A Field Experiment

Exploring the Effectiveness of Summer Learning

Sofie J. Cabus & Emily van Gool

TIER WORKING PAPER SERIES

TIER WP 14/02

A Field Experiment

Exploring the Effectiveness of Summer Learning1

Sofie J. Cabus2

Emily van Gool

Top Institute for Evidence Based Education Research (TIER)

TIER-Maastricht University Kapoenstraat 2

6211 KW Maastricht, the Netherlands Tel. +31 (0)43 388 84471 or +31 (0)6 1469 33 42

s.cabus@maastrichtuniversity.nl

Master Evidence Based Innovation in Teaching (MEBIT)

MEBIT-Maastricht University Kapoenstraat 2

6211 KW Maastricht, the Netherlands

Abstract

This paper deals with the effectiveness of summer learning programs wherein parents play a

particular role in creating a learning environment at home. A fairly simple and low-cost

evidence-based field experiment is set-up in order to estimate the effectiveness of summer

learning for children who prepare their selves in kindergarten for the transition to the first grade

of Dutch primary compulsory education. Children assigned to the intervention group received a

summer book with exercises dealing with math and language. They could practice in the summer

book for about 6 weeks. Parents were explicitly asked to assist their child with troublesome

exercises. And teachers did assess children's educational proficiency before the start of the

summer break. Standardized test scores of the treated and untreated children have been measured

before and after the intervention. Our findings show that language proficiency increased

significantly (+5.5 points) in the treated group compared to the untreated group. We did not find

a significant effect on math proficiency. It is also argued from the results that using teachers'

assessment provides better statistical modeling than using pre-test scores.

1 We are grateful to Wim Groot, Henriette Maassen van den Brink, MEBIT and TIER/DTPA participants, and the

children, the parents, and the school staff of the two schools that took part in the intervention. The authors acknowledge financial support of Platform31. The usual caveat applies. 2 Corresponding author

2

1 Introduction

The literature indicates the short run detrimental effects of the summer break on school-related

skills (e.g. Cooper et al., 1996). It is in this respect that the previous literature deals with the

concept of ‘summer learning loss’ or ‘summer learning gap’ (e.g. Alexander et al., 2001; 2007).

Alexander et al. (2001; 2007) also argue the ‘lasting consequences of the summer learning gap’,

hereby pointing to the negative effect of summer learning loss on children’s long run educational

outcomes. Several authors indicate that successful summer learning programs could potentially

oppose these detrimental effects (Borman and Dowling, 2006; McClelland et al., 2006;

Matsudaira, 2008). The idea of successful summer learning programs is that, in case summer

learning would increase children's proficiency level with respect to math and language, among

other academic, cognitive and emotional skills, children experience a better transition to the next

grade. Several determinants are discussed. First, the effectiveness of summer learning programs

might be different between educational subjects (e.g. math or language). Cooper et al. (1996)

have performed a meta-analysis including 39 studies. The authors find that, overall, children's

proficiency test scores decline over the summer break, and that math proficiency is more prone

to these harmful effects than language proficiency. Second, compared to wealthy families,

numerous studies have shown that children from poor families have, in general, rather low

proficiency scores on math and language (Cooper et al., 1996; Burkam, 2004; Currie, 2009). The

literature also indicates that children from immigrant families, who speak foreign languages at

home, or live in poor neighborhoods, experience more difficulties in school than natives (Jencks

and Mayer, 1990). Third, the literature has special attention for children's background, in general,

and parental involvement, in particular, within the scope of summer learning. Fan and Chen

(2001) discuss in their meta-analysis the positive association between parental involvement and

the educational outcomes of their children. Epstein and Sheldon (2002) and Sheldon (2007)

confirm that `parenting', i.e. parents creating a learning environment at home, is an important

determinant of children's academic/proficiency performance. Additionally, Fan and Chen (2001)

argue that parental aspirations with respect to children’s academic achievement are more

important than parenting. Fourth, considering parental involvement in relationship to aspirations,

previous research also discussed the differences in perceptions on how important education is.

Tinto (1975) and Finn (1989) conceptually discuss the process of student withdrawal, and

indicate that commitment to the school, peers and teachers may differ between boys and girls,

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and for different ethnic groups. The meta-analysis of Hattie (2009) confirms these findings,

indicating that boys are more at-risk than girls for having skills deprivation in reading and

writing during the primary school curriculum. Hurtado and Carter (1997) and Donkers and van

der Velden (2012) additionally discuss the racial climate at the school site, potentially affecting

students’ feelings of self-worth.

