The effect of track mobility on inequality of
educational attainment
A difference-in-difference analysis
Sebastian Mokross, B.Sc.
Master Thesis, Research Master Social Sciences University of Amsterdam
Supervisor: Second Reader:
s.mokross@gmail.com
Abstract
Track mobility, the possibility of a student’s transition from one track to another after initial placement plays is an institution aimed at increasing the level of equality of educational opportunity. In order to assess whether or not this is actually achieved a difference-in-difference approach is used, analysing the impact of different measures of track mobility in a comparative study using data on 15 German federal states and the Netherlands. Results indicate that track mobility does in fact decrease inequality between the fourth grade and the age of 15, but at the same time has a negative effect on test scores. Results on the effects after the age of 15 are inconclusive.
1. Introduction
In many educational systems students are allocated to hierarchically ordered tracks at some point during their educational career, usually at the time of transition to secondary education. The allocation is meant to be ability based and each educational track leads to specific eligibility for subsequent education. While research shows that the benefits of this practice are small, if any at all and that it increases inequality of educational opportunity, the dependency of a student’s educational attainment on socioeconomic background characteristics (for overview see Brunello & Checchi, 2006), very few countries have decreased the level of tracking over the last sixty years. The impact of another related institution, track mobility, the possibility of a student’s transition from one track to another after initial placement, has received far less attention, even though it may have a significant influence on inequality of educational opportunity. Studies so far were limited either to estimating the number of track changes (Bellenberg & Klemm; 1998; Bertelsmann-Stiftung, 2012), qualitative research centred around the effect on student well-being (Marsh et al., 2001; Kramer et al., 2009; Wouters et al., 2012) or case studies looking at the effect on inequality in only one or two countries (Jacob & Tieben, 2007; Tieben, 2011). The field lacks a comparative study on the effect of track mobility on educational inequality; a void that this study aims to fill using the number of actual track changes as a measure of track mobility. Based on previous research two competing hypotheses are derived, expecting either a decrease or increase in the level of inequality due to track mobility. In order to test these hypotheses several sets of analyses are carried out, using a regression and difference-in-difference models. Each of the sets is comprised of several separate models, using either total mobility as a measure, or separate measures of up- and downward mobility. In the empirical part the main focus rests on the change in the level of inequality from fourth grade until the age of 15, using PIRLS and PISA data. Additionally the effect of track mobility on inequality regarding final educational attainment is studied in another set of models. For the analysis data on the Netherlands and 15 of the 16 individual German federal states is used.
In the following the societal relevance of the issue is shortly discussed together with general theories on inequality of educational opportunity. The third part focuses on tracking and its influence on inequality of educational opportunity. Terminology is briefly explained, followed by a description of tracking policies in two states and an extensive review of the literature on the issue. The fourth part, discussing track mobility, is structured similarly. After a short introduction, the four kinds of intra-secondary transitions are presented, the rules and
regulations regarding track mobility in the two previously mentioned states are described, and the literature on the issue is extensively reviewed. Based on the existing literature, in the next part two hypotheses are derived. The sixth part introduces the empirical part. Reasons for using a difference-in-difference design are briefly discussed and data sources are described. The model is introduced step by step, describing variables and the conceptualization of indicators as they are introduced. Results are presented in the seventh part, starting with descriptives of main variables. After that the results of the regression and difference-in-difference models are introduced, followed by a short discussion of possible violations of assumptions for OLS regression.
2. Inequality of educational opportunity
Education is often regarded and advertised as the engine of social change and mobility. If one is just willing to work hard enough, the meritocratic educational system will reward him or her in terms of educational degrees and career opportunities, regardless of social origin. Improving equality of opportunity often is regarded as one of the core tasks of an educational system (Kerckhoff, 2001; Van de Werfhorst & Mijs, 2010). There is an ongoing discussion if modern educational systems really succeed in doing so (for overview see Breen & Jonsson, 2005). With education becoming universally affordable in most industrialized states and ever more people staying in education longer, it was expected that the influence of socioeconomic background on educational outcomes would disappear. Maximally maintained inequality theory (Raftery & Hout, 1993) argues that the influence of social origin declines for vertical transitions that have become universal for students from higher class background. As the transition from primary to secondary education has become universal and often compulsory, educational expansion should have caused such a decrease. An early large scale study by Shavit & Blossfeld (Shavit & Blossfeld, 1993) found that the association between origin an educational transition did not weaken. Subsequent studies with access to newer data sources with larger samples however found that in fact the expected decrease could be found (Breen el al., 2009).
These findings however only show one aspect of inequality of educational opportunity and completely disregard horizontal differentiation. Effectively maintained inequality theory (Lucas, 2001) claims that even given universal transitions inequality still remains due to qualitatively different kinds of educational tracks on the same level. The transition from primary to secondary education might have become universal, which would
indicate perfect equality whilst there is a high level of differentiation within secondary education, as it is the case. The same transition can thus produce very different opportunities for students as the degrees from different secondary tracks usually have a different value on the labour market and allow students to enter different kinds of post-secondary programs. As the allocation to these different tracks does not happen independent of social origin, inequality of educational opportunity still is a relevant issue.
In the recent past policy makers in several German federal states have reacted to the challenges posed by tracking and started reducing the number of tracks. The issue of track mobility still remains as tracking has not been abolished completely and continues to play a role even though the number of tracks has decreased.
3. Tracking
Most countries allocate students into different tracks at some point during secondary education, but national systems differ considerably. In this study tracking refers to the practice of separating students in different school types, featuring different curricula, leading to different degrees, usually being characterisable as either general or vocationally oriented, common in Europe and does not include what is often called ability grouping or streaming, the practice of allocating students to more or less demanding courses for a single subject in a fully comprehensive system, common in the US (Hallinan & Kubitschek, 1999). The allocation to different tracks often happens at the end of primary education and is meant to be ability based. In order to show what tracking entails, what its effects are and how it influences equality of educational opportunity, this section features a description of how tracking works in two systems, followed by a summary of the effects of tracking on efficiency and equality of educational opportunity, and a detailed description of how track choices are made and what these choices mean to students.
