metadata: authors: 0: author: Macdonald,Kevin Alan David
1: author: Patrinos,Harry Anthony
count: Korea, Republic of
docna: 0: docna: Within-school tracking in south Korea : an
            analysis using Pisa 2003
docty: Policy Research Working Paper
subtopic: Economics of Education,Educational Sciences,Educational Institutions & Facilities,Educational Populations,Gender and Development,Education for Development (superceded),Effective Schools and Teachers,Education For All
teratopic: Education
abstracts: cdata!: The 2003 PISA Korea sample is used to
            examine the association between within-school ability
            tracking and mathematics achievement. Estimates of a variety
            of econometric models reveal that tracking is positively
            associated with mathematics achievement among females and
            that this association declines for higher achieving females.
            No evidence of an association between males and tracking is
            detected. While this association for females cannot be
            interpreted as a causal effect, the presence of a measurable
            association indicates the need for further research on
            tracking in Korea with a particular focus on gender differences.
geo_reg_key: 517198,119225,517191
repnme: repnme: Within-school tracking in south Korea : an
            analysis using Pisa 2003
display_title: Within-school tracking in south
            Korea : an analysis using Pisa 2003
listing_relative_url: /research/2010/04/12080479/within-school-tracking-south-korea-analysis-using-pisa-2003
topicv3: Teachers Management m1326119 1523,Education m1327048 470,Learning Assessment m1327283 1555,Economics of Education m1327511 1540,Gender m1327621 615
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Education
no_of_pages: 24
author_keys: 0: author_key: 962343
1: author_key: 95903
model_extractions: WPS5266 Policy Research Working Paper 5266 Within-School Tracking in South Korea An Analysis Using Pisa 2003 _Kevin Macdonald Harry Anthony Patrinos_ The World Bank Human Development Network Education Team April 2010
Policy Research Working Paper 5266

# **Abstract**

The 2003 PISA Korea sample is used to examine the association between within-school ability tracking and mathematics achievement. Estimates of a variety of econometric models reveal that tracking is positively associated with mathematics achievement among females and that this association declines for higher achieving females. No evidence of an association between males and tracking is detected. While this association for females cannot be interpreted as a causal effect, the presence of a measurable association indicates the need for further research on tracking in Korea with a particular focus on gender differences.

This paper—a product of the Education Team, Human Development Network—is part of a larger effort in the department to analyze the determinants of learning. Policy Research Working Papers are also posted on the Web at http://econ. worldbank.org. The author may be contacted at hpatrinos@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# WITHIN-SCHOOL TRACKING IN SOUTH KOREA AN ANALYSIS USING PISA 2003

Kevin Macdonald<sup>1</sup> and Harry Anthony Patrinos<sup>2</sup>

> 1 Consultant, Human Development Network – Education Team, World Bank; <u>kadmacdonald1@worldbank.org</u> 2 Lead Education Economist, Human Development Network – Education Team, World Bank (corresponding author) <u>hpatrinos@worldbank.org</u>

The opinions expressed in this paper are that of the authors alone and should not be attributed to that of the World Bank Group.
# 1. Introduction

Understanding the relationship between learning achievement and tracking is especially relevant to Korea due to its so-called equalization or leveling policy where, from 1974 onward, different areas began to assign students to upper secondary schools using a lottery system instead of by academic performance<sup>3</sup> (Kim et al. 2006; Educators without Borders 2007). As a result, areas subject to equalization can be characterized as a mixed school system since students of different abilities attend the same schools; in the other areas, a tracked school system exists where students in each school are more homogenous in ability.

Some research has tried to measure the impact of this policy. For example, Kim et al. (2006) use a difference-in-differences method and find that the effect of the policy is negative. Kang et al. (2007) examine the impact of this policy on adult earnings and find positive effects for low ability students and smaller effects for high ability students.

Literature on tracking generally cites two paths through which tracking affects learning achievement (Kim et al. 2008; Duflo et al. 2008; Hanushek and Wößmann 2005). In the first, tracking benefits students because it creates a more ability-homogenous learning environment which allows teachers and schools to choose pedagogy better suited to a higher proportion of students. In the second, tracking inhibits low achieving students who would otherwise benefit from exposure to high achieving peers while their high achieving peers remain unaffected.

Consequently, recent empirical literature on tracking attempts to estimate the magnitude of peer effects. Some recent estimates, as presented in Ammermeuller and Pischke (2006), are small: an increase in peer composition of one standard deviation generally results in an increase in achievement between 0.05 to 0.11 standard deviations. The principle empirical challenge in this literature is distinguishing peer effects, the effect that a student’s peers have on his or her achievement, from _correlated effects_ , the effect that unobserved factors have on both the student and his or her peers. Correlated effects stem from a number of sources including an unobserved characteristic of the teacher or endogeneity in the selection of the peer group such as better students attending better schools. Several different strategies have been adopted to overcome this identification problem. For example, Ammermeuller and Pischke (2006) rely on random assignment of teachers and students to classes; Gibbons and Telhaj (2006) take advantage of random variation of primary students’ assignments to secondary schools; Schneeweis and WinterEbmer (2005) use a fixed effects model to focus on peer effects within schools where class composition is generally random, and Fertig (2002) uses an instrumental variables approach.

