Resumen del artículo ‘A peer like me? Early exposure to high achievers in math and later educational outcomes’

Importante

Este estudio ofrece importantes lecciones sobre cómo la composición de las aulas afecta el rendimiento académico y las decisiones a largo plazo. Con políticas educativas que promuevan interacciones positivas entre compañeras y compañeros de ambos géneros, se puede reducir la brecha de género en áreas STEM, sin la necesidad de recurrir a la segregación de género en las escuelas.

¿Cómo influyen las y los mejores estudiantes en matemáticas?

Un análisis de efectos de pares en la educación

La interacción entre estudiantes dentro de un aula puede tener un impacto profundo en el rendimiento académico y en las decisiones educativas a largo plazo. En un reciente estudio, Pagani y Pica (2021) exploran cómo la exposición temprana a compañeras y compañeros con alto rendimiento en matemáticas afecta el logro académico en secundaria (8º grado) y la elección de una trayectoria educativa orientada hacia las ciencias.

Este análisis de datos en Italia muestra efectos contrastantes según el género de las y los compañeros, y resalta la importancia de la composición de género en las aulas, especialmente en materias como matemática, donde tradicionalmente existe una significativa brecha de género.

Principales Hallazgos

1. Efectos positivos de pares del mismo género

Las y los estudiantes que están rodeados de estudiantes del mismo género que tienen muy buenas notas en 5º grado tienden a mejorar sus puntajes en matemáticas en el 8º grado.

Por cada aumento de una desviación estándar en la proporción de niñas destacadas en matemáticas en 5º grado, las niñas mejoran sus puntajes en el 8º grado en un 0.0241 desviaciones estándar, lo que equivale a un incremento del 0.9% en sus puntajes promedio de matemáticas.

Los niños también muestran mejoras, con un aumento similar de 0.0208 desviaciones estándar, un incremento del 0.7% en su puntaje promedio.

**2. Efectos negativos de pares del género opuesto

Por el contrario, estar expuesto a compañeras y compañeros del género opuesto con alto rendimiento en matemáticas tiende a tener un efecto negativo en el rendimiento académico.

Para las niñas, un aumento de una desviación estándar en la proporción de niños destacados reduce su puntaje en 0.0184 desviaciones estándar. Los niños experimentan una disminución de 0.0141 desviaciones estándar cuando están expuestos a niñas con alto rendimiento.

3. Decisiones de Trayectoria Educativa

La influencia de las y los compañeros afecta los logros inmediatos, y también las decisiones futuras, como la elección de una trayectoria educativa orientada hacia las ciencias.

Estar rodeado de compañeras y compañeros del mismo género que sobresalen en matemáticas aumenta la probabilidad de elegir una escuela secundaria con enfoque científico (STEM), mientras que la exposición a compañeras y compañeros del género opuesto reduce esta probabilidad.

Datos

El estudio ofrece un análisis profundo con coeficientes estadísticamente significativos que destacan los efectos diferenciales por género:

• Efecto de niñas sobresalientes en otras niñas: +0.0429 desviaciones estándar.

• Efecto de niños sobresalientes en otras niñas: -0.0440 desviaciones estándar.

• Efecto de niños sobresalientes en otros niños: +0.0266 desviaciones estándar.

Los coeficientes muestran un claro patrón donde las ylos estudiantes se benefician más cuando están rodeados de compañeros del mismo género con alto rendimiento.

Lecciones extrapolables: implicancias para la política educativa

Este estudio destaca la importancia de las influencias tempranas en la trayectoria educativa, especialmente en un área crítica como STEM. Para países como Uruguay y programas como Ceibal, las lecciones de este trabajo pueden ayudar a diseñar políticas que promuevan la equidad de género en STEM.

Fomentar modelos identificatorios del mismo género

El estudio sugiere que las niñas, en particular, se benefician enormemente de tener modelos femeninos exitosos en matemáticas, lo que muestra la necesidad de aumentar la visibilidad de mujeres en STEM, ya sea a través de profesoras o de programas de mentoría.

Promover el trabajo colaborativo estructurado

En lugar de separar a las y los estudiantes por género, se pueden diseñar estrategias de interacción entre géneros que reduzcan los efectos negativos. Promover el trabajo colaborativo entre niñas y niños, especialmente en matemáticas, puede ayudar a mitigar el impacto negativo de estar rodeado de compañeros del género opuesto.

Intervención temprana en actitudes hacia las matemáticas

El análisis destaca que las percepciones sobre la habilidad académica se forman temprano. Introducir programas que fortalezcan la confianza de niñas y niños en sus habilidades matemáticas, en lugar de permitir que los estereotipos influyan en sus decisiones, podría tener un impacto duradero en sus trayectorias educativas y laborales.

Abstract

This paper investigates whether exposure to academically gifted peers of the same and opposite gender in primary school (grade 5, at age 10) affects later academic achievement (grade 8, at age 13) and high-school track choice. For identification we exploit random allocation of kids across classes within primary schools. We document that, conditional on primary school fixed effects and grade 8 class fixed effects, as well as on baseline achievement, a higher share of same/oppositegender high-achievers in math in primary school is related, both for boys and girls, to better/worse later math academic achievement in grade 8 and to a higher/lower probability of choosing a scientific high-school track. We argue that these results are consistent with a role model channel.