Various forms of summer learning are discussed in the previous literature. For instance, children

could enroll in summer courses taught by familiar teachers at the school site, or summer camp, in

order to combat their backlog at school (Burkam et al., 2004; Borman and Dowling, 2006). But

also the parents can stimulate their children in learning at home during the summer break

(Epstein and Sheldon, 2002; Sheldon, 2007). In particular the latter form of summer learning is

explored in this paper. It is in this respect that a fairly simple and low-cost evidence-based field

experiment is set-up in order to estimate the effectiveness of summer learning for children who

prepare their selves in kindergarten for the transition to the first grade of Dutch primary

compulsory education. The evidence-based set-up of the field experiment uses a control group,

an intervention group, and the evolution of standardized ability test scores over time. Children

assigned to the intervention group received a summer book with exercises dealing with math and

language. The summer book is in line with the final educational goals set by the Ministry of

Education, Culture and Sciences with respect to kindergarten (i.e. admission criteria for primary

education). The intervention group could practice during the summer break of 2012 for about 6

weeks. The parents were asked to report in the summer book each week whether the child had

been learning or not. Furthermore, parents were explicitly asked to provide their children with

assistance to solve particular exercises. At the end of the summer holidays, children handed in

their summer book to the first grade teacher, and received a small gift from the school to reward

their work.

Before and after the summer break of 2012, both treated and untreated children had to perform

the same nationally standardized ability test (CITO). The pre-test scores and the post-test scores

could then be easily compared between the intervention and the control group as well as across

time periods. Also the parents were invited in both time periods to discuss the intervention and

its results.

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The field experiment has been applied on 41 children, 6 year olds, and enrolled in the final year

of kindergarten in two separate schools in the Netherlands, both closely located to each other,

and each school part of one management structure. The Netherlands is an interesting case study

for our intervention for at least two reasons. First, standardized ability testing is performed

during the school curriculum, including the final year of kindergarten, in order to provide the

teacher with appropriate feedback with respect to children's proficiency. The ability test is in line

with the final goals set for kindergarten. This makes test scores highly comparable across time

periods and between children. And second, recent policy debate in the Netherlands discusses

whether or not the summer break should be set shorter in order to combat the summer learning

loss. In this respect, the evolution of the control group's test scores before and after the summer

break could be highly interesting (i.e. did untreated students fell behind or not?).

This paper proceeds as follows. A brief overview of the literature is presented in Section 2. The

course and design of the intervention is discussed in Section 3. In Section 4 the data and the

results of the pilot study are discussed. Section 5 concludes.

2 Discussion in the Literature

The discussion in the literature on children’s transition to primary education puts forth two

angles: (1) being ready for the transition to first grade, briefly school readiness, is the result of

`human biology' (e.g. Snow, 2006; Gadeyne et al., 2008); and (2) school readiness is the result of

the interaction between the individual child and his/her parents, the teacher, and the comunnity

(e.g. Mashburn and Pianta, 2006). The former theory on school readiness implies that neither

parents nor the school staff can influence the child's readiness for transition. The latter theory

argues that children can be encouraged by teachers, parents, and the community wherein he/she

lives.

We explain both sides of the theory on school readiness and its theoretical thoughts on the

effectiveness of summer learning. First, we consider the `human biology model', its name

corresponding to children's school readiness as an individual characteristic. Here, school

readiness is most commonly defined as having academic, cognitive and emotional skills (among

others, see Heaviside and Farris, 1993; Ladd et al. 2006; Mashburn and Pianta, 2006). The main

questions underlying readiness are: "[...] what makes children "ready" for their first year of

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formal schooling? [...] As children enter kindergarten, what tasks must they master to adjust to

school, and progress successfully in this context? (Ladd et al., 2006, p.116)." School readiness

in the human biology model cannot be influenced by parenting and schooling but will evolve

with ageing of the child. Therefore, an intervention as summer learning would not be effective.

Second, we discuss the `interactive model', directly referring to the interactive field between

parents and their children (home), teachers and peers (school), and communities (institutions or

neighborhood). Here, school readiness is the final product of systemic factors (e.g. family and

school institutions) and individual characteristics (e.g. gender, age, and innate ability), and its

complex interaction. As such, it is not only the child's `speed of development' with respect to

academic and cognitive functions (cf. human biology), but also the cummunity as a whole that

plays a role in mastering school-related proficiencies. In this respect, Mashburn and Pianta (2006,

p.169) conclude that: "[...] school readiness is best conceived as an aspect of child functioning

that is determined by the quality and type of interactions that a child engages in with others, and

social relationships between children and parents, parents and teachers, and teachers and

children are identified as the conduits through which children become motivated and interested

in school activities and acquire competencies associated with school readiness." Thus, parenting

and schooling can support the child with being ready for the transition to primary education, for

example, by additional exercises or individual guidance. In line with this model, summer

learning could make a real difference.