Kang (2006) examines peer effects in the context of South Korea, also using random student assignment and instrumental variables. He finds higher ability peers have a causal and positive impact on the achievement of a student. Additionally, he finds that a low

> 3 Initially the policy’s official name was the “Equalization of High School Policy” (Educators without Borders 2007).

2
achieving student tends to interact more closely with other low achieving students while a high achieving student tends to interact more closely with other high achieving students; this complicates the connection between peer effects and ability tracking: exposure to high achieving students may benefit a low achiever, but he or she would be hindered by exposure to his or her low achieving peers.

The proceeding analysis also provides a Korea-specific contribution by examining the 2003 Korea PISA sample. This paper examines the association between mathematics achievement and within-school tracking where schools assign students into groups depending on their ability. Particularly, this paper focuses on how this association differs between males and females.

In the following sections, estimates of linear regression models present the association between learning achievement and tracking and reveal a statistically significant association for females, no statistically significant difference for males, and a statistically significant difference in association between genders. Using PISA’s categorical measure of achievement, its mathematics _proficiency levels_ , multinomial logit estimates show, among females, a statistically significant decline in the association between tracking and the odds of being in one proficiency level relative to the previous for higher levels of proficiency. Finally, comparisons of the standard deviation of achievement between males and females in schools with tracking and not with tracking, as well as estimates of conditional quantile regressions, reveal no evidence that tracking associates with inequities in achievement.

However, none of the proceeding results should be interpreted as causal. The crosssectional nature of the PISA dataset, in conjunction with unobserved factors, prevents establishing a counterfactual: we can not estimate the achievement of a student in a school with tracking had he or she been in a school without tracking. Furthermore, grade 10 students compose almost the entire sample, and the PISA examination occurred in June, 2003; since grade 10 is the first year of high school, students have only been in the observed school for three months; consequently, students have been exposed to tracking or non-tracking for a maximum of three months although likely less since midterm exams which are used to determine a student’s ability are often held in late April. While we find statistically significant associations, they likely reflect other factors that are correlated with tracking but not observable. However, these associations are certainly interesting and expose a need for more in-depth, empirical research on tracking in Korea.

3
# 2. Data

The Programme for International Student Assessment (PISA) is the Organization for Economic Cooperation and Development’s (OECD) international student assessment targeted to 15 year olds in grade 7 or higher, and it has been conducted every three years since 2000. In addition to testing students’ ability in mathematics, science, and reading, PISA also collects background data about each student, his or her family, and his or her school. Schools are the primary sampling unit in PISA, and they are selected by one or more sampling frames or explicit strata. In Korea, there are several strata which divide the sample into general and vocational schools and by metropolitan, urban, and rural areas. For this paper, only observations from the general school strata and for grade 10 students were included.

Both the 2003 and 2006 PISA school questionnaires include questions about tracking within school; however, in 2003, the question specifies tracking among mathematics classes while in 2006, the questions specifies any subject. In order to clearly estimate the association between tracking and learning achievement, this paper uses the 2003 dataset and focuses on mathematics achievement. The school tracking question for 2003 is drawn from the principal’s questionnaires: Schools sometimes organize instruction differently for students with different abilities and interests in Mathematics. Which of the following options describe what your school does for 15-year-old students in Mathematics classes? (question 16) The options included (a) Mathematics classes study similar content, but at different levels of difficulty; (b) Different classes study different content or sets of Mathematics topics that have different levels of difficulty; (c) Students are grouped by ability within their Mathematics classes; (d) In Mathematics classes, teachers use a pedagogy suitable for students with heterogeneous abilities (i.e. students are not grouped by ability). For each option, a principal could choose either “for all classes,” “for some classes” or “not for any classes.” The three different types of tracking captured by parts (a) through (c) of question 16 all occur in Korea. The Ministry of Education encourages schools to divide and instruct students in three cohorts based on ability, although some schools divide students into two cohorts. Additionally, many schools will divide students by ability only for a portion of the weekly instruction and maintain mixed classes for the remainder in response to parents and students wanting homogeneous assessment of students. Table 1 outlines how school principals responded to the question: 4
|Classes:|All|Some|None|
|---|---|---|---|
|a| Mathematics classes study similar content but at different levels<br>of difficulty|0.1038<br>(0.03512)|0.5626<br>(0.0811)|0.35534<br>(0.0079)|
|b) Different classes study different content or sets ofMathematics|o.02|0.5206|0.4595|
|topics that have different levels of difficulty|f0.01)|(0.0798)|(0.0809)|
|aa<br>;<br>;<br>cl) Students are grouped by ability within their Mathernatics classes|0.0763<br>(0.0341)|0.66<br>0.07)|0.2657<br>(0.0618)|
|dj In mathernatics classes, teachers use a pedagogy suitable for<br>«students with heterogeneous abilities><br>Source: 2003 PISA School Sarnple, General High School Strata<br>Note:Standarderrorsarereportedinparentheses.|0.1333<br>(0.0373)|0.75?<br>(0.052)|O.11<br>(0.03)|