El documento 'CEFES-WP-474.pdf' contiene 9576 palabras y se centra principalmente en share, grade, school, math, high, top, girls, girl, class, boys. El texto exhibe un tono predominantemente positive. Los temas clave que surgen del análisis incluyen primary school, 5th grade, top girls, top boys, 1 girl. Las palabras que más contribuyen al sentimiento positivo son top, achievement, positive, well, better, mientras que las que más contribuyen al sentimiento negativo son deviation, negative, errors, anxiety, randomly. Las principales oraciones del documento son: 47

Table A2: Heterogeneous effects on 8th grade math scores by quartiles of the 5th grade math scores
distribution

                                                                                                         (1)
                          VARIABLES                                                             8th grade math score

                          Share of top girls in math in 5th grade                                   -0.0090***
                                                                                                      (0.0032)
                          Share of top girls in math in 5th grade × Girl                             0.0429***
                                                                                                      (0.0038)
                          Share of top boys in math in 5th grade                                     0.0266***
                                                                                                      (0.0033)
                          Share of top boys in math in 5th grade × Girl                             -0.0440***
                                                                                                      (0.0038)
                          Q1                                                                        -0.1104***
                                                                                                      (0.0084)
                          Q4                                                                         0.1119***
                                                                                                      (0.0087)
                          Girl dummy × Q1                                                             0.0117**
                                                                                                      (0.0059)
                          Girl dummy × Q4                                                           -0.0895***
                                                                                                      (0.0059)
                          Share of top girls in math in 5th grade × Q1                                 0.0006
                                                                                                      (0.0049)
                          Share of top girls in math in 5th grade × Girl × Q1                       -0.0204***
                                                                                                      (0.0065)
                          Share of top boys in math in 5th grade × Q1                               -0.0186***
                                                                                                      (0.0054)
                          Share of top boys in math in 5th grade × Girl × Q1                         0.0188***
                                                                                                      (0.0065)
                          Share of top girls in math in 5th grade × Q4                              -0.0170***
                                                                                                      (0.0048)
                          Share of top girls in math in 5th grade × Girl × Q4                          0.0008
                                                                                                      (0.0066)
                          Share of top boys in math in 5th grade × Q4                                -0.0108**
                                                                                                      (0.0048)
                          Share of top boys in math in 5th grade × Girl × Q4                           0.0043
                                                                                                      (0.0064)

                          Observations                                                                351,277
                          R-squared                                                                    0.6181
                          Primary school FE                                                             YES
                          8th grade class FE                                                            YES
                          Individual controls                                                           YES
                          Class controls                                                                YES
                          Coeff: share of top girls (1 + below 25)                                   -0.00834
                          F -test: share of top girls (1 + below 25)                                    3.522
                          P > F : share of top girls (1 + below 25)                                    0.0606
                          Coeff: share of top girls (1 + above 75)                                    -0.0260
                          F -test: share of top girls (1 + above 75)                                    35.41
                          P > F : share of top girls (1 + above 75)                                  2.84e-09
                          Coeff: share of top girls (1 + girl)                                         0.0339
                          F -test: share of top girls (1 + girl)                                         110
                          P > F : share of top girls (1 + girl)                                           0
                          Coeff: share of top girls (1 + girl + below 25 + girl × below 25)            0.0141
                          F -test: share of top girls (1 + girl + below 25 + girl × below 25)           9.386
                          P > F : share of top girls (1 + girl + below 25 + girl × below 25)          0.00220
                          Coeff: share of top girls (1 + girl + above 75 + girl × above 75)            0.0177
                          F -test: share of top girls (1 + girl + above 75 + girl × above 75)           14.61
                          P > F : share of top girls (1 + girl + above 75 + girl × below 25)         0.000134
                          Coeff: share of top boys (1 + below 25)                                     0.00804
                          F -test: share of top boys (1 + below 25)                                    2.776
                          P > F : share of top boys (1 + below 25)                                     0.0958
                          Coeff: share of top boys (1 + above 75)                                      0.0159
                          F -test: share of top boys (1 + above 75)                                     13.61
                          P > F : share of top boys (1 + above 75)                                   0.000227
                          Coeff: share of top boys (1 + girl)                                         -0.0174
                          F -test: share of top boys (1 + girl)                                         32.28
                          P > F : share of top boys (1 + girl)                                       1.40e-08
                          Coeff: share of top boys (1 + girl + below 25 + girl × below 25)            -0.0171
                          F -test: share of top boys (1 + girl + below 25 + girl × below 25)            17.77
                          P > F : share of top boys (1 + girl + below 25 + girl × below 25)          2.54e-05
                          Coeff: share of top boys (1 + girl + above 75 + girl × above 75)            -0.0238
                          F -test: share of top boys (1 + girl + above 75 + girl × above 75)              26
                          P > F : share of top boys (1 + girl + above 75 + girl × above 75)          3.53e-07
Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic scores, a migrant dummy and (within 5th grade) gender-specific
rank. | 49

Table A4: Heterogeneous effects on the probability to choose Liceo Scientifico by quartiles of the 5th
grade math scores distribution

                                                                                                            (1)
                                VARIABLES                                                             Liceo scientifico