3.1. Description of Bavaria and North-Rhine-Westphalia
All states in this study have in common that they track at a rather early age and most have three separate tracks. Beyond these similarities, there are some differences between systems. To understand these differences and tracking in general, let’s take a look at the possibilities students have after finishing primary school in the German federal states of Bavaria and North-Rhine-Westphalia (NRW). In Germany, federal states are responsible for education
and thus have a lot of freedom in arranging educational systems (KMK, 2000). States are bound however to have a tracked system and due to convention and agreements, most educational systems are rather similar in their basic structure. Regarding this basic structure they only differ in the timing of tracking, the number of tracks and the existence of a comprehensive track in secondary education. Based on these characteristics states are sometimes grouped into clusters. The two states we are looking at belong to the same cluster (Bertelsmann-Stiftung, 2012).
Both start tracking at the end of the fourth grade. At this point students are commonly ten years old. Since the 60s the three main tracks Hauptschule, Realschule and Gymnasium exist in their present form (for more extensive review of the German system see Schneider, 2008; for Bavaria see BayEUG, 2000; for NRW see Schulgesetz NRW, 2005). The Hauptschule, the lowest ranking track, is aimed at providing students with the basic knowledge and skills for the labour market. It takes five years to complete. The Realschule is a vocationally oriented, intermediate track, taking six years to complete. The Gymnasium is the academically most demanding track and prepares for further education at university. It takes nine years to complete. Recent reforms made it possible for students to attain the Abitur after eight years, but these reforms do not affect the individuals in this study. In the late 70s the Gesamtschule (comprehensive school) was introduced in NRW, but enrolment does not exceed 15% of students per year.
After four years of primary education students are allocated to the different tracks based on their academic ability. In NRW every student receives a non-binding teacher recommendation in addition to his or her grades in the final diploma. Teachers’ recommendations are not purely based on grades, but also on their professional opinion which school type might be best suited for a student, considering a variety of factors. In Bavaria recommendation is supposed to be based upon on grades more strictly. In both systems parents can decide against the recommendations, but some minimal requirements exist for the two most demanding tracks. In Bavaria students also have a chance to take entrance exams if the do not qualify for admission based on their grades.
3.2. Effects of tracking on inequality of educational opportunity
The basic idea of tracking is to make learning more efficient by teaching students in more homogeneous groups (Cook, 1924; Coxe, 1936). Students are meant to be allocated to a learning environment that best fits their abilities and needs. Slower learners would have the
chance to learn at their own speed and faster learners would not be held back. Additionally, the link between school and labour market should be strengthened, smoothening the transitions from school to work. There is however little to no evidence that tracking improves educational outcomes, while on the other hand, there is evidence that tracking does increase inequality of educational opportunity, the degree to which a student’s achievement is determined by his or her socioeconomic background (Gamoran & Mare, 1989; Van de Werfhorst & Mijs, 2010; Nam & Huang, 2009). Only the positive effect on reducing youth unemployment has been proven to exist (Breen, 2005). Studies show that the level of inequality increases as tracking takes place earlier and there are more tracks available (Bol & Van de Werfhorst, 2013). Several studies have confirmed these findings in different contexts (see Brunello & Checchi, 2006 for overview). Studies on the issue operationalize socioeconomic background in several different ways. Measures that are often used are parents’ level of education, parents’ occupation, culturally significant possessions, such as the number of books a family owns, composite measure derived from the previous indicators, or belonging to a certain social class or strata. While each of these factors may have its unique way of influencing a student’s educational chances, they are highly correlated and all have a positive influence on test scores as well as final educational attainment. In the following, if not further specified, socioeconomic background refers to all of these factors.
In order to understand how tracking affects equality of educational opportunity, we first have to look at the mechanisms at work when it comes to making the decisions which track to choose and then analyse what being in a certain track means for a student. When approaching the issue on the individual level, there are two kinds of effects that determine a student’s or the students’ parents’ decision, primary and secondary effects (Boudon, 1974; Jackson et al., 2007).
Primary effects summarize the influence of socioeconomic background on academic performance. Theoretically school should benefit each student equally well, so it is not immediately clear why children with more affluent and better-educated parents should have an advantage when it comes to being placed in a higher track. An important factor is the head start students have at the beginning of primary school. Better educated parents are more likely to stimulate their children intellectually even before school starts, by simply reading to them for example or buying more cognitively stimulating toys. Bowey (Bowey, 1995) showed that differences in cognitive ability due to socioeconomic background already exist at pre-school age and are a good predictor for abilities at the end of first grade. Increasing these differences at the very beginning of education is the Matthew Effect (Merton, 1968), saying
that the ones, who already have plenty, will be given a lot more. In the case of students, in the first years of their educational careers, this translates to students from better educated parents hit the ground running and can benefit more from school than their peers, thus making more progress early on (Luyten & Bruggencate, 2011). After this initial phase, students from more affluent background still have advantages. Being able to afford out of school tutorship, having access to a private computer or other multimedia devices and participating in other intellectually stimulating activities depends on the parents’ financial situation. The education of parents also has an important influence on a student’s development during education. Looking at primary school children in Norway, Hassan (Hassan, 2009) found that better educated parents are a lot more likely to help their children with their homework or supervise them doing it, while it was found for lower educated parents that they actively refrain from doing so.
Additionally, other kinds of involvement in school activities, such as PTA meetings, for example are much more likely to be attended by highly educated parents (Hill et al., 2004). This active involvement is negatively correlated with behavioural issues (Mc Neal, 1999), whilst having a positive influence on a student’s academic self-concept (Gonzales – DeHaas et al., 2005; Grolnick et al., 1991). Behavioural issues being an active hindrance for academic success and one’s academic self-concept having a positive effect on academic ability (Topor et al., 2010), the gap between students is widened. Parent involvement also has a positive influence on students’ career aspirations (Trusty, 1999) and student teacher relationships (Hill & Craft, 2003). While it is not certain to what extent career aspirations influence students’ effort and abilities at primary school age, student teacher relationships were found to be important at a very young age (Birch & Ladd, 1997). Student - teacher relationships are also directly influenced by parents’ social class and their cultural capital (Bourdieu, 1973). As children pick up values, norms, way of speaking, or habitus to put it in Bourdieu’s words from their parents, they unconsciously adopt their cultural capital, which in turn is recognized by teachers and positively reacted upon (Kalmijn & Kraaykamp, 1996). Thus students from privileged backgrounds have a better chance at higher grades and thus a better chance of matching the criteria for a higher track. Primary effects, especially the head start, have a stronger influence on track placement in systems track earlier because school as a mediocritizing agent has less time to level the playing field.