Source: 2003 PISA School Sarnple, General High School Strata Note: Standard errors are reported in parentheses.
# 3. Stochastic Model

We assume that the observations of the PISA’s school, student and family background variables do not exactly determine the corresponding levels of student achievement, but rather that they give us more information about what these achievement levels could be. In this sense, the vector of achievements for the sampled group of students, _y_ , is a random variable conditionally distributed by the set of background variable observations, matrix _x_ , as expressed by the following stochastic model: Furthermore, we assume that the conditional mean of the distribution function _f_ has the following property: where  is a column vector of regression coefficients comprised of one parameter for each background variable in _x_ . Given the setup of (1) and (2), each regression coefficient can be interpreted as the change in a student’s expected achievement _associated_ with a marginal change in the value of the coefficient’s corresponding variable; since (2) is an assumption about the conditional distribution function, _f_ , and not derived from a cognitive production function or any framework implying causation, the regression coefficients are not interpreted as marginal effects.

For analyzing how background variables associate to the dispersion of the conditional distribution, _f_ , we assume that the 20<sup>th</sup> , 40<sup>th</sup> , 60<sup>th</sup> and 80<sup>th</sup> conditional quantiles of _y_ | _x_ are linear functions of the background variables, _x_ .

(3) prob{ _yi_  _xi_  _q_ } = _q_  _q_  {0.2, 0.4, ..., 0.8},  _i_  _I_ where _I_ is the set of sampled students, _yi_ and _xi_ are student _i_ ’s achievement and background variable observations, respectively, and  q is a column vector of q<sup>th</sup> quantile regression coefficients with one parameter for each background variable. Analogous to the linear regression coefficients,  , each _q_<sup>th</sup> quantile regression coefficient of  _q_ can be interpreted as the change in the _q_<sup>th</sup> quantile of a student’s distribution of achievement associated with a marginal change in the corresponding background variable. In other words, while the regular regression coefficients measure how variables associate with the mean of a student’s distribution of possible achievements given his or her background variables, the _q_<sup>th</sup> quantile regression coefficients measure how variables associate with the _q_<sup>th</sup> quantile of a student’s distribution of possible achievements given his or her background variables. Examining how these coefficients change for different quantiles describes how variables associate with the dispersion of the conditional distribution; a variable that is, for example, positively associated with the 80<sup>th</sup> quantile and negatively with the 20<sup>th</sup> quantile would be associated with an increase in this dispersion.

6
In order to use PISA’s categorical measure of achievement, its proficiency levels, we assume that the probability of a particular student’s proficiency level, _pi_ , is conditionally distributed on _xi_ by a multinomial logistic function: (4) where _K_ is the number of proficiency levels and  j is the column vector of multinomial logit coefficients with one parameter for each background variable. (4) implies that or, in other words, that the association between a marginal change in any particular background variable and the log change in the odds of being in proficiency level _j_ relative to _j – 1_ is the corresponding component in the vector equal to  _j_ -  _j-1_ .

Estimating (4<sup>/</sup> ) is conceptually similar to dividing the sample into subsamples comprised of consecutive pairs of proficiency levels and then estimating logit models for each subsample. If the association between the odds of being in the next proficiency level and variables such as _some tracking_ are stronger for lower achieving students than higher achieving students, estimations of (4<sup>/</sup> ) will capture this. Additionally, statistical tests can reveal whether these association change for higher achieving students versus low achieving students.

# 4. Variables

In order to focus as much as possible on the association between learning achievement and _some tracking_ , the variation in achievement attributable to other variables needs to be accounted for. Typical analyses of tracking and peer effects assume cognitive production functions and use similar variables. Table 2 lists variables used in some of these recent studies which can be generally classified into three levels: student level variables which includes student personal characteristics as well as those of their families, class level variables which includes characteristics of their teachers, classrooms, and peers, and school level variables which includes characteristics of the school.

