先前的研究發現，國三學生參與數學補習雖有正面的效果，但效果值並不大。由於補習是放學後一種補充性的學習活動，一項合理的假設是：開始補習的時間愈久，補習的效果也會愈好。本文使用台灣教育長期追蹤資料庫（Taiwan Education Panel Survey, TEPS）追蹤樣本驗證此種假設是否成立。依據開始補習數學的時間，TEPS的國中樣本可區分出國一到國三上學期都有補習者、國二開始補習者、國三開始補習者，以及國中期間從未補習者等四種類型。本文運用傾向分數配對法進行資料分析，以國中期間從未補習者做為對照組，分別探討前三種補習類型，若在不給予補習的情況下，其補習數學的平均效果為何？
研究結果發現：一、數學補習的時間愈久，補習者與不補習者間，在個人特性與家庭背景等的差異處就愈多；二、從國二開始補習數學者的平均效果值最大，以滿分100分的情況來看，其效果值約為三分。從國一開始連續補習，或者從國三開始補習，其效果值都不明顯。
Our previous research has shown that attending a cram school in 9th grade in Taiwan has a positive but fairly small effect on math performance. Since a cram school provides supplementary learning after school, it is possible that the earlier a student starts participating in a cram school program, the bigger the effect is. We explore this possibility by using the core panel data of the Taiwan Education Panel Survey (TEPS).
We identify four types of students in terms of the length of their attendance of math cram schools during the junior-high school years. We use the method of propensity score matching (PSM) to explore the average treatment effect on the treated (ATT) by comparing those who have attended a math cram school since the 7th, 8th, and 9th grades separately with those who have never attended a math cram school during their junior-high years.
With different matching estimators, all results of PSM analysis indicate a small or no effect of cram school attendance on math performance, irrespective of how long attendance is. The largest ATT found is for those who have participated in math cramming since the 8th grade. The size of the effect is around 3 points if the highest math ability score is 100. For those who attend math cram schools from the 7th grade or only in the 9th grade, there are virtually no gains.
APA 格式
關秉寅 、李敦義(Ping-Yin Kuan, Duen-Yi Lee)（2010年06月30日），〈國中生數學補得愈久，數學成就愈好嗎？傾向分數配對法的分析 〉。《教育研究集刊》，2014年01月25日取自
MLA 格式
關秉寅 、李敦義(Ping-Yin Kuan, Duen-Yi Lee)，〈國中生數學補得愈久，數學成就愈好嗎？傾向分數配對法的分析 〉。《教育研究集刊》第 56 期（2010），取自
第五十六輯．第二期 - 2010-06-30