Secondary effects describe the mechanisms by which students and their parents’ educational choices are affected regardless of cognitive ability, but directly related to their socioeconomic background (Breen & Goldthorpe, 1997; Erikson & Jonsson, 1996). Rational
choice approaches are most commonly used in explaining these differences and can be expressed in terms of perceived costs and perceived benefits. While the actual costs for choosing a secondary track that takes longer to complete are rather small in most developed countries, the relative costs may differ according to socioeconomic background. Staying in school longer means that students enter the workforce later and start earning money later. Actual costs can increase when tuition has to be paid as well as housing away from home during tertiary education. While costs regarding university do not matter immediately when decisions about secondary track choice are made, the highest track usually leads to entering university or another lengthy training process. At some point these costs may endanger the financial security of a low-income family, especially when the outcomes are uncertain, which brings us to the benefits. The perceived benefits are twofold, firstly there is the perceived chance of success and secondly the perceived benefit of success. The objective probability of success for students of equal cognitive ability from different class backgrounds should be the same, but it may be perceived differently. Parents who attended higher education or at least higher tracks during secondary education themselves are more likely to see it as something that can be accomplished compared to people who have never experienced it. Accordingly, parents from lower class backgrounds take the risk of failure a lot more serious when it comes to deciding to enrol their child in a higher track (Gambetta, 1987) and vocational education is seen as a means of reducing the risk of failure and unemployment (Arum & Shavit, 1995). Similarly, the perception of future benefits in terms of earning potential and job security might differ as well. The effect of additional schooling or a higher degree may be underestimated by someone who has not experienced it him- or herself. These factors show how chances and benefits of completing a more demanding track can be judged differently and even the same perceived chances of success bear a greater perceived risk for students form lower class backgrounds.
A related factor that also uses rational choice theory is relative risk aversion (Van de Werfhorst & Hofstede, 2007; Davis et al., 2002), stating that students’ aspirations derive from using their parents as reference and parents having the primary goal of avoiding downward mobility for their children, meaning they try to achieve the level of education their parents did. All educational choices are made in order to ensure that this goal is achieved, which becomes especially important at the points when choices about educational tracks have to be made, which determine future life chances. While people from all social classes should be equally concerned about this, the implications are that children from a higher class
background have to stay in school longer and aim for better tracks to maintain their parents status.
In addition to the different views on costs and benefits due to social class, the information on the chances to succeed in a given school type parents and students receive differs for students with the same abilities. Even in systems without a binding advice from the primary school, a teacher’s advice at the end of primary school may still be considered the most objective and complete assessment of a student’s chances. As we have seen when discussing primary effects, teachers can be biased towards awarding more attention to students from higher socioeconomic backgrounds and looking on them more favourably in general. This becomes particularly important at the point of track choice as teachers’ recommendations also have been found to be biased (Ditton et al., 2005; Driesen, 2005; Luyter & Bosker, 2004), tending to give more positive advice to students from higher social strata in comparison to their peers with the same grades. This advice also is likely to be followed more closely by lower educated who do not have as much faith in their own ability to judge their children’s ability accurately. So secondary effects are stronger than what might be expected due to relative risk aversion alone as the information upon which decision should be made is biased itself. As a result, the academic ability of students varies greatly between students who have received the same recommendation for a given track at the end of primary education (Bos et al., 2004). Even though students from different federal states are grouped together, which might account for of the heterogeneity, differences are too big to be explained by this factor alone and standards should be similar across sates. This might be an indication as to why tracking fails to be more efficient, as groups are not homogenous enough. To sum it up, children from a higher socioeconomic background are far more likely to follow a higher track than their peers and this is only partly due to differences in actual academic performance.
The most prominent difference between the tracks is that they lead to different degrees. But even before finishing a track and attaining a degree, differences exist. Curriculums differ between tracks and are more demanding in higher tracks, indicating that students in these tracks would learn more within the same amount of time. While peer effects are already present during primary school (Ammermueller & Pischke, 2006) and neighbourhood peer effects have been found to influence educational decisions (Bobonis & Finan, 2009), they become more important after tracking has taken effect (Hanushek et al., 2003). Peer effects have a twofold influence on students’ academic development. Firstly, shared norms and values are reinforced. Regarding education, this refers to students’ attitudes
towards the school as an institution and the importance of learning. As we have seen previously, there is positive correlation between a positive attitude towards school and achievement, while there is a negative correlation with behavioural issue, making it more likely to be placed in a higher track. Thus schools and classes should be a lot more homogeneous in terms of attitudes than it was the case in primary education, increasing the reinforcement of norms and positive attitude or negative attitude depending on which school type one visits. Secondly, students stimulate each other academically during classroom interaction and benefit from each other’s abilities. These effects are also supposedly stronger as groups get more homogeneous. While most researchers agree that peer effects that increase differences exist in some form, some aspects of it are contested. Some researchers found that peer effects do not have a positive influence on high ability students, but only a negative one on low ability students (Zimmer, 2003). This would however still indicate that differences increase. A different study on the other hand also indicates that all students can benefit more from students with similar IQ (Dobbelsteen et al., 2002). Similarly to the influence on attitudes towards education, educational expectations are also influenced by track choice (Buchmann & Park, 2009), adjusting them according to the track one is enrolled in.
The overwhelming amount of evidence shows that educational tracking does increase the inequality of educational opportunity via a plurality of mechanisms. This happens in terms of final educational attainment as well academic ability during education.
4. Track mobility
Track mobility, often also referred to as permeability or student choice (Kerckhoff, 2001), is a characteristic of an educational system, describing the extent to which a change from one educational track to another is possible. In some cases permeability might also refer to transitions between secondary and tertiary programs and to what extent a tertiary program can be followed with multiple kinds of secondary diplomas, in this study however it refers specifically to intra-secondary transitions, changes from one secondary track to another. In the following the different kinds of track changes are shortly explained. Then the rules and regulations regarding track changes in Bavaria and NRW are presented and descriptive statistics for all states are shown. After that the previous research on track mobility is presented and two conflicting hypotheses are derived from it, assuming either to have a negative or a positive effect on equality of educational opportunity.
4.1. Four types of transitions
Mobility between tracks can happen in three ways, via downgrades, upgrades and supplements. Downgrades are track demotions that can happen during a school year, but mostly happens at the end in order to prevent class repetition, while it also may be used in anticipation of future results and more strategically, which is discussed later. In some cases downgrades may be forced upon students, for example students who already repeated a class.