7
|Study|Topic|Background Variables|
|---|---|---|
|Eim et al. (2008)|Tracking|gender,<br>mother’s<br>education,<br>father’s<br>education,<br>mother<br>is<br>a<br>housewife, school’s teacher's average age, average experience,<br>school size, private school, girls school, boys school|
|Ammermeuller et al. (2006)|Peer Effects|age, gender, parent's origin, language spoken at home, number<br>of books at home, number of persons living in household, class<br>size, teacher's gender, teacher's education, teacher’s experience,<br>community<br>size,<br>daily<br>instruction<br>hours,<br>shortage<br>of<br>staff,<br>teaching materials andbuildings|
|Gibbons et al. (2006)|Peer Effects|gender,<br>ethnicity,<br>free-school-meal<br>entitlement,<br>special<br>educational needs, age, year|
|echneeweiss et al. (2005)|Peer Effects|gender, grade, single parent family, number of siblings, ethnic<br>Austrian,<br>mother’s<br>education,<br>socioeconomic<br>status,<br>cultural<br>communication, books<br>at home, educational resources, parents<br>unemployed, school size, total hours of instruction, urban school|
|Zimmer (2003)|Peer Effects in Tracking|gender,<br>father’s<br>occupation,<br>mother’s<br>occupation,<br>father’s<br>education,<br>mother’s<br>education,<br>teacher's<br>gender,<br>teacher's<br>experience, teacher's age, teacher's education, class size|
|Fertig,M (2002)|PeerEffects|gender, whether parents work,<br>intact family, native<br>student,<br>parent born abroad, second generation, other languages at home,<br>parents education, homework feedback, poor school conditions,<br>regular<br>tests,<br>teacher<br>shortages,<br>discipline<br>problems,<br>student<br>teacher ratio|
|Betts and Shkolnik (1998)|Tracking|student teacher ratio, teacher education, teacher experience, race|
<u>Table 3: School Variables Correlated with Tracking</u>

|Variable|Desc. of Association with<br>Tracking|Proportion<br>of sample<br>true (%)|
|---|---|---|
|Public|positive|48|
|autonomy – hiring teachers|negative|33|
|autonomy – teacher salary increases|negative|90|
|autonomy – course offering|positive|96|
|student teacher ratio|positive|-|
|locatedin metropolitanstratum relative torural|positive|-|
|Source: Korea PISA 2003|||

The variables measuring autonomy over hiring teachers and teacher salary increases are positively correlated with each other and negatively correlated with tracking. Since autonomy over hiring teachers displays more variation, it can serve as a proxy for autonomy over salary increases and any other unobserved characteristics that both might reflect. Autonomy over course offering has very little variation since 96 percent of schools reported this characteristic; this variable was tested for correlation with achievement, and the results were not statistically significant; for this reason, it will be excluded from the models.

Additionally, several variables are of interest in the Korean context. Whether a particular school is subject to the equalization policy or not can not be observed in the 2003 PISA sample, but the importance a school places on a student’s academic record for his or her admission can be observed. Consequently, this variable is included. Also, some schools are co-educational and some are strictly male or female. Schools report the number of female students and the number of male students which can be used to construct a binary variable of whether the school is co-ed or not. Table 4 lists all the variables used in this analysis with some descriptive statistics.

9
||Mean|Std Dev.|25th Guantile|Fath Guantile|
|---|---|---|---|---|
|.<br>Math<br>Ach<br>ritFull<br>Sarnpi<br>CHIEMEMENE<br>PUN<br>SITS|542 23<br>(3.24)|92.59<br>(2414)|479.26<br>(3.74)|606.14<br>(4.23)|
|.<br>Math<br>Ach<br>rt,<br>|<br>Strata,<br>Grade<br>10<br>chievement,<br>General<br>Strata,<br>Grade|570.02<br>(4.01)|63.11<br>(2.55)|51475<br>(4.64)|B26.27<br>(4.48)|
|:<br>Same Tracking for MathClasses|oF<br>(0.05)||||
|.<br>Public<br>School<br>ublic<br>Schoo|O.3F<br>(n.04)||||
|a:<br>Hi<br>Teachers<br>Aut<br>iting<br>Teachers<br>Autonomy|O38<br>(0.05)||||
|Located inthe Metropolitan Stratum|0.52<br>(0.014||||
|:<br>Locatedin the<br>Urban<br>Strat<br>ocated<br>in<br>the<br>Urban<br>Stratum|0.38<br>(o.01)||||
|Located inthe RuralStratur|oot)||||
|.<br>Student<br>Teacher<br>Rat<br>nent<br>|eaener<br>ale|16.41<br>(0.15)|1.55<br>(0.27)|16.44<br>(0.2)|74<br>(0.15)|
|Co-ed<br>School<br>o-ed<br>Schoo|O43<br>(0.05)||||
|Student Record Important for School Admission|0.5<br>(0.05)||||
|Femal<br>ema’|O38<br>(0.04)||||
|oo<br>Hi<br>f<br>Instruct<br>Math<br>ours<br>ob inetncsenin|43<br>(0.07)|16<br>(0.15)|3.33<br>0)|5<br>(0.42)|
|Mother'sEducation:Mone|OD||||
|Mother'sEducation: Primary|‘O||||
|Mother's Education: Lower Sec<br>,<br>,|0.16<br>(0.014||||
|Mother'sEducation:UpperSec.|oor||||
|Mother'sEducation: PostSec.|‘Oy||||
|O-10books athome|o.03<br>oy||||
|10-100books athome|O.39<br>(0.01)||||
|100+ books athome|0.58<br>(0.01)||||
|Source: PISA, 20035 Korea, General High School Str<br>Note:Standarderrorsreportedinparentheses.|ata, Grade 10|Students (tirst|row includes all o|bservations)|
# 5. Mathematics Achievement and Tracking