                                Share of top girls in math in 5th grade                                  -0.0043**
                                                                                                          (0.0021)
                                                              th
                                Share of top girls in math in 5        grade × Girl                      0.0125***
                                                                                                          (0.0027)
                                                                  th
                                Share of top boys in math in 5         grade                             0.0151***
                                                                                                          (0.0022)
                                                                  th
                                Share of top boys in math in 5         grade × Girl                     -0.0233***
                                                                                                          (0.0026)
                                Q1                                                                      -0.0405***
                                                                                                          (0.0052)
                                Q4                                                                       0.0385***
                                                                                                          (0.0063)
                                Girl dummy × Q1                                                          0.0366***
                                                                                                          (0.0036)
                                Girl dummy × Q4                                                         -0.0457***
                                                                                                          (0.0042)
                                Share of top girls in math in 5th grade × Q1                                0.0027
                                                                                                          (0.0030)
                                Share of top girls in math in 5th grade × Girl × Q1                        -0.0058
                                                                                                          (0.0040)
                                Share of top boys in math in 5th grade × Q1                             -0.0112***
                                                                                                          (0.0033)
                                Share of top boys in math in 5th grade × Girl × Q1                      0.0128***
                                                                                                          (0.0040)
                                Share of top girls in math in 5th grade × Q4                            -0.0090***
                                                                                                          (0.0032)
                                Share of top girls in math in 5th grade × Girl × Q4                         0.0048
                                                                                                          (0.0046)
                                Share of top boys in math in 5th grade × Q4                                -0.0020
                                                                                                          (0.0033)
                                Share of top boys in math in 5th grade × Girl × Q4                         -0.0008
                                                                                                          (0.0045)

                                Observations                                                             289,960
                                R-squared                                                                  0.2762
                                Primary school FE                                                           YES
                                8th grade class FE                                                          YES
                                Individual controls                                                         YES
                                Class controls                                                              YES
                                Coeff: share of top girls (1 + below 25)                                 -0.00162
                                F -test: share of top girls (1 + below 25)                                 0.369
                                P > F : share of top girls (1 + below 25)                                   0.544
                                Coeff: share of top girls (1 + above 75)                                  -0.0133
                                F -test: share of top girls (1 + above 75)                                  21.88
                                P > F : share of top girls (1 + above 75)                                2.97e-06
                                Coeff: share of top girls (1 + girl)                                      0.00813
                                F -test: share of top girls (1 + girl)                                      14.59
                                P > F : share of top girls (1 + girl)                                    0.000135
                                Coeff: share of top girls (1 + girl + below 25 + girl × below 25)         0.00502
                                F -test: share of top girls (1 + girl + below 25 + girl × below 25)         4.068
                                P > F : share of top girls (1 + girl + below 25 + girl × below 25)         0.0437
                                Coeff: share of top girls (1 + girl + above 75 + girl × above 75)        0.00394
                                F -test: share of top girls (1 + girl + above 75 + girl × above 75)        1.685
                                P > F : share of top girls (1 + girl + above 75 + girl × below 25)          0.194
                                Coeff: share of top boys (1 + below 25)                                   0.00393
                                F -test: share of top boys (1 + below 25)                                   1.865
                                P > F : share of top boys (1 + below 25)                                   0.172
                                Coeff: share of top boys (1 + above 75)                                    0.0131
                                F -test: share of top boys (1 + above 75)                                  21.84
                                P > F : share of top boys (1 + above 75)                                 3.03e-06
                                Coeff: share of top boys (1 + girl)                                      -0.00814
                                F -test: share of top boys (1 + girl)                                       17.73
                                P > F : share of top boys (1 + girl)                                     2.59e-05
                                Coeff: share of top boys (1 + girl + below 25 + girl × below 25)         -0.00652
                                F -test: share of top boys (1 + girl + below 25 + girl × below 25)         9.333
                                P > F : share of top boys (1 + girl + below 25 + girl × below 25)         0.00226
                                Coeff: share of top boys (1 + girl + above 75 + girl × above 75)          -0.0109
                                F -test: share of top boys (1 + girl + above 75 + girl × above 75)          12.80
                                P > F : share of top boys (1 + girl + above 75 + girl × above 75)        0.000349

Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic scores, a migrant dummy and (within 5th grade) gender-specific
rank. | A      Appendix: Additional Tables

Table A1: Heterogeneous effects on 8th grade math scores on kids with/without high achievers in 8th
grade

                                                                                               (1)
                    VARIABLES                                                         8th grade math score

                    Share of top girls in math in 5th grade                                -0.0087**
                                                                                            (0.0034)
                    Share of top girls in math in 5th grade × Girl                         0.0201***
                                                                                            (0.0044)
                    Share of top boys in math in 5th grade                                 0.0114***
                                                                                            (0.0037)
                    Share of top boys in math in 5th grade × Girl                         -0.0303***
                                                                                            (0.0043)
                    With at least one high achieving in 8th grade (except oneself)         -0.0092**
                                                                                            (0.0041)
                    Girl dummy × At least one HAP                                             0.0063
                                                                                            (0.0053)
                    Share of top girls in math in 5th grade × At least one HAP               -0.0059
                                                                                            (0.0043)
                    Share of top girls in math in 5th grade × Girl × At least one         0.0286***
                                                                                            (0.0057)
                    Share of top boys in math in 5th grade × At least one HAP              0.0191***
                                                                                            (0.0046)
                    Share of top boys in math in 5th grade × Girl × At least one           -0.0144**
                                                                                            (0.0056)