Upgrades are the counterpart to downgrades and mostly happen at the end of the school year before the end of an educational track. Upgrades are designed to allow upward mobility for students as early as possible in the educational careers in order not to fall behind too much compared to students in higher tracks. Many systems demand some kind of proof that a student has the ability for a higher track, either in the form of grades, teacher recommendations or entrance exams.
Supplements, as upgrades, are an upward move. Unlike upgrades however, they take place at the end of a track. Students thus attain a diploma and then continue in the next higher track.
These are the kinds of intra-secondary mobility used in the most recent studies on the issue (Tieben, 2011). Besides these transitions used in the literature, there is a fourth kind that is important to mention here, the transition out of the educational system, leaving school without the intended diploma. While it is not an intra-secondary transition, as it does not happen within the secondary educational system, it is another option students have, that has to be kept in mind. In order to visualize the identified forms of track mobility, the following graphic depicts various forms of transitions possible in educational system that exists in NRW, Bavaria and many other German states.
Graphic 1, Various types of transitions between secondary tracks
Graphic 1 shows the three-tiered educational systems as it exists in several German states. The numbers next to the model of the system, indicate grade levels. Upgrades are depicted by a full green arrow, downgrades by a dotted red arrow and supplements by a dashed yellow arrow. It shows an upward transition from the end of eighth grade at the Realschule to the beginning of eighth grade at the Gymnasium, an upgrade including class repetition. It also shows an upgrade without class repetition from the end of fifth grade at the Hauptschule directly to the beginning of the sixth grade at the Gymnasium, skipping an intermediate step to the Realschule. The transition from the end of the sixth grade at the Gymnasium to the beginning of the seventh year at the Realschule shows a downward move that was used to prevent class repetition, while the downward move from the Realschule to the Hauptschule shows a downward move including class repetition. The supplements show a transition after finishing the last year in the track and attaining a diploma.
4.2. Rules and regulations in Bavaria and NRW
Again, we take a look at Bavaria and NRW. As with tracking in general, both systems share some similarities when it comes permeability as well. In both states transitions are possible throughout the part of secondary education during which two or more tracks are available. Curricula of all tracks are aligned with one another, meaning that the subjects taught and the content of the subjects is as similar as possible, taking into consideration the different levels of difficulty. In the first two years of secondary education special regulations apply.
In NRW the first two years are a phase of increased monitoring regarding a student’s possibility of track mobility. In the laws and regulations (Schulgesetz NRW §46; MSW NRW, 2006: p. 5) the focus rests on upward mobility and demands that at the end of every semester the possibility of changing tracks has to be discussed by all teachers. Rules governing when a student is entitled to being accepted at a higher school type have long been clearly spelled out in terms of GPA and special requirements in certain subjects. Schools however have the freedom to use less rigid criteria when admitting new students. Upgrades and supplements are possible in two ways, students can either repeat the grade at the new school or continue in the next grade level, the second option being the more common one. Upward moves never are compulsory, only track demotions can be forced onto students in case of multiple class repetitions. Schools however do not have to demote students, but can decide on a case-by-case basis.
In Bavaria (RSO § 26 – 35) students are also monitored more extensively during the first two years, but schools are not required to discuss each student’s possibility of track mobility. For the rest, rules and regulations are almost identical to the ones in NRW, only GPAs required for upward moves differ slightly.
4.3. Effects of track mobility on inequality of educational opportunity
While track mobility might also have serious implications for equality of educational opportunity, it is a far less researched topic than tracking itself. Tracking has long existed as an educational institution and has been a feature of numerous national systems since they have been established in their modern form. Mobility between tracks has not been an issue in the beginning and it was assumed that the interests of society were served sufficiently if ‘normal’ educational careers were focussed upon, meaning following the track one was allocated to after primary education. The sputnik crisis in 1957 (Picht, 1965) and an increased societal concern for social mobility and equality of educational opportunity lead to changes in educational systems, especially changes in regulations regarding tracking. In the case of Finland and Sweden the systems were de-tracked and compulsory, comprehensive schooling was prolonged (Pekkarinen et al., 2006; Meghir & Palme, 2004). Other states, such as Germany (Cortina et al., 2001), including NRW and Bavaria, and the Netherlands (van der Heiden, 2004) went a different way. While still tracking at a very early age, it was tried to increase permeability between the tracks by converging curricula and implementing other rules and regulations making it possible to switch between tracks after having made an initial
choice. While increasing equality of educational opportunity was presented as the main goal, the reforms were also meant to increase efficiency (Cortina et al., 2001). Equality of opportunity was thought to be increased as students and their parents should be able to correct mistakes that were made at the initial placement in a secondary track and also react to changes in a student’s academic abilities. Efficiency was thought to be increased by making learning groups more homogeneous as students who were especially strong academically would be upwardly mobile and the ones who performed far below average were downwardly mobile. It was realized that track allocation was not working perfectly and students should be able to react once they realized the school type they are visiting is a bad fit for them, given their academic abilities. This way a highly tracked system could be kept while chances for students from all social backgrounds were still equalized and the system was made more efficient. Today policy advisors and makers still share this view and try to further increase permeability (Heinrich-Böll-Stiftung, 2001; VO-raad 2012).
Track mobility has been institutionalized and an issue since more or less 40 years, still there are no studies yet dealing explicitly with the effect of permeability on equality of educational opportunity in terms of test scores or final educational attainment. Early research was mainly concerned with the question to what extent track changes were happening at all (Kemmler, 1976) and it is still an issue, allowing for more recent studies focussing on the mere number of students (Bellenberg & Klemm, 1998, Bertelsmann-Stiftung, 2012). This provided policy makers and researchers with an idea of to what extent the policy measures taken attained the goal of increasing permeability, but gave little information on the real ends to which these measures were instituted, increasing efficiency and equality of opportunity. Studies in the late 80s included students’ socioeconomic backgrounds in their analyses (Bofinger, 1985; Kemnade, 1989) and describe factual school careers of students, but do not give an indication whether education has become more efficient or meritocratic. The first studies, which give an indication how inequality of opportunity was influenced, hint that track mobility is influenced by socioeconomic background and the mechanisms might be the same as the secondary effects discussed earlier (Henz, 1997; Hillmert and Jacob, 2005). The study by Henz shows that children of better-educated parents are more likely to be upwardly mobile, while their peers from less educated parents are at higher risk of being downwardly mobile. It also shows that the effect of socioeconomic background has decreased over time. The question however remains if this is due to the reforms as effects started decreasing before the reforms were implemented.