Estimation of our models is complicated by the plausible value estimates of mathematics achievement as well as the presence of intra-cluster correlation and other issues related to the complex survey design. The estimation methodology used in this paper adheres strictly to the methodology recommended by the OECD (2005) which provides unbiased estimators and standard errors assuming the other standard, requisite assumptions for each model are met.

Table 5 presents three estimates of the linear regression model of (2). The first includes only the _some tracking_ variable; the estimate of this coefficient is equivalent to the difference in the mean achievement of students in schools with tracking versus those in schools without tracking. As can be seen, this estimate is positive, implying students at tracking schools have a higher level of achievement, but it is not statistically significant implying the difference could simply stem from sampling variation.

The second estimation includes only the school variables, and the third includes all other variables. Only with the inclusion of student and family characteristics does the positive difference between tracking students and non-tracking students become statistically significant.

Being female is negatively associated with mathematics achievement which is a typical result for many countries. Additionally, being located in an urban or metropolitan stratum instead of a rural stratum is positively associated with achievement, even when differences in student and background characteristics are controlled for. Having a mother’s education less than upper secondary is negatively associated with achievement. Having a mother with more than an upper secondary education is also negatively associated with achievement; however, Table 4 reveals that this represents a small proportion of the sample. Finally owning books positively associates with achievement as well.

11
|(1)<br>(2)|(3)|
|---|---|
|;<br>6.29<br>9.08<br>Some<br>Tracking for Math Classes<br>(12.08)<br>(1018)|1?.96*<br>(6.89)|
|.<br>-14.49<br>Public School<br>(9.59)|-11.51<br>(6.31)|
|..<br>-6,.95<br>Hiring Teachers Autonorny<br>6.99)|“5.435<br>7.39)|
|.<br>.<br>4760°"<br>Located<br>in the Metropolitan Stratum<br>(17.53)|26.24<br>(16.88)|
|.<br>42.63"<br>Located<br>in the Urban Stratum<br>(16.34)|29.63°*<br>(14.22)|
|.<br>451*<br>StudentTeacher Ratio<br>(2.49)|3.96*<br>(2.21)|
|Co-ed School|-5.65<br>(1.61)|
|Student<br>R<br>d<br>|<br>ttant<br>forSchool<br>Admissi<br>udent<br>Record<br>Irnportant<br>for<br>School<br>Admission|10.02<br>Gan)|
|Female|-15.15"*<br>(4.72)|
|Hours of Instruction in Math|i<br>(1.30)|
|;<br>;<br>Mother's Education: None (relative ta Upper Sec.)|-705<br>@.17)|
|\<br>.<br>.<br>.<br>Mother's Education: Primary (relative to Upper Sec.)|-11.01<br>vat|
|1<br>a<br>Mother's Education: Lower Sec. (relative to Upper Sec.)|-10.06**<br>(4.28)|
|.<br>a<br>.<br>Mother's Education: Post Sec. (relative to Upper Sec.)|-12.60**<br>6.17)|
|.<br>O- 10 books at hore (relative to 10-100)|-43,55°*<br>6.39)|
|.<br>100+ books at home (relative ta 10-100)|36.16***<br>3.71)|
|Canstant<br>566.1***<br>455.067"<br>onstan<br>(10.35)<br>(36.85)|452.57***<br>(34.51)|
|NMurmber of Observations<br>a524<br>a404|2795|
|Average R-oquare<br>O.0012<br>0.0695|O.1b2|
|Mote: Standard errors are reported in parentheses and significance at the 1%, 5%, 10%<br>denoted “***, and *, respectively. Estimates were calculatetd using 5 plausible values <br>estimates of achievernent and Balanced Repreated Replication with Fays(0.5) adjustme<br>to estimate the standard errors.<br>Sourcedata:PISA2003Korea,GeneralSchoolStrata,Grade10Students|levels is<br> for<br>nt were used|
|(4)|(5)|(6)|
|---|---|---|
|Female<br>21.10"<br>(4.96)|Gd<br>(9.75)|B21<br>(7.96)|
|;<br>someTracking torMath Classes|7.3<br>(10.91)|fest!<br>8.87)|
|;<br>Female x Some Tracking|43.85***<br>(10.84)|30.05*°**<br>(10 49)|
|Other Controls<br>Na|Mo|Yes|
|Constant<br>Bais"<br>(4.22)|S8a.s1—*<br>(9.05)|4e4.94*<br>(31.65)|
|Nurniber of Observations<br>aba2|a524|2739|
|Average R-Square<br>0.0154|O.0272|0.165|
|;<br>Female +Some Tracking x Female|-5.59*<br>627)|-6.16<br>6.09)|
|;<br>;<br>someTracking +Some Tracking x Fernale<br>Note: Standard errors are reported in parentheses and significance at the 1<br>denoted ***,<br>| and *, respectively. Estimates were calculatetd using 5 plau<br>astimates ofachievement and Balanced Repreated Replication with Fays(0.<br>to estimate the standard errors.<br>Source data: PISA 2003 Korea, General School Strata, Grade 10 Students|31.56**<br>(14.91)<br>%, 5%, 10% <br>sible values <br>5) adjustme|af647<br>(1.97)<br> levels is<br> for<br>nt were used|
Finally, model (5)’s coefficient for _some tracking_ is the difference between males in tracking schools versus those not in tracking schools. As can be seen, there is no significant difference. In other words, we observe a measurable difference in achievement between tracking and non-tracking schools only for females. Model (6) differs from model (5) with the inclusion of controls for other school, student, and family background variables. The conclusions drawn from this model are the same as drawn from (5), except, now they have taken into account differences in the other background variables. The chief conclusion of these results is that _some tracking_ is positively associated with mathematics achievement for females; no evidence of this exists for males. Additionally, the association is different for males than females.