3 The course and design of the intervention

3.1 Working in the summer book

In order to combat potential summer learning loss, children received a book with exercises to be

solved during the summer holidays. Note that, in the Netherlands, the school year starts mid-

August after 6 weeks of summer holidays. The summer book consists of 45 pages in total. The

summer book helps the treated child to obtain the final goals of kindergarten with respect to math

and language as stipulated by the Ministry of Education, Culture and Science. However, the

summer book provides, additionally, also children to learn the first letters and numbers that

children learn in first grade (i.e. first year of primary education). For every day of the summer

break, there is a different page, so that a child can work every day on a different exercise. After 6

days (one week), the children are explicitly asked in an exercise to search for a letter or number

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they have learned during the week. For instance: "Where did you hear the letter M this week?

Can you draw a painting about this on this page."

3.2 Asking for parental involvement

The previous literature indicates the effectiveness of parental (community) involvement in

positively influencing student behavior both at home and at school (e.g. Epstein and Sheldon,

2002; Sheldon, 2007; Patall et al., 2008; Sheridan et al., 2010). In line with these findings, we

acknowledge that parents (and the neighborhood wherein they live) have an important role in

successfully supporting the child's learning during the summer break. Therefore, we explicitly

asked the parents to assist their child with troublesome exercises in three different ways. First,

we organized an information session at the school site just before the holidays to inform the

parents about the course of the intervention. The other way was written in the summer book. On

the first page, one finds a description of the intervention for the parents of the children, and the

question to provide their child with assistance. Here, we provide a transcript of the first Dutch

phrases: "Dear parents or caregivers, This summer book provides exercises that your child can

make during the summer break. Some exercises can be done independently by the child, other

exercises will be too difficult and will need your assistance." And third, parents were also asked

to write down in the summer book on the 7th day of each week how well the child had been

practicing in that week.

3.3 Rewarding and intrinsic motivation

Rewards may stimulate participants of the intervention group to increase intrinsic motivation

(Deci et al., 1999). There are several types of rewards, such as tangible rewards (the free ticket

for the playground) or verbal rewards (the positive feedback). Deci et al. (1999) discuss that

tangible rewards are less effective than feedback when it comes to `free choice' behavior (i.e. the

child freely chooses to do the exercises). As follows, we have dealt with the reward incentive in

the intervention in order to increase the motivation of the children and their parents. After the

summer break, the intervention ends, and parents were asked to hand in the summer book to the

primary school teacher. In case the child did hand in his/her summer book, they were given a

reward together with feedback on the summer book. The reward was a small gift from the school,

namely: a free ticket for the playground in the neighborhood. The feedback also included a

sticker on the summer book. Note that all children handed in their summer book. There is one

specific paragraph in the letter to the parents (i.e. the first page of the summer book) that refers to

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this reward. It was also mentioned during the information session before the summer holidays.

However, it was only mentioned that their child would receive a small reward without stipulating

what exactly this reward would be. It was also mentioned that their child would receive feedback

on the summer book when handed in after the summer holidays. As such, at the start of the

intervention the reward was verbally mentioned, and repeated in the summer book, but not

specific, and, thus, not tangible.

3.4 The Outcome variable

The intervention uses the standardized exam (CITO) that every child makes before the transition

to primary education. In order to provide the teacher with appropriate feedback with respect to

children's proficiency, standardized ability testing is common practice in the Netherlands. The

ability test is in line with the learning goals of kindergarten set by the Ministry of Education,

Culture, and Science. This makes test scores highly comparable across time periods and also

between schools. The standardized CITO exams are widely used in the Netherlands, and are

considered reliable and valid for measuring children's proficiency. Note that the June and August

standardized CITO exam was exactly the same in order to measure learning gains over the

summer break.

3.5 The assignment of treatment and control Group

We are interested in the effect of summer learning on children's language and math proficiency

test scores. Therefore, we performed an evidence-based education research aiming at children

enrolled in the final school year of kindergarten. Two Dutch schools (further abbreviated by

School A and School B) participated in a pilot case in 2012. Both schools are under one

management structure, and, consequently, are liable to similar school policies. Further note that

the intervention was implemented in a fast and prompt way in January 2012, so that parents did

not choose a school based on our intervention.