Newer research (Tieben, 2009; Jacob & Tieben, 2007) takes a closer look at the mechanisms governing track changes. The main finding is that relative risk aversion also seems to be one of the mechanisms when it comes to intra-secondary transitions. They found that not only the parents’ absolute education was of influence on students changing between tracks, but parents’ relative education also was an important factor when it comes to upward moves. In her study on the Netherlands, Tieben found that the effects of parents absolute education disappear when parents education relative to their children is included, interpreting that as a clear sign of students trying to reach at least their parents level of education. She initially also found the same effect for downward moves, but after including initial track placement the effect disappeared and downward moves were seemingly neither influenced by parents’ absolute nor relative education. The study by Jacob and Tieben found similar effects in Germany. In Germany however also downgrades seem to be influenced by parental education even after controls have been added. The models in both studies showed that before controls of initial placement and parents’ relative education were included, all transitions were socially selective in both countries and favoured children of better educated parents. When looking at the findings, it has to be said that they use data on students born between 1939 and 1971 (Jacob & Tieben, 2007), and 1915 and 1986 (Tieben, 2009) respectively, using cohort dummies to correct for period effects. The situation today might thus differ, but their findings are a good starting point as it is the most sophisticated quantitative analysis on the influence of track mobility on inequality of educational opportunity so far. Their approach of grouping all German federal states together also raises concerns as we have seen above that there is considerable variation between German states regarding permeability.
Another important finding from these studies is that upgrades and supplements seem to be similarly influenced by socioeconomic factors. The chances for either of the two forms of upgrades to happen is about equally big and the controls have the same effect. In the Netherlands, variation is a little bigger, but this is likely due to the extreme small number of students who opted for upgrades in the sample. From a theoretical point it might be reasonable to assume differences between the two, as supplements are less risky because the chance of total failure is not given as one degree is already attained. Thus it might be more appealing to children from lower class backgrounds, but there is no indication. The data only shows that there might be different mechanisms at work regarding up- and downgrades.
Showing that relative risk aversion plays an important role not only when it comes to initial track placement, but also regarding track changes, gives reason to assume that the
other factors discussed previously also play a role. The bias of teachers towards children from better educated parents is likely to persist during secondary education and thus influence teachers decisions when it comes to giving recommendations for track changes. Similarly, parents and students might still evaluate the risk and possible benefits differently when it comes to transitions in the same way they do when it comes to initial track choice. Less educated parents and their children also might not regard upgrades as necessary for reasons apart from rational choice discussed earlier, such as career aspirations or just not being familiar with a given educational track. Theoretically the effects could be similar regarding downgrades as parents have the possibility of opting for class repetition in order to prevent their children from being demoted to a lower track, but the fact that at some point downgrades are unavoidable might be a reason different effects have been found. Another factor that should be especially important when it comes to downgrades is that track demotions are not only an option when students have a lower academic ability than is sufficient for a given track, but can also be used as a disciplinary measure (Freyberg & Wolff, 2005: p. 5).
The presented studies however do not tell the whole story. It is shown that the transitions themselves are socially selective. It is however not clear how students react to track changes and how it influences test scores and final educational attainment. Upgrades and supplements might not necessarily lead a degree and can end in dropping out of the educational system with no degree or the one previously already attained. Just as well, downgrades might lead to better performance, as students are not overburdened any more. The effect of transitions on performance might be socially selective in nature as well and students from a lower socioeconomic background might benefit more. There are two recent qualitative studies that look at track changes as a process and try to answer some of these remaining questions. Wouters et al. (Wouters et al., 2012) look at how downgrades influence the academic self-concept and performance of students in Belgium. Liegmann (Liegmann, 2008) extensively looks at the process of track changes from starting to think about switching until a year after the track change and also discusses institutional factors.
Wouters et al. test the big fish little pond effect (BFLPE) with a sample of 2747 students from Flanders and track students during grades seven until twelve. The BFLPE originally developed by Marsh (Marsh & Parker, 1984) assumes that comparing one’s own performance to one of his or her immediate peers determines one’s academic self-concept. As we have seen previously academic-self concept has been found to have a strong influence on performance. When applying the effect to track changes it is expected that students who are
performing way below average in their class and thus have a poor academic self-concept, would benefit from downward moves as they would be relatively smarter compared to their previous position in class. As a result their academic ability should also be improved. It was found that the academic self-concept of students who switched to a lower track indeed improved. On the other hand their academic achievement suffered from the change and test scores worsened. A similar study on students in the German town of Hamburg (Roeder & Schmitz, 1995) found that even though students’ achievement might suffer, they, students who opt for a downgrade do better in the long run than comparable peers who choose to repeat a grade. Track demotion might thus have a negative effect on achievement, but might still be the better alternative to class repetition.
In her study on 42 students from NRW, Liegmann investigates what the reasons for track changes are and how they are perceived by students, using interviews with the students. While not focussing on socioeconomic differences, some of her findings show that factors that correlate with socioeconomic background influence the decision making process when it becomes clear that a track change might be possible or necessary. Regarding moves in both directions students’ and their parents’ aspirations play a big role, making it more likely for children of higher educated parents to opt for upgrades or choose class repetition over track demotion. Students for a big part also value their teachers opinion on what move would be best for them. As shown before, aspirations as well teacher recommendations are influenced by parents’ educational level. Peer effects, most prominently the loss of friendships also play a big role, but do not seem to be socially selective. When looking at how they are doing after transitions, similar effects as the ones described by Wouters et al. were described regarding downgrades. Some students succeed in initially getting better grades, this however can not be regarded as an increase in academic ability, but rather as a new grading scheme applied to the same ability. The study does not follow students long enough to analyse the long term effects of downgrades over the educational career. The success rate of students who were upwardly mobile differed greatly, resulting in two out of 13 students to drop down to their old school shortly after the upgrade.
An interesting pattern emerged as the author grouped different kinds of upwardly and downwardly mobile students. These groups differ regarding their motivation and how they deal with the changes. The most promising group, which she labelled ‘focussed on upward social mobility’ (Liegmann, 2007: p. 228), is the one with the best chances of success at the new school. All of them have clearly defined goals, are not discouraged by initial setbacks and show the most commitment in terms of time spend studying. This group consist of five of
the 13 upwardly mobile students. The remarkable thing is that all of these students have a migratory background. As mentioned, the study did not focus on socioeconomic differences and from a migratory background, socioeconomic status can not be inferred, it does however show that groups that have been discriminated at the time of first selection do better than average after an upward move. As the sample procedure used did produce a representative sample and the sample itself is very small, it is not possible to generalize from her findings. Still it is reasonable to assume that groups who are generally less likely to make upward moves due to non-academic reasons have better chances at succeeding after making the transition as they need to show a higher level of academic ability to be willing to make the move.