                    Observations                                                            351,277
                    R-squared                                                                0.6174
                    Primary school FE                                                         YES
                    8th grade class FE                                                        YES
                    Individual controls                                                       YES
                    Class controls                                                            YES
                    Coeff: share of top girls (1 + girl)                                     0.0115
                    F -test: share of top girls (1 + girl)                                    9.821
                    P > F : share of top girls (1 + girl)                                   0.00173
                    Coeff: share of top girls (1 + SC)                                      -0.0146
                    F -test: share of top girls (1 + SC)                                      19.10
                    P > F : share of top girls (1 + SC)                                     1.26e-05
                    Coeff: share of top girls (1 + girl + SC + girl × SC)                    0.0342
                    F -test: share of top girls (1 + girl + SC + girl × SC)                   100.2
                    P > F : share of top girls (1 + girl + SC + girl × SC)                      0
                    Coeff: share of top boys (1 + girl)                                     -0.0190
                    F -test: share of top boys (1 + girl)                                     31.19
                    P > F : share of top boys (1 + girl)                                    2.46e-08
                    Coeff: share of top boys (1 + SC)                                        0.0304
                    F -test: share of top boys (1 + SC)                                       80.40
                    P > F : share of top boys (1 + SC)                                          0
                    Coeff: share of top boys (1 + girl + SC + girl × SC)                    -0.0143
                    F -test: share of top boys (1 + girl + SC + girl × SC)                    19.80
                    P > F : share of top boys (1 + girl + SC + girl × SC)                   8.79e-06
Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic scores, a migrant dummy and (within 5th grade) gender-specific
rank. | 48

Table A3: Heterogeneous effects on the probability to choose Liceo Scientifico on kids with/without
high achievers in 8th grade

                                                                                                   (1)
              VARIABLES                                                                      Liceo scientifico

              Share of top girls in math in 5th grade                                           -0.0060**
                                                                                                 (0.0023)
              Share of top girls in math in 5th grade × Girl                                     0.0057*
                                                                                                 (0.0031)
              Share of top boys in math in 5th grade                                           0.0091***
                                                                                                 (0.0025)
              Share of top boys in math in 5th grade × Girl                                    -0.0163***
                                                                                                 (0.0031)
              With at least one high achieving in 8th grade (except oneself)                      -0.0024
                                                                                                 (0.0029)
              Girl dummy × At least one HAP                                                     0.0106***
                                                                                                 (0.0036)
              Share of top girls in math in 5th grade × At least one HAP                          -0.0004
                                                                                                 (0.0029)
              Share of top girls in math in 5th grade × Girl × At least one                      0.0082**
                                                                                                 (0.0039)
              Share of top boys in math in 5th grade × At least one HAP                          0.0080**
                                                                                                 (0.0032)
              Share of top boys in math in 5th grade × Girl × At least one                      -0.0100**
                                                                                                 (0.0040)

              Observations                                                                        289,960
              R-squared                                                                            0.2752
              Primary school FE                                                                     YES
              8th grade class FE                                                                    YES
              Individual controls                                                                   YES
              Class controls                                                                        YES
              Coeff: share of top girls (1 + girl)                                              -0.000310
              F -test: share of top girls (1 + girl)                                               0.0173
              P > F : share of top girls (1 + girl)                                                0.896
              Coeff: share of top girls (1 + SC)                                                 -0.00634
              F -test: share of top girls (1 + SC)                                                  8.682
              P > F : share of top girls (1 + SC)                                                 0.00323
              Coeff: share of top girls (1 + girl + SC + girl × SC)                               0.00750
              F -test: share of top girls (1 + girl + SC + girl × SC)                               11.95
              P > F : share of top girls (1 + girl + SC + girl × SC)                             0.000552
              Coeff: share of top boys (1 + girl)                                                -0.00715
              F -test: share of top boys (1 + girl)                                                 10.80
              P > F : share of top boys (1 + girl)                                                0.00102
              Coeff: share of top boys (1 + SC)                                                    0.0172
              F -test: share of top boys (1 + SC)                                                  57.42
              P > F : share of top boys (1 + SC)                                                      0
              Coeff: share of top boys (1 + girl + SC + girl × SC)                               -0.00917
              F -test: share of top boys (1 + girl + SC + girl × SC)                               19.69
              P > F : share of top boys (1 + girl + SC + girl × SC)                              9.28e-06
Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic scores, a migrant dummy and (within 5th grade) gender-specific
rank. | 41

Heterogeneous effects on the probability to choose Liceo Scientifico

Figure 12: Heterogeneous effects on the probability to choose scientific liceo for kids with and without
high achievers from primary school in 8th grade




Note: This figure shows the effect of the share of own and opposite gender high achievers on girls and boys’ probability
to choose scientific liceo based on the estimates reported in Table A3

                                                          42

Figure 13: Heterogeneous effects on the probability to choose scientific liceo by 5th grade math score

    Figure 14: Bottom quartile, interquartile range and top quartile of the 5th grade math score

Note: This figure shows the effect of the share of own- and opposite-gender high achievers on girls and boys’ probability
to choose scientific liceo based on the estimates reported in Table A4