Our assignment rule of children to the intervention group or the control group was fairly simple:

children enrolled in School A were assigned to the intervention group, whereas children in

School B to the control group. Random assignment of children was not possible owing to

practical and ethical reasons. We argue the advantages and disadvantages of such an assignment

rule, and deal with the disadvantages.

8

3.5.1 Advantages

Parental involvement was part of the set-up of our intervention. As such, we strongly wish to

avoid communication between parents of children in the intervention group with parents of

children in the control group. Communication between parents from treated and untreated

children would induce spill-over effects, for example, by exchanging the summer book or

sensitization of parents with respect to summer learning. This exchange of information would

directly violate the stable unit treatment value (SUTVA) assumption arguing that treatment may

not be spilled over from treated to untreated students (Rubin, 1974).

In case both the intervention group and the control group would have been mixed in schools by

random assignment, it would have been impossible to support the SUTVA. In contrast, by taking

School A as the intervention school and School B as the control school, we could control for

exchanging information. In addition, we explicitly did not tell parents that School B was the

control group at information sessions for parents in School A.

3.5.2 Disadvantages

Most importantly, non-random assignment can create underlying differences between the

intervention group and the control group that bias the estimation results (i.e. omitted variables

bias) (Rubin, 1974). As previously argued, there are several determinants that make `children at-

risk' of poor performance in school, and, consequently, school failure. These determinants

include among others: gender; ethnicity, cultural differences, and class composition;

socioeconomic status; parental involvement; perception of teachers with respect to school

readiness and school failure; and educational and school policy (for an elaborated discussion, see

Hattie, 2009). Ideally, treated and untreated students are, on average, highly comparable with

respect to these determinants. Of some characteristics, we have information so that we can

control for it in a multivariate regression (i.e. gender, ethnicity and socioeconomic status).

However, we do not observe all determinants of children's proficiency test scores, like innate

ability, or the general dislike of school. It is in this respect that we indicate that, in general,

parents choose the kindergarten at closest distance to their home. This distance criterion, i.e. the

two schools closely located to each other in the same neighborhood, make one believe that, on

average, treated children should be comparable to untreated children.

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To further overcome this disadvantage of our experimental set-up, we have measured children's

math and language proficiency before the intervention took place: June and January 2012. Before

the summer, children developed their proficiency in school and at home, so that we are able to

measure the success rate of schooling, which is a combination of "teachers' valued added", the

innate ability to learn, as well as environmental factors (e.g. parental involvement and class size

composition) and children's characteristics (e.g. gender and migrant status).

In the first instance, we control only for the June pre-test in a multivariate regression,

additionally controls for unobserved determinants of proficiency test scores. We can formally

express this multivariate regression as:

∑ (1)

where subscript i∈{1,2,...N} denotes all individuals assigned to either the control group (I=0) or

the treatment group (I=1); children's proficiency scores in August (i.e. the post-test);

children's proficiency scores June (i.e. the pre-tests); a vector of individual characteristics;

and the error term. The effect of interest is β, which is the effectiveness of summer learning.

Second, we also look at the evolution in test scores from January over June to August 2012. This

visualizes the performance gains of students over the school year, including learning at school

(value added of teaching). Ideally, students' performance gains over time in the control group and

the treatment group are, on average, the same in order to support the parallel time trend

assumption (Rubin, 1974). This assumption implies that, in absence of the intervention, children

proficiency would have moved parallel over the summer break. Note that, as a result of different

teachers in School A and School B, differences in performance gains between the treated and

untreated students can be expected between January and June. However, by definition, and with

reference to the summer learning gap, we expect no evolution in the control group during the

summer break, and a positive evolution in the treatment group. Having additional information on

the pre-test, we can control for the pre-trend in a multivariate regression.

