Mathematical abilities are indispensable for science, technology, engineering and mathematics (STEM). However, there are challenges for the develop and assurance of high ability levels. Due to demographic reasons, we see a growing emergence of heterogeneous students (UNHCR, 2019). To this end, studies still show differences due to gender (Cascella, 2020a), socioeconomic status (SES; Bodovski et al., 2020) and to migration background (Cascella, 2020a) in mathematics achievement. These differences lead to inequality of educational opportunities and outcomes which predicts continuing inequality of social opportunities. Therefore, it is still important for the education policy to examine these factors (Boudon, 1974). 

To disentangle interdependencies between different factors contributing to inequality, we applied an intersectional approach as proposed in Cascella (2020a) to address heterogeneity of students and social inequalities in education. Effects of intersectionality of different social identities becomes important in educational research and helps to understand these counteracting variables. The model of intersectionality describes multiple characteristics of a person which function in isolation. While Crenshaw (1989) introduced intersectionality as grounded in Black feminist and critical race theories, Harris and Patton (2019) describe it as a traveling theory in different academic disciplines. 

Regarding differences with respect to the heterogeneity of students, there is still an ongoing discussion about the gender gap across different countries. Some studies show higher scores for male than for female students in mathematics and the opposite pattern in language proficiency assessments (Matteucci & Mignani, 2021). Other studies show that even though the gender gap still persists, equality increases. In some countries we even find no or a reversed gap (Meinck & Brese, 2019). Generally, we observe an underrepresentation of women working in STEM fields (Steot & Geary, 2018).

Differences in mathematics achievement are also connected to migration background and are mostly explained by language proficiency (Prediger et al., 2018). Research in English speaking countries shows an effect of reading proficiency on mathematics and science performance (Noble et al., 2014). We offer an intersectional approach to investigate challenges regarding mathematics achievement as described in the following studies: 

(a) Female Black and Latina schoolchildren show lower attainment values in mathematical motivational beliefs as compared to their male peers (Hsieh, 2021).

(b) “Girls’ disadvantage in mathematics increases, thus suggesting that such a disadvantage is mediated by girls’ reading skills, higher than boys’ reading skills” (Cascella, 2020a, p. 137).

(c) Regarding mathematical achievement, boys benefit more from high SES than girls (Cascella, 2020b).

In our research we focus on data from Austria, a country which experiences an emergence of heterogeneity in schools. In Austria, mathematical achievement is based on an ability model which shows some similarities to other European countries (KMK, 2003) and which consists of four mathematical action-related abilities [MARA] (representing & modelling, calculating & operating, interpretation, reasoning & justification), which vary in terms of complexity (BIFIE, 2013).

Based on the Austrian ability model and research about the relationship between reading skills and mathematics (Cascella, 2020a; Prediger et al., 2018) we assume a difference between more language-complex (interpretation, reasoning & justification) and less language-complex abilities (representing & modelling, calculating & operating). Therefore, we use an intersectional approach framework with a focus on mathematical achievement in our population-based study. We investigate how gender, migration background and SES affect MARA as well as the differences in interaction effects of gender, migration background and SES on MARA with respect to the level of language complexity of the MARA?

We use data from a population-based study conducted in Austrian schools by the Federal Institute for Quality Assurance [Institut des Bundes für Qualitätssicherung im österreichischen Schulwesen]. The data were collected as part of the educational standardized assessment in mathematics for eighth-graders (on average, 13-14 years old) in 2017. The assessment involved 72 704 students from 3 998 classes in 1 386 lower secondary schools. There are two different secondary school types: general secondary school (Allgemeine Pflichtschule [APS], 47 672 students) and academic secondary school (Allgemeinbildende höhere Schule [AHS], 25 032 students). Students attending AHS will be enrolled until twelfth grade and afterwards may enrol at university. Students attending the APS will be enrolled until eighth grade and then students change school for the compulsory ninth grade. Additionally, the students filled out questionnaires and provided information on their gender, family migration background, first language, and socioeconomic background. Performance data were based on the four MARA (representing & modelling, calculating & operating, interpretation, reasoning & justification). We will use the plausible values for these MARA. In order to explore intersectionality, we will investigate interaction effects between gender and migration, gender and SES as well as migration and SES on the four MARA. Because of the nested structure (individual, class, school) we plan to run a multilevel regression model for each of the four MARA and for the overall performance in mathematics. To answer our research questions, we: (a) First, we observe for each model how gender, migration background and SES affect MARA and overall performance. (b) Second, we compare the four models with the different MARA as a dependent variable to each other in order to detect differences in interaction effects of gender, migration background and SES across MARA. (c) Third, we investigate specific interactions with gender differences applying multigroup analyses for boys and girls for each MARA. Our analyses will show any differences between the less language-complex and the more language-complex abilities of MARA in terms of their relation to student background. We are also going to look for differences in model fit separately for boys and girls. Through our analyses, we will reveal whether boys and girls of differing SES and migration background have a higher/lower likelihood of getting into a high achieving group. We will perform all analyses in MPlus 8.8.

In order to answer our research questions, we are expected the following results based on previous findings. (a) The gender difference in mathematical performance could either still show a gender gap or support the hypothesis that the equality is increasing (Meinck & Brese, 2019). We assume that migration background and low SES will have a negative effect on MARA and overall performance. (b) The difference between girls with and without migration background will be higher in the more language-complex MARA than in the less language-complex. (c) The difference between boys with and without migration background will be higher in the less language-complex MARA than in the more language-complex. The expectation of the outcomes in (b) and (c) are based on the findings of Cascella (2020a) and Hsieh et al. (2021) in a way that migration background mediates the relationship between gender and mathematical performance. Nowadays it is of educational significance that we know more about the influence of intersectionality regarding characteristics of students’ background which do not only function in isolation. Our research could bring some insides about required action in policy and practice to ensure equal opportunities (OECD, 2018). One of the practical implications of our study would be to raise awareness among educational researchers and teachers about heterogeneity and intersectional effects on students’ achievement. For example, a possible approach could be the concept of differentiated instruction to support the students’ diverse learning needs. Homogenous and heterogeneous grouping of students in one classroom with the same learning goals could be an economically favorable possibility in terms of teachers’ resource (Smale-Jacobse et al., 2019).

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