# 7. Low Achievers and Tracking

Low achieving students may benefit from tracking due to a homogenous learning environment or may be inhibited by tracking due to a lack of exposure to higher achieving peers. In the preceding estimations, a significant difference in math achievement associated with tracking is found only among females, and this difference is positive. While this result tends to be consistent with the connection between learning and ability-homogeneous peers, the preceding estimations do not relate this difference to achievement level; it is possible, for example, that tracking associates negatively for low achievers while positively for middle and higher achievers.

Previous studies which sought to measure peer effects among low achieving students typically have baseline data on the achievement of students in their sample (Duflo et al. 2008). For the PISA 2003 dataset, this is not the case. In order to use the PISA dataset to examine differences in tracking’s association across the distribution of achievement, the multinomial logit model for proficiency levels of (4) is estimated. As shown in (4<sup>/</sup> ), this model allows us to estimate the odds ratio associated with _some tracking_ for different consecutive pairs of proficiency levels. This reflects whether this association is stronger or weaker for lower achieving students versus higher achieving students. Table 7 presents estimates of the proportion of general high school, grade 10 students at the various levels of mathematics proficiency. Table 7 reveals that most students are concentrated in levels 3 through 5.

14
|Level 6|oon|
|---|---|
|Level5|aan|
|Level4|aan|
|Level3|pot|
|Level 2|oon|
|Level 1|oat|
|Level<1|‘oO|