                                                           43

Robustness checks

                                        Table 5: Robustness (8th grade math achievement)

                                                       (1)              (2)                     (3)                  (4)                    (5)
 VARIABLES                                        Full sample   14 < Class size < 27   High achievers from 8   No math score FE   Correction for cheating

 Share of top girls in math in 5th grade          -0.0134***        -0.0153***              -0.0197***            -0.0773***            -0.0128***
                                                    (0.0025)          (0.0028)                (0.0025)              (0.0028)              (0.0027)
 Share of top girls in math in 5th grade × Girl    0.0376***        0.0399***                0.0407***             0.1536***            0.0331***
                                                    (0.0028)          (0.0030)                (0.0027)              (0.0033)              (0.0029)
 Share of top boys in math in 5th grade            0.0205***         0.0191***              0.0147***              0.0792***             0.0163***
                                                    (0.0026)          (0.0028)                (0.0026)              (0.0029)              (0.0028)
 Share of top boys in math in 5th grade × Girl    -0.0383***        -0.0384***              -0.0346***            -0.1567***            -0.0340***
                                                    (0.0028)          (0.0030)                (0.0027)              (0.0033)              (0.0029)
 Girl dummy                                        0.0079***         0.0075***               0.0080***            -0.0887***            0.0126***
                                                    (0.0027)          (0.0029)                (0.0027)              (0.0033)              (0.0028)

 Observations                                      361,329            318,797                351,277               351,277               351,277
 R-squared                                         0.6170              0.6195                 0.6173               0.5567                 0.5896
 Primary school FE                                   YES                YES                    YES                  YES                    YES
 8th grade class FE                                  YES                YES                    YES                  YES                    YES
 Individual controls                                 YES                YES                    YES                  YES                    YES
 Class controls                                      YES                YES                    YES                  YES                    YES
 Coeff: share of top girls (1+Girl)                 0.0242             0.0246                 0.0210               0.0762                 0.0203
 F -test: share of top girls (1+Girl)               87.12               74.61                 66.61                 732.1                  53.83
 P > F : Share of top girls (1+Girl)                   0                  0                      0                    0                      0
 Coeff: share of top boys (1+Girl)                 -0.0178            -0.0193                -0.0199               -0.0776               -0.0177
 F -test: share of top boys (1+Girl)                52.17              51.08                  65.08                  818                   45.99
 P > F : Share of top boys (1+Girl)                    0                  0                      0                    0                      0

Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic score (ESCS), a dummy for migrant and 5th grade gender-specific
rank in math in grade 5.. Un análisis comparativo entre la palabra más positiva ('top') y la más negativa ('deviation') se muestra en el gráfico adjunto.

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LexRank Summary:
47

Table A2: Heterogeneous effects on 8th grade math scores by quartiles of the 5th grade math scores
distribution

                                                                                                         (1)
                          VARIABLES                                                             8th grade math score

                          Share of top girls in math in 5th grade                                   -0.0090***
                                                                                                      (0.0032)
                          Share of top girls in math in 5th grade × Girl                             0.0429***
                                                                                                      (0.0038)
                          Share of top boys in math in 5th grade                                     0.0266***
                                                                                                      (0.0033)
                          Share of top boys in math in 5th grade × Girl                             -0.0440***
                                                                                                      (0.0038)
                          Q1                                                                        -0.1104***
                                                                                                      (0.0084)
                          Q4                                                                         0.1119***
                                                                                                      (0.0087)
                          Girl dummy × Q1                                                             0.0117**
                                                                                                      (0.0059)
                          Girl dummy × Q4                                                           -0.0895***
                                                                                                      (0.0059)
                          Share of top girls in math in 5th grade × Q1                                 0.0006
                                                                                                      (0.0049)
                          Share of top girls in math in 5th grade × Girl × Q1                       -0.0204***
                                                                                                      (0.0065)
                          Share of top boys in math in 5th grade × Q1                               -0.0186***
                                                                                                      (0.0054)
                          Share of top boys in math in 5th grade × Girl × Q1                         0.0188***
                                                                                                      (0.0065)
                          Share of top girls in math in 5th grade × Q4                              -0.0170***
                                                                                                      (0.0048)
                          Share of top girls in math in 5th grade × Girl × Q4                          0.0008
                                                                                                      (0.0066)
                          Share of top boys in math in 5th grade × Q4                                -0.0108**
                                                                                                      (0.0048)
                          Share of top boys in math in 5th grade × Girl × Q4                           0.0043
                                                                                                      (0.0064)