To sum it up, permeability measures were originally implemented to increase equality of educational opportunity. There is however evidence that transitions themselves are socially selective and show a pattern similar to the one observed when it comes to tracking. It remains unclear what role academic ability plays in the decision making process on track changes and how track changes influence students’ achievement. Regarding downward moves, it has been shown that academic performance does not improve in the long run, but students who are downwardly mobile compared to their peers with similar grades who choose to stay in the higher track. When it comes to upward moves, there is some indication that disadvantaged groups do better after upgrades.
5. Hypotheses
The findings from studies presented above are not conclusive when it comes to the question what the influence of track mobility is on equality of educational opportunity and lead me to formulate two competing hypotheses. The transitions being socially selective lead me to my first hypothesis:
H1: The level of track mobility decreases equality of educational opportunity.
The original idea of fostering track mobility however was to increase equality of educational opportunity and this vision is still shared by policy makers and advisors. Additionally, the number of quantitative studies is rather limited and the qualitative studies show that socially selective transitions might not necessarily lead to increased inequality in terms of test scores and final educational attainment. This leads me to the formulation of my second hypothesis:
H2: The level of track mobility increases equality of educational opportunity.
6. Research Design
For the empirical testing of these hypotheses I use two sets of difference-in-difference (DiD) model and present three sets of regression models. The regression models show the level of inequality of educational opportunity at three different points in time, in the fourth grade, at the age of 15 and at the end of one’s educational career. Using the difference-in-difference models, I look at the change in the level of inequality from the fourth grade to age 15. In the following, methodological considerations for using a difference-in-difference model are briefly discussed. Then the data is presented. After that, the models are introduced and their variables and the necessary data manipulation described. Lastly, assumptions of the difference-in-difference methodology and their possible violations are discussed, as well as other methodological issues.
6.1. Difference-in-difference
When analysing the effects of institutions on educational inequality, difference-in-difference models are often used (Ammermueller, 2005; Hanushek & Woessmann, 2005; Waldinger, 2006; Van de Werfhorst, 2013) as they enable researchers to model the influence of institutions dynamically. This makes them more suitable than purely cross-sectional models, which can only be used to study inequality statically, at one point in time. Using cross-sectional models produces information on different levels of inequality of opportunity in educational systems and how these correspond with institutional factors. They are however only a snapshot and usually disregard pre-existing levels of inequality. When looking at inequality of educational opportunity at age 15 for example and one awards all the differences between systems to institutional characteristics, such as level of tracking or track mobility, one disregards the level of inequality at the end of primary education, before the institutional factors even play a role. Difference-in-difference models solve this endogeneity problem by comparing the level of inequality in a population at two different points in time. Two different groups of the same population are identified, and undergo measurement of a characteristic at two points. Before the first measurement none of the groups has received a treatment. After the first measurement, one of the groups receives a treatment. The other
group, not having received the treatment serves as a control group at the time of the second measurement. The difference between the two groups can thus be completely attributed to the treatment. As this basic design of difference-in-difference models is (quasi-) experimental, it has to be adjusted to be applied to compare educational systems and analyse the effect of institutional factors. These adjustments will be discussed when the model is presented, but the basic logic stays the same.
6.2. Data
Individual level data from four different data sets is used, the Progress in International Reading Literacy Study (PIRLS/IGLU-E), the Program for International Student Assessment (PISA/PISA-E), the European Social Survey (ESS) and the European Value Survey (EVS). For the system level variables, data from national statistical services is used. In case of all German states, but Hamburg full information is available on all years during the period from 2001 to 2010 on the number of students per track and grade level and the track they visited the previous year. For the Netherlands, full data on all tracks and track changes is only available for the years 2010 - 2012. For the years 2004 – 2012 data on track changes from the third grade level onwards is available on the number of students per grade year and track as well as the track they visited the following year. To harmonize the data sets and impute the missing data for the Netherlands, several steps were undertaken. It is assumed that the ratio of students changing from a specific track and grade level into a specific track and grade compared to students who change from this specific track and grade level into a specific track and any grade level is constant. Furthermore, it is assumed that the ratio of the percentage of track changes from the first two grade levels compared to the percentage of track changes from the third grade level for a specific track is also constant.
The PIRLS study is conducted with primary school children in the fourth grade, which means that most children in this study are of age ten or eleven. A standardized test on reading ability is administered to at least 4000 students in 150 schools in most countries. Tests are not based on a particular curriculum, but supposed to measure general reading abilities. A questionnaire is also administered to the parents, providing information about the child’s socioeconomic background. PIRLS data from the year 2001 is used. The IGLU-E study is a German version of PIRLS, gathering data on federal state level. Data from the same year is used as from the international version.
The PISA study assesses the skill of 15 year old students in the categories reading, mathematics and science using a standardized test. As in the PIRLS study, background variables are on individual students are also included. Sampling procedures and minimum sample requirements are also similar, with the notable difference that PISA looks at an age group, whereas PIRLS looks at a grade level. Data from the year 2006 and is used. PISA-E is the German version of the study, comparing German federal states. Data from this study is used for the year 2003.
The ESS and EVS are studies looking at a plurality of social issue in many European countries, gathering data in a comparable manner. For this study the information on socioeconomic background and educational attainment for young adults is used. EVS data from the years 2008 to 2010 is used. ESS data is used from the years 2002, 2004, 2006, 2008, 2010 and 2012.
In order to better understand how the data is used and at which points measurements are taken, the following graphic shows the transition of a students through the three tiered German system, highlighting the measurements.
Graphic 2, Timing of measurements
Graphic 2 depicts the way of a student who visits the Realschule after finishing primary school and goes on to take an upgrade after attaining his or her diploma to go to the Gymnasium and upon graduation attain a Bachelor’s degree at university as final level of education. Nearing the end of fourth grade, students take part in the PISA study. At the age of
15, which means at the end of the ninth grade for most students in Germany, the PISA study is conducted. The final level of educational attainment is not a test administered at a single point in time, but describes the highest-ranking degree someone has attained after finishing one’s educational career.