3.6 Teachers’ perception of being ‘at-risk’

We acknowledge that proficiency test scores are, in fact, screen shots of a particular moment in

time. It can be that, at the pre-test or the post-test, a child was ill or tired, in turn having bad test

scores. Alternatively, recent policy debate in the Netherlands argues for an increasing share of

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teachers' perception in formulating advice on children's educational proficiency. Harlen (2005)

indicates the costs and benefits of teachers' assessment in a literature review. She concludes that,

overall, teachers' perception on children proficiency may be unreliable and biased, but, also, that

it should be considered against the potentially low validity or reliability of tests. The main

advantage of teachers' assessment with respect to the child's performance is that it is not a screen

shot. Instead, their assessment may be a good indicator for children's performances in the first

year of the primary school.3

Therefore, as a robustness check, we formulate an alternative multivariate model specification

replacing the pre-test score with an indicator of `being at-risk' (of low performance on math or

language), as to predict the post-test scores. The at-risk indicator is based on teachers' assessment

of children's proficiency. Therefore, the intervention included a questionnaire for the teacher of

the control group and the treatment group. Before the pre-test in June was made, teachers had to

report the `at-risk status' of every child on a five point Likert scale (i.e. 1 denotes no risk of

failing the proficiency test; 5 denotes high risk of failing the proficiency test). The teacher in

both the control group and the treatment group filled in the at-at-risk status of the child, in

general, and with respect to math, language, learning attitude, and behavior, in particular. Having

the at-at-risk status of every child, we can control for it in a multivariate regression. We then

replace with and rewrite equation (1) as:

∑ (2)

The effect is again the effectiveness of the intervention.

3.7 A short note on statistical power

In case the statistical power would be rather low, we could falsely conclude that our intervention

did not have any effect (i.e. the type-2 error). We use the G-power software to first calculate the

sample size when one would like to have a statistical power of at least 0.80, and error probability

of 0.05. Our finding indicates that for a small effect size of 0.2, we need at least 191 children in

total. Increasing the effect size to 0.5, we need 26 children in total. For large effect sizes of 0.8,

we need 7 children in total. As such, we need at least an effect size of 0.5 in order to correctly

3 Note that the proficiency test scores are based on the standardized exams administered by the Ministry of

Education, Culture and Science, so that teachers cannot directly influence the post-test results because of their assessment within the scope of this intervention.

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accept insignificant results. Further note that we can enforce the statistical power by controlling

for individual and family characteristics in a multivariate regression.

4 Data and Results

The intervention group consists of 22 children, and the control group of 19 children. We

summarize the descriptive statistics of the individual characteristics in Table 1. We also include

the difference between the intervention group and the control group and the corresponding

significance level. In general we do not find any significant differences between the intervention

group and the control group with respect to the observed characteristics, except for age in months.

About 47 percent of the children in the control group is male, compared to 41 percent in the

treatment group. Children are, on average, 6 year olds at the start of primary education, with a

significant mean difference between the control group (77 months) and the treatment group (73

months) of -4 months. Most children have the Dutch ethnicity: 42 percent and 55 percent in the

control and treatment group, respectively. There are slightly more (about 6 percentage points)

Moroccan and Turkish children in the control group than in the treatment group. About 79

percent (control group) and 68 percent (intervention group) of parents have a diploma of

secondary or higher education; 5 percent (control and intervention group) a diploma of pre-

vocational education; and 16 percent (control group) and 27 percent (intervention group) a

diploma of only primary education. To conclude, we have information on cultural differences

(difference between the child and his parents with respect to having the Dutch culture or not) at

the side of one or both parents. We indicate a mean difference between control and treatment

group of 8 percentage points at father's side, and -11 percentage points at mother's side.

Next, we plot the evolution of the children's proficiency scores on a graph (max. sore is 108 for

language and 137 for math). Figure 1 deals with math proficiency scores and Figure 2 with

language proficiency scores. We distinguish between the evolution of treated children (dotted

line) and untreated children (solid line) over the period January to August 2012. These figures

clearly show the learning gains in school of children from January to June.

First, consider the results with respect to language proficiency. The treatment group increased

their language proficiency from 64 to 68, i.e. an increase of about 4 points over the summer

break. The language proficiency scores of the control group were unchanged (pre-test and post-

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test about 63/108). If we now compare the post-test scores on language between the intervention

group and the control group, we observe a significant difference of +5.5 points.

For math proficiency, we observe a minor difference between the treated and untreated children

of -1.5 points and not significant. The descriptive statistics show that untreated children slightly

increased their math proficiency over the summer break from 85 to 87. This increase is not

statistically significant. The intervention group did not increase their math proficiency (pre-test

and post-test about 85/137).

As follows, we include all control variables, namely age, gender, education of the parents, and

cultural differences, into a multivariate regression. Note that we correct the standard error for

heteroskedasticity (χ²=14.13;P-value=0.0002). We estimate two specifications: one specification

additionally controlling for the pre-test scores of June, and one specification additionally

controlling for teachers' perception on the at-risk status of children with respect to language

deficiency (see Section 3). Full model estimation is available with the author upon request.