                          Observations                                                                351,277
                          R-squared                                                                    0.6181
                          Primary school FE                                                             YES
                          8th grade class FE                                                            YES
                          Individual controls                                                           YES
                          Class controls                                                                YES
                          Coeff: share of top girls (1 + below 25)                                   -0.00834
                          F -test: share of top girls (1 + below 25)                                    3.522
                          P > F : share of top girls (1 + below 25)                                    0.0606
                          Coeff: share of top girls (1 + above 75)                                    -0.0260
                          F -test: share of top girls (1 + above 75)                                    35.41
                          P > F : share of top girls (1 + above 75)                                  2.84e-09
                          Coeff: share of top girls (1 + girl)                                         0.0339
                          F -test: share of top girls (1 + girl)                                         110
                          P > F : share of top girls (1 + girl)                                           0
                          Coeff: share of top girls (1 + girl + below 25 + girl × below 25)            0.0141
                          F -test: share of top girls (1 + girl + below 25 + girl × below 25)           9.386
                          P > F : share of top girls (1 + girl + below 25 + girl × below 25)          0.00220
                          Coeff: share of top girls (1 + girl + above 75 + girl × above 75)            0.0177
                          F -test: share of top girls (1 + girl + above 75 + girl × above 75)           14.61
                          P > F : share of top girls (1 + girl + above 75 + girl × below 25)         0.000134
                          Coeff: share of top boys (1 + below 25)                                     0.00804
                          F -test: share of top boys (1 + below 25)                                    2.776
                          P > F : share of top boys (1 + below 25)                                     0.0958
                          Coeff: share of top boys (1 + above 75)                                      0.0159
                          F -test: share of top boys (1 + above 75)                                     13.61
                          P > F : share of top boys (1 + above 75)                                   0.000227
                          Coeff: share of top boys (1 + girl)                                         -0.0174
                          F -test: share of top boys (1 + girl)                                         32.28
                          P > F : share of top boys (1 + girl)                                       1.40e-08
                          Coeff: share of top boys (1 + girl + below 25 + girl × below 25)            -0.0171
                          F -test: share of top boys (1 + girl + below 25 + girl × below 25)            17.77
                          P > F : share of top boys (1 + girl + below 25 + girl × below 25)          2.54e-05
                          Coeff: share of top boys (1 + girl + above 75 + girl × above 75)            -0.0238
                          F -test: share of top boys (1 + girl + above 75 + girl × above 75)              26
                          P > F : share of top boys (1 + girl + above 75 + girl × above 75)          3.53e-07
Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic scores, a migrant dummy and (within 5th grade) gender-specific
rank.
49

Table A4: Heterogeneous effects on the probability to choose Liceo Scientifico by quartiles of the 5th
grade math scores distribution

                                                                                                            (1)
                                VARIABLES                                                             Liceo scientifico

                                Share of top girls in math in 5th grade                                  -0.0043**
                                                                                                          (0.0021)
                                                              th
                                Share of top girls in math in 5        grade × Girl                      0.0125***
                                                                                                          (0.0027)
                                                                  th
                                Share of top boys in math in 5         grade                             0.0151***
                                                                                                          (0.0022)
                                                                  th
                                Share of top boys in math in 5         grade × Girl                     -0.0233***
                                                                                                          (0.0026)
                                Q1                                                                      -0.0405***
                                                                                                          (0.0052)
                                Q4                                                                       0.0385***
                                                                                                          (0.0063)
                                Girl dummy × Q1                                                          0.0366***
                                                                                                          (0.0036)
                                Girl dummy × Q4                                                         -0.0457***
                                                                                                          (0.0042)
                                Share of top girls in math in 5th grade × Q1                                0.0027
                                                                                                          (0.0030)
                                Share of top girls in math in 5th grade × Girl × Q1                        -0.0058
                                                                                                          (0.0040)
                                Share of top boys in math in 5th grade × Q1                             -0.0112***
                                                                                                          (0.0033)
                                Share of top boys in math in 5th grade × Girl × Q1                      0.0128***
                                                                                                          (0.0040)
                                Share of top girls in math in 5th grade × Q4                            -0.0090***
                                                                                                          (0.0032)
                                Share of top girls in math in 5th grade × Girl × Q4                         0.0048
                                                                                                          (0.0046)
                                Share of top boys in math in 5th grade × Q4                                -0.0020
                                                                                                          (0.0033)
                                Share of top boys in math in 5th grade × Girl × Q4                         -0.0008
                                                                                                          (0.0045)

                                Observations                                                             289,960
                                R-squared                                                                  0.2762
                                Primary school FE                                                           YES
                                8th grade class FE                                                          YES
                                Individual controls                                                         YES
                                Class controls                                                              YES
                                Coeff: share of top girls (1 + below 25)                                 -0.00162
                                F -test: share of top girls (1 + below 25)                                 0.369
                                P > F : share of top girls (1 + below 25)                                   0.544
                                Coeff: share of top girls (1 + above 75)                                  -0.0133
                                F -test: share of top girls (1 + above 75)                                  21.88
                                P > F : share of top girls (1 + above 75)                                2.97e-06
                                Coeff: share of top girls (1 + girl)                                      0.00813
                                F -test: share of top girls (1 + girl)                                      14.59
                                P > F : share of top girls (1 + girl)                                    0.000135
                                Coeff: share of top girls (1 + girl + below 25 + girl × below 25)         0.00502
                                F -test: share of top girls (1 + girl + below 25 + girl × below 25)         4.068
                                P > F : share of top girls (1 + girl + below 25 + girl × below 25)         0.0437
                                Coeff: share of top girls (1 + girl + above 75 + girl × above 75)        0.00394
                                F -test: share of top girls (1 + girl + above 75 + girl × above 75)        1.685
                                P > F : share of top girls (1 + girl + above 75 + girl × below 25)          0.194
                                Coeff: share of top boys (1 + below 25)                                   0.00393
                                F -test: share of top boys (1 + below 25)                                   1.865
                                P > F : share of top boys (1 + below 25)                                   0.172
                                Coeff: share of top boys (1 + above 75)                                    0.0131
                                F -test: share of top boys (1 + above 75)                                  21.84
                                P > F : share of top boys (1 + above 75)                                 3.03e-06
                                Coeff: share of top boys (1 + girl)                                      -0.00814
                                F -test: share of top boys (1 + girl)                                       17.73
                                P > F : share of top boys (1 + girl)                                     2.59e-05
                                Coeff: share of top boys (1 + girl + below 25 + girl × below 25)         -0.00652
                                F -test: share of top boys (1 + girl + below 25 + girl × below 25)         9.333
                                P > F : share of top boys (1 + girl + below 25 + girl × below 25)         0.00226
                                Coeff: share of top boys (1 + girl + above 75 + girl × above 75)          -0.0109
                                F -test: share of top boys (1 + girl + above 75 + girl × above 75)          12.80
                                P > F : share of top boys (1 + girl + above 75 + girl × above 75)        0.000349

Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic scores, a migrant dummy and (within 5th grade) gender-specific
rank.
A      Appendix: Additional Tables

Table A1: Heterogeneous effects on 8th grade math scores on kids with/without high achievers in 8th
grade

                                                                                               (1)
                    VARIABLES                                                         8th grade math score

                    Share of top girls in math in 5th grade                                -0.0087**
                                                                                            (0.0034)
                    Share of top girls in math in 5th grade × Girl                         0.0201***
                                                                                            (0.0044)
                    Share of top boys in math in 5th grade                                 0.0114***
                                                                                            (0.0037)
                    Share of top boys in math in 5th grade × Girl                         -0.0303***
                                                                                            (0.0043)
                    With at least one high achieving in 8th grade (except oneself)         -0.0092**
                                                                                            (0.0041)
                    Girl dummy × At least one HAP                                             0.0063
                                                                                            (0.0053)
                    Share of top girls in math in 5th grade × At least one HAP               -0.0059
                                                                                            (0.0043)
                    Share of top girls in math in 5th grade × Girl × At least one         0.0286***
                                                                                            (0.0057)
                    Share of top boys in math in 5th grade × At least one HAP              0.0191***
                                                                                            (0.0046)
                    Share of top boys in math in 5th grade × Girl × At least one           -0.0144**
                                                                                            (0.0056)

                    Observations                                                            351,277
                    R-squared                                                                0.6174
                    Primary school FE                                                         YES
                    8th grade class FE                                                        YES
                    Individual controls                                                       YES
                    Class controls                                                            YES
                    Coeff: share of top girls (1 + girl)                                     0.0115
                    F -test: share of top girls (1 + girl)                                    9.821
                    P > F : share of top girls (1 + girl)                                   0.00173
                    Coeff: share of top girls (1 + SC)                                      -0.0146
                    F -test: share of top girls (1 + SC)                                      19.10
                    P > F : share of top girls (1 + SC)                                     1.26e-05
                    Coeff: share of top girls (1 + girl + SC + girl × SC)                    0.0342
                    F -test: share of top girls (1 + girl + SC + girl × SC)                   100.2
                    P > F : share of top girls (1 + girl + SC + girl × SC)                      0
                    Coeff: share of top boys (1 + girl)                                     -0.0190
                    F -test: share of top boys (1 + girl)                                     31.19
                    P > F : share of top boys (1 + girl)                                    2.46e-08
                    Coeff: share of top boys (1 + SC)                                        0.0304
                    F -test: share of top boys (1 + SC)                                       80.40
                    P > F : share of top boys (1 + SC)                                          0
                    Coeff: share of top boys (1 + girl + SC + girl × SC)                    -0.0143
                    F -test: share of top boys (1 + girl + SC + girl × SC)                    19.80
                    P > F : share of top boys (1 + girl + SC + girl × SC)                   8.79e-06
Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic scores, a migrant dummy and (within 5th grade) gender-specific
rank.
48

Table A3: Heterogeneous effects on the probability to choose Liceo Scientifico on kids with/without
high achievers in 8th grade

                                                                                                   (1)
              VARIABLES                                                                      Liceo scientifico

              Share of top girls in math in 5th grade                                           -0.0060**
                                                                                                 (0.0023)
              Share of top girls in math in 5th grade × Girl                                     0.0057*
                                                                                                 (0.0031)
              Share of top boys in math in 5th grade                                           0.0091***
                                                                                                 (0.0025)
              Share of top boys in math in 5th grade × Girl                                    -0.0163***
                                                                                                 (0.0031)
              With at least one high achieving in 8th grade (except oneself)                      -0.0024
                                                                                                 (0.0029)
              Girl dummy × At least one HAP                                                     0.0106***
                                                                                                 (0.0036)
              Share of top girls in math in 5th grade × At least one HAP                          -0.0004
                                                                                                 (0.0029)
              Share of top girls in math in 5th grade × Girl × At least one                      0.0082**
                                                                                                 (0.0039)
              Share of top boys in math in 5th grade × At least one HAP                          0.0080**
                                                                                                 (0.0032)
              Share of top boys in math in 5th grade × Girl × At least one                      -0.0100**
                                                                                                 (0.0040)