6.3. Models
In the following, the DiD models and variables are introduced. I start by describing a very simple model, only featuring a dependent and one independent variable and subsequently add more independent variables, explaining their function and operationalization as they are introduced. The set of models comparing inequality of educational opportunity between fourth grade and ninth grade is introduced first. After the final model has been introduced, alternative models are presented. Regarding the regression models, only changes in relation to the DiD models are explained, as both are very similar.
(1) yits = β0 + γ1PEits + εits
Model 1 is the simplest model possible and does not feature a difference-in-difference component. The dependent variable y is the test score on PIRLS and PISA tests. The subscripted letters indicated that the score differs per individual (i), is time varying (t), meaning that it has a different value at different points in time, and varies over states (s). Data from the PIRLS study 2001 and PISA study 2006 is used. The test scores from each of the data sets are standardized individually to a mean of 500 and a standard deviation of 100, and then merged. As PIRLS only covers reading abilities, only the corresponding test scores from the PISA study are used. The intercept is marked by β0.
The parameter γ1 is a measure for parental education. It is based on the highest degree
attained by the better educated parent. A score on a continuous scale is derived by using a measure introduced by Buis (Buis, 2007; 2010: pp. 54 - 60). Values are assigned to educational categories so that they best predict occupational status. Information from all waves of the ESS data and the latest wave of the EVS data is used to calculate the scores. Only respondents in the age group corresponding of the age group of parents in PISA and PIRLS are selected. Occupational status is measured on the ISEI scale (Ganzeboom, De Graaf & Treiman, 1992). In the estimation procedure it is controlled for gender, immigrant
status and experience of the respondent, as well as the wave of the study. The relative distance between scores is similar to the institutional duration of the corresponding degrees.
This measure was chosen, as information on parental educational attainment is the only variable included in all data sets. Compared to the years of institutional duration or years of education completed, it offers two advantages. Firstly, degrees with the same institutional duration may signal different levels of cognitive ability or cultural capital. An example would be degrees from Hauptschule and Realschule, which in some federal German states both take ten years to attain. Compared to actual years of education, another advantage is that issues such as grade repetition are not applicable. Secondly, this measure is derived from the ISEI scale, which is based on education necessary for and income generated from an occupation. So the measure by Buis not only covers cultural aspects, but also economic ones and thus is a better proxy for socioeconomic background. The score is derived individually for each country to take into account national differences in values of degrees. Educational categories were collapsed, so that they fit the coding in the PISA and PIRLS data. The scale is standardized with a mean of 500 and a standard deviation of 100, just as the test scores.
The individual error term is captured by the last component, εits.
(2) yits = β0 + γ1PEits + γ2LTts + εits
In model 2 a difference-in-difference component is introduced. The γ2 parameter indicates the
level of tracking. It is coded as 0 at fourth grade level as the educational system in none of the states is tracked at that time. At the time of second measurement at age 15 it is coded as the number of years the system has been tracked. The variable thus depicts the effect tracking has on test scores. As it has been mentioned previously, this design differs slightly from the purely experimental one because all states have tracked systems at the time of second measurement. The difference-in-difference methodology can however be applied as individual states have received a different dosage of the treatment. In the final model, the level of tracking is used as a control in order not to bias the results as the level of inequality is assumed to increase more strongly in the states that track at an early age.
(3) yits = β0 + γ1PEits + γ2LTts + γ3TMts + εits
Model 3 adds the level of track mobility as a variable, parameter γ3. The indicator for the
common to use dummy a variable (Waldinger, 2006; Van de Werfhorst, 2013), or policy based indicator (Bol & Van de Werfhorst, 2013) for the level tracking, it is not applicable when it comes to track mobility. The general structure of an educational system, when tracking starts and how many tracks there are, is regulated by a governing body that makes rules followed by every part of the educational system. Schools neither have any influence on these regulations, nor any freedom when it comes to their implementation. This is very different however when it comes to track mobility. While there are general regulations regarding track mobility, schools have considerable freedom in implementing them. A school accepting students can choose to apply less rigid criteria, thus increasing the level of track mobility. Similarly, schools can choose to enforce rules regarding downward mobility less or more rigid. Also the information schools give students about their possibilities to change tracks may inhibit or increase track mobility. Similarly teachers can have a strong influence as well. As we have seen, even non-binding recommendations can have a big impact on students’ or their parents’ decision making process. Teachers may not be purely focussed on the best fit between student ability and the demands a track poses, but factors such as getting rid of difficult students (Freyberg & Wolff, 2005) or not wanting to lose top students that are crucial for the learning effect for the whole class (Liegmann, 2008) may also play a role. While these factors would not necessarily bias a measure, they would make it a lot less reliable. Additionally, there is the issue of how long it would take a policy measure to take effect. When the number of tracks in a system is reduced or comprehensive schooling prolonged, the effect is immediate. Regarding changes on track mobility policies, it is however to be expected that it would take several years until the policy measures would be fully effective. For example a new policy measure has been recently implemented in NRW, making it obligatory for teachers to discuss the possibility of a track change for each student every six months during the first two years of secondary education. Even when assuming that teachers take this policy measure serious and discuss every case, it will take time until they find the most efficient way and even more time before the behavirioul change leads to a change in attitude, making them get used to flexible educational careers that require constant monitoring and re-evaluation of options. Thus two systems that look alike on paper, may widely differ in practice. As we have seen when comparing Bavaria and NRW, big differences in permeability indeed exist between states with a similar tracking structure and regulations regarding track mobility.
The level of track mobility is measured as the percentage of students that change tracks form one year to the next within the hierarchically ordered system. This excludes
special needs education, comprehensive schools and alternative forms of education. This may introduce a small bias as the definition of and the allocation of students to special needs education differs per country. In most German states for example, students who are in need of special attention in the educational process due to behavirioul problems or learning disabilities, but neither physically nor mentally impaired, are more likely to be placed in special needs education, while in the Netherlands those students would be placed within the Leerwegondersteunend Onderwijs (LWOO), which is part of the VMBO, the lowest secondary track. These students are less likely of making upward moves, and thus lower the level of track mobility. The number of students who changed tracks is divided by the total number of students enrolled. For most states the percentage of students changing tracks is calculated for a specific cohort. This means that students who enter fifth grade the year after the corresponding PIRLS study are followed until they reach the grade level corresponding to PISA. The number of students who changed tracks during that period is added up and divided by the total number of students of the corresponding grade levels combined. The first grade of secondary education is included in this calculation to include students who are mobile and then repeat a grade level. For the regression models using ESS data, students that finished the tracked part of the tracked educational system in 2008 were followed through the educational system.
