Supplementary materials: online appendix (not intended for publication)

Appendix A. Additional tables

Table A1. Non-native students in the Italian school system, by school level and school year.

School year / All levels / Kindergarten / Primary school / Junior high school / High school
Total No. / % / Total No. / % / Total No. / % / Total No. / % / Total No. / %
1996/97 / 59389 / 0.7 / 12809 / 0.8 / 26752 / 1.0 / 11991 / 0.6 / 7837 / 0.3
2001/02 / 181767 / 2.3 / 39445 / 2.5 / 84122 / 3.0 / 45253 / 2.5 / 27594 / 1.1
2002/03 / 232766 / 3.0 / 48072 / 3.0 / 100939 / 3.7 / 55907 / 3.1 / 34890 / 1.3
2003/04 / 282683 / 3.5 / 59500 / 3.6 / 123814 / 4.5 / 71447 / 4.0 / 52380 / 2.0
2004/05 / 361576 / 4.2 / 74348 / 4.5 / 147633 / 5.3 / 84989 / 4.7 / 63833 / 2.4
2005/06 / 424683 / 4.8 / 84058 / 5.0 / 165951 / 5.9 / 98150 / 5.6 / 83052 / 3.1
2006/07 / 501445 / 5.6 / 94712 / 5.7 / 190803 / 6.8 / 113076 / 6.5 / 102829 / 3.8
2007/08 / 574133 / 6.4 / 111044 / 6.7 / 217716 / 7.7 / 126396 / 7.3 / 118977 / 4.3
2008/09 / 629360 / 7.0 / 125092 / 7.6 / 234206 / 8.3 / 140050 / 8.0 / 130012 / 4.8
2009/10 / 673592 / 7.5 / 135632 / 8.1 / 244457 / 8.7 / 150279 / 8.5 / 143224 / 5.3
2010/11 / 711046 / 7.9 / 144628 / 8.6 / 254.644 / 9.0 / 158261 / 8.8 / 153513 / 5.8

Notes.Elaboration from MIUR-ISMU Foundation (2011). Primary school (grades 1-5); Junior high school (grades 6-8); high-school (grades 9-13).Children enrolled in kindergartens are from 3 up to 5 years old and start primary school the month of September of the year they turn 6.

Table A2. Non-native students born in Italy and abroad, by school level (2008-09 school year).

School level / Percentage with respect to the total student population / Percentage with respect to the non-native student population
Born in Italy / Born abroad / Born in Italy / Born abroad
Kindtergarden / 5.5 / 2.1 / 73.3 / 26.7
Primary school / 3.7 / 4.6 / 45.0 / 55.0
Junior high school / 1.5 / 6.5 / 18.8 / 81.2
High school / 0.3 / 4.5 / 7.5 / 92.5
Total / 2.6 / 4.4 / 37.0 / 63.0

Source: elaboration from MIUR (2009).

Table A3. Descriptive statistics.The three main problems experienced by teachers in approaching non-native students.

Main problems faced by teachers / Average
North-West
Difficulties in communication because of the language / 2.7
Problematic family background / 2.5
Slowing down teaching activities / 2.3
North-East
Problematic family background / 2.9
Difficulties in communication because of the language / 2.8
Adapting teaching activities to non-native students / 2.6
Centre
Difficulties in communication because of the language / 3.1
Adapting teaching activities to non-native students / 2.7
Slowing down teaching activities / 2.7
South and Islands
Difficulties in communication because of the language / 2.7
Slowing down teaching activities / 2.1
Problematic family background / 2.1

Notes.Elaboration from CENSIS (2008, Table 13), “Main problems faced by teachers in approaching non-native students, distribution by geographical macro-area”. Average points: 1 means “no problems”, 4 means “a lot of problems”. We report the three answers with the highest average points.

Table A4. Descriptive statistics.Students’ perceptions about studying difficulties and classroom teaching activity.

Native / Non-native / High ability / Low ability / All
“Studying Math is more difficult for me than for others” / 29.76 / 37.54 / 23.26 / 27.17 / 30.54
“Studying Language is more difficult for me than for others” / 24.48 / 39.36 / 19.9 / 33.9 / 25.96
“During Math lessons, we dedicate a lot of time to the same issue because class-mates do not understand” / 58.89 / 58.11 / 59.88 / 57.54 / 58.81
“During Language lessons, we dedicate a lot of time to the same issue because class-mates do not understand” / 47.83 / 47.49 / 48.33 / 46.36 / 47.8
N / 462,390 / 51,347 / 296,550 / 217,187 / 513,737

Notes.The data are taken from the Student Questionnaire of the Invalsi National Evaluation Program, school year 2009/10. The population refers to all sixth grade students enrolled in Italian junior high schools. High ability and low ability students are classified according to whether the teachers’ mark for each student at the end of the first semester (late January) is above or below median mark for all students.

Appendix B. Analytics

We provide a simple formalization of the integration model presented in section 4. To this purpose we transform the non-native propensity not to disrupt (pF ) into a decreasing function of the proportion of non-native students θ (i.e. pF (θ)). Define pF(θ) as a continuous, twice differentiable function satisfying the following properties:

/ [B.1]
/ [B.2]

whereand .

In particular, notice that if non-native share is sufficiently small, the propensity of non-disruption of non-natives approaches the natives’ one (i.e. ) as a result of the integration process. On the contrary, if non-native share increases, the gap in the propensity of non-disruption between the two types grows (i.e. ). Then, complete the properties and definitions concerning with the properties of the second derivative:

/ [B.3]

where: .

The second derivative of yI with respect to θ takes the following form:

/ [B.4]

The sign of the second derivative globally depends on functional form. However, it is possible to derive its sign for θ→0+ that together with the information on first derivative is sufficient for an horizontal inflection point to exist in a neighborhood of θ=0+ (assuming ). In fact, for θ→0+:

/ [B.5]

For θ→0.5- the second derivative is different from zero, but undetermined as it depends on the values :

/ [B.6]

As a result, the integration model determines important differences in the predicted effects due to non-native students’ school share with respect to the simple bad apple model. In fact, contrary to the bad apple, which generates strictly negative externalities, the integration model allows for non-positive externalities (i.e. negative or null) on students’ outcomes:

/ [B.7]

In particular, the integration mechanism makes the non-native peers’ negative spillovers - due to the disruption mechanism - decrease for sufficiently low values of the non-native school share:

/ [B.8]

wherek is a negative real number. Finally, notice that all the properties demonstrated so far hold log-transforming equations [1] and [2].

1