Table 1 Dependent and independent variables used in the analysis

Dependent variable

 Mathematics achievement

A normalized (mean 500, standard deviation 100) measure of student performance on PISA mathematics test

Independent variables

 Student-level

  First-generation

A binary indicator variable that takes value 1 for students who reported that they were born outside the US and whose parents were also born outside of the United States

  Second-generation

A binary indicator variable that takes value 1 for students who reported that they were born in the US and that at least one parent was born outside of the US

  Gender

A binary indicator variable where 1 denotes female, and 0 denotes male student

  Race/ethnicity

A series of six binary indicator variables indicating one of the race/ethnicity categories from the US PISA 2012 data: White, Black or African American, Hispanic, Asian, multiracial, and other racial/ethnic group

  Parental education

A series of three binary indicator variables that denote a level of parental education based on the categories from the US PISA 2012 data: less than high school, high school diploma and some college, and college degree and above

  Wealth

Wealth is an OECD-calculated index based on students’ responses to survey questions about to their families’ possessions including: their own rooms, a link to the internet, a DVD player, cellular phones, televisions, cars, and the numbers of rooms with a bath or shower (OECD 2014c). The variable is standardized so that the OECD mean equals zero and the standard deviation is one

  Language other than English

A binary indicator variable where 1 denotes that a student reported that they speak language other than English at home, and 0 otherwise

  Grade level

A series of three binary indicator variables that denote whether a student attended Grades 8–9, Grade 10, or Grades 11–12 when the assessment took place

 School-level

  Public

A binary indicator variable where 1 denotes public school

  Urban

A binary indicator variable where 1 denotes schools located either in an urban area or inside a principal city

  Suburban

A binary indicator variable where 1 denotes schools located in a town with 15,000 to 100,000 people

  Rural

A binary indicator variable where 1 denotes rural area or a small town with fewer than 15,000 people

  Free and reduced lunch greater than 75%

An indicator variable where 1 denotes schools where more than 75% of the students are eligible for free and reduced price lunch

  School size

Total school enrollment

  Class size

The average size of the student’s English classes

  Student–mathematics teachers ratio

An OECD-created variable calculated by dividing school size by the number of mathematics teachers

  No math teacher shortage

A binary indicator variable where 1 denotes schools where principal reported “not at all” to a survey item asking if a lack of qualified mathematics teachers hindered the school’s capacity to provide instruction

  Share of mathematics teachers with a bachelor’s or master’s degree in mathematics

An OECD-created variable where the total number of full and part-time mathematics teachers with mathematics degrees was divided by the total number of mathematics teachers

  Dropouts greater than 10%

An indicator variable that denotes schools in which school principals reported dropout rate greater than 10%

  Student climate

An index variable created by summing school principals’ responses on eight variables that assessed the extent to which the following student behaviors and attitudes hindered student learning: truancy, skipping classes, tardiness for school, absenteeism at required school events and activities, lack of respect for teachers, disruption of classes, use of alcohol or drugs, and bullying. Principals’ responses ranged from 1 “Not at all” to 4 “A lot.” We reverse-coded the variables before creating the index so that a higher value indicated a more positive school climate