(4) yits = β0 + γ1PEits + γ2LTts + γ3TMts + δ1LTts * PEits + εits
In model 4 an interaction term between the level of tracking and parental education is added. The parameter δ1 indicates how much stronger the influence of parental education becomes
as the level of tracking increases.
(5) yits = β0 + γ1PEits + γ2LTts + γ3TMts + δ1LTts * PEits + δ2TMts * PEits + εits
The parameter δ2 added in model 5 has a similar function. It is the main component of the
model, indicating the influence of parental education on test scores for different levels of track mobility.
Model 6 introduces the control parameter β1. It is a dummy, coded 0 for respondents from the
PIRLS data and 1 for respondents from the PISA data. The parameter controls for any systematic difference between the two tests uncorrelated with socioeconomic background. In the simple regression models, this variable is not included as it becomes meaningless.
(7) yits = β0 + β1Tt + β2Ss + γ1PEits + γ2LTts + γ3TMts + δ1LTts * PEits + δ2TMts * PEits + εits
In model seven another control, β2 is added. It is a series of dummies, applying fixed effects
for every state. The control is added to account for between state variation not caused by institutional factors, but by what might be referred to as cultural factors.
(8) yits = β0 + β1Tt + β2Ss + β3Ii + γ1PEits + γ2LTts + γ3TMts + δ1LTts * PEits + δ2TMts * PEits +
εits
The final model, model 8, adds a last group of controls. Parameter β3 entails two dummified
controls. The first one controls for second-generation immigrant status. Respondents who were themselves born in the country of testing, but who have at least one parent who was born abroad are coded as second-generation immigrants. The other one controls for the gender of the respondent. Both controls are added to control for a cultural bias that might differ between tests, as well as uneven distributions between samples. First generation immigrants are excluded from the sample as it is not possible to determine at which point in their lives they came into the country and what the effect of the educational institutions were after immigration.
(9) yits = β0 + β1Tt + β2Ss + β3Ii + γ1PEits + γ2LTts + γ3UMts + δ1LTts * PEits + δ2UMts * PEits +
εits
Model 9 is an alternative model that is also tested. Parameters γ3 and δ2 are modified. Instead
of using total track mobility as a measure, only upward mobility is used. The method of calculating the score is analogous to the one used calculating the level of total mobility.
(10) yits = β0 + β1Tt + β2Ss + β3Ii + γ1PEits + γ2LTts + γ3DMts + δ1LTts * PEits + δ2DMts * PEits +
In model 10 parameters γ3 and δ2 are modified again. This time the indicators are based on
downward mobility.
(11) yits = β0 + β1Tt + β2Ss + β3Ii + γ1PEits + γ2LTts + γ3DMts + γ4UMts + δ1LTts * PEits +
δ2DMts * PEits + δ3UMts * PEits + εits
Model 11, the last model of the first set, adds two parameters, γ4 and δ3. The effects of
downward as well as upward mobility are estimated simultaneously. Models 9 – 11 are tested because effects might differ for different kinds of mobility as indicated in the theoretical part. Models 8 – 12 are also tested without the tracking parameters γ2 and δ1.
(12) yits = β0 + β2Ss + β3Ii + γ1PEits + γ3TMts + δ2TMts * PEits + εits
Model 12 is the model used for the regression models. It does include neither the β1
parameter, nor the γ2 and δ1 parameters for level of tracking. For the models using ESS data,
the dependent variable is the continuous score for final educational attainment based on the measure by Buis (Buis, 2007; 2010: pp. 54 - 60) introduced above. Scores are again standardized just as the test score scores. From the ESS and EVS respondents are selected who match the age group plus or minus five years, but are at least 22 years of age.
6.3. Assumptions, possible violations and other methodological issues
A first issues arises when critically looking at the tests used for assessing students’ reading abilities. Both studies assume to measure an underlying ability that exists independent of the test. There is a discussion if that really is the case or if each test measures a slightly different concept of reading skill (see Van de Werfhorst & Mijs, 2010). If this were the case, it would pose a challenge to one of the fundamental assumptions of difference-in-difference models. The dependent variable is supposed to be measured in a comparable way at both time points. Despite these potential problems, PIRLS and PISA data are used difference-in-difference designs (Ammermüller, 2005; Hanushek & Wößmann, 2005; Waldinger, 2006).
A second important assumption for difference-in-difference models is that the trends would be equal in the absence of a treatment. As the design is non-experimental it is impossible to test whether a certain group would react the same too the treatment as another
group did. There are however no reasons to assume that treatments would have significantly different effects.
A third implicit assumption is that the populations tested at the two time points are the same. Individuals are not the same, but random sampling should ensure that representative samples are used for every point in time. There is however the problem of mobility. It is possible for a student to be in group A at the first measurement and in group B at the time of the second measurement. While this problem might be minimal for the first set of models as this specific age group is unlikely to be geographically mobile, it is relevant for the second set of models. Young adults are among the group that is most mobile, especially highly educated young adults. While this may not be in issue in studies using only countries as a grouping variable, which makes mobility less likely, it could be an issue for this study as geographical mobility within a country is not uncommon. The migration within Germany also does not happen at random, but some states structurally have a positive migration balance, while others have a negative one. The annual rate of migration however usually does not exceed 0.5% (Flöthmann, 2002). The bias thus should be minimal.
7. Results
The results section is divided into three parts. In the first part, descriptive statistics on the various track mobility measures as well as the scores awarded based on the educational degrees for parents as well as for the respondents from ESS/EVS data are presented. The second part shows some simple regression models using the PISA 2006 data, as well as several models using ESS/EVS data. In the third part, the difference–in-difference models are introduced. After that possible of OLS regression assumptions are shortly discussed. In both, the regression and the DiD models, the state dummy controls are not included in the tables, they are however controlled for in the models. This is to ensure that single states are not identified, which is a requirement for attaining data access.
7.1 Descriptive Statistics
So far it has been talked a lot about track mobility and its effects without showing how many students it actually affects. To get an idea of the numbers table 1 presents the overall track mobility of students in 2006 who were enrolled in a grade level at which more than one track