Mote: Standard errors reported in parentheses. source: PISA 2003 Korea, General School Strata, Grade 10 Students
|Lag<br>of<br>°F!|(7a)<br>Pf{Level 4}<br>PrLevel <4}|(7b)<br>P{Level 5}<br>PfLevel4}|(7c)<br>P{Level 6}<br>PfLevelS}|(Ba)<br>PfLevel 4)<br>| P{Level <4}|(ab)<br>PfLevel 5}<br>PfLevel 4}|(8c)<br>PfLevel 6}<br>PfLevel 5}|
|---|---|---|---|---|---|---|
||O13|0.23|O24|Oa|0.18|O.2|
|SameTrackingforMathClasses|(0.19)|(0.16)|(0.22)|(0.18)|(0.21)|(0.26)|
|<br>|[1.14]<br>|[0.73]<br>|[0.73]<br>|[1.31]<br>|[0.84]<br>|[1.22]<br>|
|Female|-0.86"*<br>(0.13)|0.4**2**"<br>(0.4|-**0**.07<br>(.31)|O%**2**"<br>(0.3)|0**.**42<br>(031)|0.**3**5<br>(0.6)|
||[0.43]|<br>[0.66]|<br>[0.93]|<br>[0.49]|<br>[0.66]|<br>[0.70]|
||o.7a"*|O27|0.05|Oo.65°|0.33|0.16|
|Female x Some Tracking|(0.19)|(0.21)|(0.34)|(0.25)|(0.32)|(0.37)|
||[2.05]|[1.31]|[0.92]|[1.91]|[1.33]|[1.17]|
|Other Controls||No|||Yes||
||0.12|0.15|0.14|-0.07|-0.08|0.19|
|Female+SomeTrackingxFernale|(0.11)|(0.12)|(0.12)|(0.15)|(0.17)|(0.16)|
||[0.89]|[0.86]|[0.87]|[0.93]|[0.45]|[0.83]|
||a.er*|0.05|0.52|og26*|O.16|0.36|
|Sore Tracking + Some Tracking x Fernale|(0.2)|(0.19)|(0.38)|(0.21)|(0.23)|(0.36)|
|Note: Cells indicate the association between the ro<br>these are calculated by using a linear combination <br>are reported in square brackets below. Standard er<br>denoted **, **, and *, respectively. Estirnates were <br>Repreated Replication with Fays(0.5) adjustment w<br>Source data: PISA 2003 Korea, General School Str|[2.39]<br>w's denoted va<br> of the standard<br>rors are reporte<br> calculatetd us<br>ere used to es<br>ata, Grade 10|[1.05]<br>riable and the <br> coefficients es<br>d in parenthes<br>ing 5 plausible <br>timate the stan<br> Students|[0.73]<br>change in the <br>timated in the <br>es and signifi<br> values for est<br>dard errors.|[2.51]<br>log of the colurn<br> rnultinornial lo<br>cance at the 1%<br>imates of achie|[1.17]<br>n's denoted <br>git models. <br>, 5%, 10% l<br>vernent and|[1.43]<br> odds ratio;<br>Odds ratios<br>evels is<br>Balanced|
|from|(fal to (7b)|(fa) to fc)|(8a) ta (Bb)|(8a) to (8c)|
|---|---|---|---|---|
|;<br>Female +SameTracking x Female|-0.05<br>0.13)|-0.02<br>0.15)|0.01<br>(0.28)|-0.11<br>0.21)|
|.<br>;<br>Some Tracking +Sore Tracking x Fernale|-0.62"*<br>(0.29)|-1.418"*<br>a.44)|0.76"<br>(0135)|-0.55<br>(0.42)|
|Same Trackin<br>4|-0.516<br>(0.29)|0.57<br>(0.26)|0.44<br>(0.33)|-0.07<br>(0.26)|
|Female<br>x8<br>Tracki<br>emale x<br>Some<br>Tracking<br>Note: Cells indicate the change in the estimated coe<br>using a linear combination ofthe standard coefficien<br>errors are reported in parentheses. Significance at t<br>Source: PISA 2003 Korea, General School Strata, G|-0.46<br>0.31)<br>fficients present<br>ts estimated in t<br>he 1%, 5%, 10% <br>rade 10 Student|0.61"<br>(0.39)<br>ed in the previous<br>he previous multi<br> levels is denoted <br>s.|0.32<br>(0.48)<br> table; these are <br>nomial lagit mode<br> “*, **, and *, re|-0.49<br>37)<br> calculated by a<br>ls. Standard<br>spectively.|
||Tracking|No Tracking|| F(e0,80)|
|---|---|---|---|
|Males|a1?<br>(3.6)|33.03<br>(4.08)|1.077|
|Ferales|rey<br>G64)|af2<br>94)|1.131|
|FfSs0 80)|1.061|1.01||
|.<br>Guantile<br>o2|o4|0.6|0.8|diff.<br>in coets<br>o8-o2|
|---|---|---|---|---|
|F<br>-42.19"*<br>emale<br>(12.63)|-36.47*<br>(12.09)|-40.42°"<br>(13.73)|-471.49"*<br>(12.44)|74<br>(15.6)|
|.<br>14.3<br>Some Tracking forMath Classes<br>(11.94)|6.6<br>(10.25)|3.66<br>(6.59)|3.57<br>6.24)|10.73<br>(9.52)|
|Female x Same Trackin<br>22.6<br>3<br>(14.62)|afar<br>(13.65)|24.76"<br>(14.66)|20.00°*<br>(12.57)|6.29<br>(15.65)|
|Other Controls<br>Yes|Yes|Yes|Yes||
|Constant<br>ao9.62""<br>(41.24)|466.967"<br>(39.05)|Aga<br>(40.24)|570.57<br>(37.21)|180.95"<br>(30.677)|
|Number of Observations<br>2970|2970|2970|2970||
|Average R-Square<br>ta|ra|ra|ra||
|;<br>“4.59<br>Female +Some Tracking x Female<br>8.18)|“11.2<br>6.82)|-10.66<br>G64)|-13.01*<br>6.53)|3.42<br>(7.86)|
|.<br>36.69"<br>Some Tracking +Some Tracking x Female<br>(13.52)<br>Note: Standard errors are reported in parentheses and signific<br>* respectively. Estimates were calculatetd using 5 plausible v<br>Repreated Replication with Fays(0.5) adjustment were used to<br>Source data: PISA 2OOS Korea, General School Strata, Grade|33.67"<br>(13.18)<br>ance at the 1%<br>alues for esti<br> estimate the <br> 10 Students|33.41"<br>(14.13)<br>, 5%, 10% le<br>mates of achiev<br> standard error|a2.45**<br>(13.13)<br>vels is denote<br>ernent and Ba<br>s.|-4.44<br>(13.39)<br>d ***, **, and<br>lanced|
||Metropolitan|Urban|Rural|
|---|---|---|---|
|Trackin<br>|563.67<br>|5a0.37<br>|521.04<br>|
|J|(6.53)|(11.2)|(16.69)|
|NoTrackin<br>|616.74<br>|525.51<br>|504.69<br>|
|<br>J|(39.33)|(15.03)|(14.31)|
|Difference|-45.0F|55.06"**|1h.3¥|
||(39,42)|(19.96)|(18.33)|