Following the first specification, we find that our intervention `summer learning' has a small to

medium effect size of 0.27 on language proficiency test scores significant at 10 percent level.

Following the second specification, we estimate a medium effect size of 0.44 significant at 5

percent level.

In conclusion, we find that teachers' assessment is a strong and highly significant predictor of the

level of the post-test scores. From the results we argue that using teachers' assessment provides

better statistical modeling than using pre-test scores, as it pushes up the statistical power of our

analyses to 0.86. These findings can have two underlying explanations: (1) teachers' perception

on children's educational deficiency is directly related to these children their performances (i.e.

teachers' value added; see also Nye et al., 2004; Jussim and Harber, 2005). Or (2), irrespectively

of the teachers' value added, teachers can better indicate than test scores whether a child is

skilled enough for making the transition to primary education (e.g. Okpala, 2007).

5 Conclusion

The literature indicates that children proficiency test scores decline over the summer break (e.g.

Cooper et al., 1996). Summer learning could oppose these detrimental effects on school-related

skills. The literature additionally indicated the positive impact of parental involvement on

achievement (e.g. Epstein and Sheldon, 2002; Sheldon, 2007; Patall et al., 2008). As such, we

13

explicitly incorporated the role of the parents into the intervention by providing them with the

learning material, namely: the summer book. Previous research also argued that summer learning

programs can only be effective in the `interactive model', but not in the model of `human

biology' (Ladd et al., 2006; Mashburn and Pianta, 2006). The former model stipulates that school

readiness can be influenced by providing children with additional exercises, whereas the latter

theory argues that ageing is the main process underlying children's readiness for primary

education.

This paper explores the set-up of a fairly simple and low-cost intervention in order to estimate

the effectiveness of summer learning for 6 year olds children in transition to the first grade of

primary education in the Netherlands. It consists of a summer book helping children to master

the final learning goals of kindergarten set by the Ministry of Education, Culture and Science.

The intervention has been tested in two Dutch schools including a small sample of 41 children,

information on their parents, and teachers’ perception on being at-risk. The effectiveness of the

intervention ‘summer learning’ is promising with respect to language proficiency, but not with

respect to math proficiency. Our findings show that, owing to the intervention, language

proficiency increased significantly (+5.5 points) in the treated group compared to the untreated

group. We observe a summer learning gap for children in the control group, as they did not

increase in points, but remain stable over time. These findings are robust to two different model

specifications and control variables. With respect to math proficiency, we did not observe any

significant effect of the intervention.

Further research should deal with larger sample sizes in order to confirm the results. It could also

explore summer learning as a potential alternative for grade retention, a common practice in the

Netherlands.

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6 Tables and figures

Table 1: Descriptive statistics of children characteristics and outcome variables

Control

Group

Intervention

Group Difference P-value

(1) (2) (2)-(1)

1. Children characteristics

Gender (%) (male=1) 0.47 0.41 -0.06 0.687

Age (Months) 76.933 73.442 -3.491 0.010*

Country of origin

Netherlands (%) 0.4211 0.5455 0.1244 0.4395

Morocco (%) 0.1053 0.0455 -0.0598 0.4759

Turkey (%) 0.1053 0.0455 -0.0598 0.4759

Other (%) 0.3684 0.3636 -0.0048 0.9755

Education of the parents

Secondary and higher⁽¹⁾ (%) 0.7895 0.6818 -0.1077 0.4505

Pre-vocational education⁽¹⁾ (%) 0.0526 0.0455 -0.0072 0.9179

Primary education (%) 0.1579 0.2727 0.1148 0.3884

Cultural differences⁽²⁾

Father's side 0.1053 0.1818 0.0766 0.5015

Mother's side 0.2105 0.0909 -0.1196 0.2915

2. Outcome variables

proficiency test 84.6842 85.5455 0.8613 0.8294

math June (max. 137)

proficiency test 62.8421 64.2727 1.4306 0.6441

language June (max. 108)

proficiency test 86.8947 85.4091 -1.4856 0.7171

math August (max. 137)

proficiency test 62.947 68.455 5.508 0.1235

language August (max. 108)

Note 1: The pre-vocational and primary education level indicate parents without a valid secondary school-leaving

certificate.

Note 2: Cultural differences denote that the mother, the father, or both is an ethnic minority.

15

Figure 1: Evolution of math proficiency test scores over time (January, June and August

2012).

Figure 2: Evolution of language proficiency test scores over time (January, June and

August 2012).

16

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