (3)更多相关研究见文献综述。
• (4)这里的录取分数线可以是大学本科的录取分数线,也可以是初中升高中的录取分数线。我们这里讨论的是大多数学校的普遍目标。在现实中,特定学校的目标会有不同,比如省重点中学的目标是使得更多学生的分数超过985或211大学的录取分数线。
• (5)基于学生数量足够多,学生i的学习努力程度相对于同学总体的努力程度小的可以忽略,所以我们可以近似假设所有同学也包括学生i,即■。这样既可以简化数学分析,也不失一般性。
• (6)如Calvó-Armengol and Zenou (2004),Ballester et al.(2006,2010)和Calvó-Armengol et al.(2009)。
• (7)学习能力可以通过学生入学成绩来测度。
• (8)老师的教学能力可以通过老师的教学经验、荣誉称号来衡量,比如特级教师、高级教师。
• (9)这里我们假设一个学校的考生数量相对于全国或者全省全市所有考生来说数量非常小,所以对录取线的影响可以忽略不计。
• (10)这一假设是符合现实的,学校往往是根据以往学校的学生上线率以及学生成绩掌握学校分数所处的位置。