Note: Standard errors reported in parentheses. source: 4003 PISA Korea Sample, Female Students, General Highschool Strata, Grade 10 Students
In the Korea PISA data, girls’ schools were no more or less likely to be a school with tracking than boys’ schools or co-ed schools. Also, since we control for co-ed schools, it is unlikely that the measured association between achievement and tracking, as well as the gender difference in this association, reflects being at a girls school. Furthermore, schools where a student’s academic record is important for admission (our proxy for schools subject to equalization) were no more likely to be a school with tracking than a school where academic record was not important to admission. As a result, it is unlikely the association between achievement and tracking reflects equalization.

Alternatively, being in a tracking school might have an immediate effect on mathematics achievement through a student’s attitude or motivation towards mathematics. It is plausible that this effect would differ across the genders, and a follow-up analysis using PISA 2003 could gather more evidence relating to this.

Consequently, while we can not conclude from our analysis that tracking has an effect on student achievement, we do find a very interesting pattern in the 2003 dataset, and our results are especially interesting due to the gender difference aspect. Given the ongoing debate around the Korea’s equalization policy, these results expose the need for more research on tracking in Korea with an emphasis on gender differences.

References Ammermueller, A. and J. Pischke (2006), “Peer Effects in European Primary Schools: Evidence from PIRLS”, National Bureau of Economics R Working Paper 12180, Cambridge, MA.

Betts, J. and J. Shkolnik (2000), “The Effects of Ability Grouping on Student Achievement and Resource Allocation in Secondary Schools”, _Economics of Education Review_ 19 1 - 15 Duflo, E., P. Dupas, and M. Kremer (2008), “Peer Effects and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya” Educators without Borders (2007), “Are Korean Kids Smart or Working Hard? Some Reasons behind Top-level achievers of Korean Students”, Occasional Paper No. 1, Educators without Borders, Seoul, Korea Fertig, M (2003), “Educational Production, Endogenous Peer Group Formation and Class Composition - Evidence from the PISA 2000 Study”, IZA Discussion Papers, 714, Bonn Gibbons, S. and S. Telhaj (2005), “Peer effects and pupil attainment: Evidence from secondary school transition”, London School of Economics, mimeo.

21
Hanushek, E. and L. Wößmann (2005), “Does Educational Tracking Affect Performance and Inequality? Differences-in-Differences Evidence Across Countries”, _NBER_ , Working Paper 11124.

Kang, C. (2007), “Classroom Peer Effects and Academic Achievement: QuasiRandomization Evidence from South Korea”, _Journal of Urban Economics_ , Vol 61, No. 3, pp 458 - 495 Kang C, C. Park, and M. Lee (2007), “Effects of Ability Mixing in High School on Adult Earnings: Quasi-Experimental Evidence from South Korea”, _Journal of Population Economics_ , Vol. 20, No. 2, pp 269-297 Kim, T., J. Lee, and Y. Lee (2008), “Mixing versus sorting in schooling: Evidence from the equalization policy in South Korea”, _Economics of Education Review_ OECD (2003), _PISA 2003 Technical Report_ , Paris: OECD OECD (2005), _PISA 2003 Data Analysis Manual_ , Paris: OECD OECD (2007), _PISA 2006 Science Competencies for Tomorrow’s World Volume 1: Analysis_ , Paris: OECD Schneeweiss, N and R. Winter-Ebmer (2005), “Peer Effects in Austrian Schools”, Department of Economics, University of Linz, Working Paper No. 0502 Zimmer, R (2003), “A new twist in the educational tracking debate”, _Economics of Education Review_ , 22 307 – 315 22