              Observations                                                                        289,960
              R-squared                                                                            0.2752
              Primary school FE                                                                     YES
              8th grade class FE                                                                    YES
              Individual controls                                                                   YES
              Class controls                                                                        YES
              Coeff: share of top girls (1 + girl)                                              -0.000310
              F -test: share of top girls (1 + girl)                                               0.0173
              P > F : share of top girls (1 + girl)                                                0.896
              Coeff: share of top girls (1 + SC)                                                 -0.00634
              F -test: share of top girls (1 + SC)                                                  8.682
              P > F : share of top girls (1 + SC)                                                 0.00323
              Coeff: share of top girls (1 + girl + SC + girl × SC)                               0.00750
              F -test: share of top girls (1 + girl + SC + girl × SC)                               11.95
              P > F : share of top girls (1 + girl + SC + girl × SC)                             0.000552
              Coeff: share of top boys (1 + girl)                                                -0.00715
              F -test: share of top boys (1 + girl)                                                 10.80
              P > F : share of top boys (1 + girl)                                                0.00102
              Coeff: share of top boys (1 + SC)                                                    0.0172
              F -test: share of top boys (1 + SC)                                                  57.42
              P > F : share of top boys (1 + SC)                                                      0
              Coeff: share of top boys (1 + girl + SC + girl × SC)                               -0.00917
              F -test: share of top boys (1 + girl + SC + girl × SC)                               19.69
              P > F : share of top boys (1 + girl + SC + girl × SC)                              9.28e-06
Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic scores, a migrant dummy and (within 5th grade) gender-specific
rank.
41

Heterogeneous effects on the probability to choose Liceo Scientifico

Figure 12: Heterogeneous effects on the probability to choose scientific liceo for kids with and without
high achievers from primary school in 8th grade




Note: This figure shows the effect of the share of own and opposite gender high achievers on girls and boys’ probability
to choose scientific liceo based on the estimates reported in Table A3

                                                          42

Figure 13: Heterogeneous effects on the probability to choose scientific liceo by 5th grade math score

    Figure 14: Bottom quartile, interquartile range and top quartile of the 5th grade math score

Note: This figure shows the effect of the share of own- and opposite-gender high achievers on girls and boys’ probability
to choose scientific liceo based on the estimates reported in Table A4

                                                           43

Robustness checks

                                        Table 5: Robustness (8th grade math achievement)

                                                       (1)              (2)                     (3)                  (4)                    (5)
 VARIABLES                                        Full sample   14 < Class size < 27   High achievers from 8   No math score FE   Correction for cheating

 Share of top girls in math in 5th grade          -0.0134***        -0.0153***              -0.0197***            -0.0773***            -0.0128***
                                                    (0.0025)          (0.0028)                (0.0025)              (0.0028)              (0.0027)
 Share of top girls in math in 5th grade × Girl    0.0376***        0.0399***                0.0407***             0.1536***            0.0331***
                                                    (0.0028)          (0.0030)                (0.0027)              (0.0033)              (0.0029)
 Share of top boys in math in 5th grade            0.0205***         0.0191***              0.0147***              0.0792***             0.0163***
                                                    (0.0026)          (0.0028)                (0.0026)              (0.0029)              (0.0028)
 Share of top boys in math in 5th grade × Girl    -0.0383***        -0.0384***              -0.0346***            -0.1567***            -0.0340***
                                                    (0.0028)          (0.0030)                (0.0027)              (0.0033)              (0.0029)
 Girl dummy                                        0.0079***         0.0075***               0.0080***            -0.0887***            0.0126***
                                                    (0.0027)          (0.0029)                (0.0027)              (0.0033)              (0.0028)

 Observations                                      361,329            318,797                351,277               351,277               351,277
 R-squared                                         0.6170              0.6195                 0.6173               0.5567                 0.5896
 Primary school FE                                   YES                YES                    YES                  YES                    YES
 8th grade class FE                                  YES                YES                    YES                  YES                    YES
 Individual controls                                 YES                YES                    YES                  YES                    YES
 Class controls                                      YES                YES                    YES                  YES                    YES
 Coeff: share of top girls (1+Girl)                 0.0242             0.0246                 0.0210               0.0762                 0.0203
 F -test: share of top girls (1+Girl)               87.12               74.61                 66.61                 732.1                  53.83
 P > F : Share of top girls (1+Girl)                   0                  0                      0                    0                      0
 Coeff: share of top boys (1+Girl)                 -0.0178            -0.0193                -0.0199               -0.0776               -0.0177
 F -test: share of top boys (1+Girl)                52.17              51.08                  65.08                  818                   45.99
 P > F : Share of top boys (1+Girl)                    0                  0                      0                    0                      0

Note: Individual controls include fixed effects for each decile of the distribution of 5th grade math scores, fixed effects
for each decile of the distribution of socio-economic score (ESCS), a dummy for migrant and 5th grade gender-specific
rank in math in grade 5.

Nota

El documento ‘CEFES-WP-474.pdf’ contiene 9576 palabras y se centra principalmente en share, grade, school, math, high, top, girls, girl, class, boys. El texto exhibe un tono predominantemente positive. Los temas clave que surgen del análisis incluyen primary school, 5th grade, top girls, top boys, 1 girl. Las palabras que más contribuyen al sentimiento positivo son top, achievement, positive, well, better, mientras que las que más contribuyen al sentimiento negativo son deviation, negative, errors, anxiety, randomly.