Predicting mathematical performance: The role of language proficiency, digital competencies, and demographic factors

The INVALSI national assessment is a large-scale standardized testing program implemented across Italian schools to evaluate students’ competencies in Italian language, mathematics, and English as a foreign language. These assessments are conducted annually at key stages of the education system, that is, grades 2, 5, 8, and 13 (last year of upper secondary school), and are designed to provide objective, comparable data on student learning outcomes across regions, school types, and demographic groups (INVALSI, 2022, 2025). The mathematics test evaluates numerical skills, geometry, data analysis, and problem-solving abilities, aligned with national curriculum standards.

INVALSI plays a pivotal role in monitoring system-level equity and effectiveness in education by producing disaggregated performance data based on student background variables such as gender, ESCS, and geographic area (INVALSI, 2022, 2025). Its longitudinal and comparative nature makes it particularly useful for identifying regional disparities (e.g., North–South divide) and differences linked to school typology (Agasisti & Longobardi, 2014).

Student performance in mathematics is influenced by several interrelated factors that extend beyond cognitive ability, as demonstrated in both international and national standardized assessments (cf. Ayebale et al., 2020; Gamazo & Martínez-Abad, 2020; Mosia et al., 2025; Wang et al., 2023). Language proficiency has been repeatedly shown to be a strong predictor of mathematics achievement, particularly because word problems and test instructions often rely on reading comprehension skills (Ajello et al., 2018; Arikan et al., 2017; Prediger et al., 2018; Wang et al., 2023). For example, PISA 2018 results emphasized that students with higher reading literacy tend to perform better in mathematics, highlighting the interdependence of these domains (OECD, 2019). Similar associations have been found in INVALSI assessments in Italy, where students with stronger Italian language skills also demonstrated higher mathematics scores (Ajello et al., 2018; Azzolini et al., 2012; INVALSI, 2022).

Gender differences in mathematics performance continue to be debated (Else-Quest et al., 2010; Lu et al., 2023). While boys have traditionally outperformed girls in some countries, the gap has narrowed or reversed in others (Else-Quest et al., 2010). PISA 2018 showed minimal overall gender differences in OECD countries, but with variability by context and task type (OECD, 2019). In Italy, INVALSI data indicate a modest but persistent advantage for male students, which is therefore treated as a control factor in the present analyses (Contini et al., 2017; Giofrè et al., 2020; INVALSI, 2022).

ESCS is one of the most robust predictors of academic achievement across all subjects (Acıslı-Celik & Yesilkanat, 2023; Eriksson et al., 2021; Lee & Stankov, 2018; Wang et al., 2023). Students from higher socioeconomic backgrounds generally have access to more learning resources, both at home and in school, which contributes to better mathematics outcomes. According to PISA data, ESCS accounts for a significant portion of performance variance across countries (OECD, 2019). In Italy, the INVALSI results echo this pattern, demonstrating that students with higher ESCS tend to achieve better results, while those from disadvantaged backgrounds are at greater risk of underperformance (Agasisti & Longobardi, 2014; Cornoldi et al., 2013; Giofrè et al., 2020; INVALSI, 2022).

School typology, that is, the type of upper secondary education track (e.g., lyceum, technical, vocational), also plays a critical role in Italy (Argentin & Triventi, 2015). In the Italian system, lyceums (e.g., scientific, classical) are academically oriented upper secondary schools preparing students primarily for university education. Technical institutes offer applied training in fields like technology or business, while vocational schools focus on job-specific skills. Students in lyceum tracks, especially scientific and classical lyceums, typically score significantly higher in mathematics than their peers in technical or vocational schools (INVALSI, 2022). This gap reflects both selection effects and differences in curricular rigor and instructional quality. These differences reflect both prior selection and curricular differentiation, making school track an essential contextual variable rather than a purely instructional one.

Geographic macroregions (North East, North West, Center, South, South and Isles) are another significant factor in national assessments (Daniele, 2015; Giofrè et al., 2020). INVALSI data consistently show a persistent performance gap between Northern and Southern Italy, with students in the North achieving markedly higher mathematics scores. This geographic inequality reflects broader disparities in school infrastructure, teacher qualifications, and socioeconomic conditions (Agasisti & Vittadini, 2012; Costanzo & Desimoni, 2017; Giofrè et al., 2020).

Digital competencies are becoming increasingly relevant in contemporary educational assessments. In general terms, digital competence refers to students’ ability to use digital tools, process information, solve problems in digital environments, and engage critically with digital content (Vuorikari et al., 2022). These skills are increasingly recognized as transversal competencies that may support learning across subjects, including mathematics. Digital skills have been associated with problem-solving and data-handling abilities that are critical for mathematics. As digital technologies become more embedded in instructional practices and assessment formats, students’ ability to engage with digital tools appears to have a growing impact on their academic success (Fraillon et al., 2020). Most existing studies have focused on the use of digital technologies, such as specific mathematics software, reporting a positive relationship between technology use and mathematics achievement (cf. Engelbrecht & Borba, 2024; Viberg et al., 2023). However, far fewer studies have examined the direct relationship between measured digital competencies and mathematics performance. While technology use in mathematics classrooms has been widely studied, the role of students’ underlying digital skills, independent of specific software or instructional tools, remains underexplored in mathematics education research.

Digital skills are related to algorithmic thinking (Csernoch & Biró, 2015; Moylan & Code, 2024), problem-solving skills (Luengo-Aravena et al., 2024; Van Laar et al., 2017), critical thinking (Meirbekov et al., 2022; Van Laar et al., 2017), and reasoning (Gregersen & Baccaglini-Frank, 2023). All these skills are also connected to mathematics literacy (OECD, 2018). In the Italian context, the INVALSI (2025) assessment measured digital competence using the European DigComp 2.2 framework (Vuorikari et al., 2022). DigComp provides a structured way to assess students’ digital skills across multiple domains, enabling empirical investigation of how such skills relate to mathematics outcomes. Within DigComp 2.2, five competence areas are identified: Information and data literacy, Communication and collaboration, Digital content creation, Safety, and Problem solving. In this study, DigComp serves as an operational tool for measuring digital competence, rather than as a theoretical foundation for defining the research gap. Chaw and Tang (2024) found that all competence areas except safety significantly predicted students’ learning performance, including information and data literacy, communication and collaboration, digital content creation, and problem-solving. These findings suggest a plausible connection between digital competencies and mathematics performance.

Based on national and international literature, it might be stated that mathematics performance in standardized assessments is not solely a function of innate mathematical ability but is shaped by a network of linguistic, socio-demographic, and even technological factors. Understanding the interplay among these variables is essential for designing interventions and policies aimed at promoting equity and excellence in mathematics education.

The primary aim of this study was to identify and analyze the key demographic, linguistic, and digital competence factors that predict students’ mathematics performance as measured by the INVALSI assessment in Italy. Specifically, the study sought to:

Based on the results, the study addressed the following research questions:

RQ1: Which factors (language proficiency, digital competencies, and demographic variables) are the strongest predictors of mathematics performance?

RQ2: What is the structural role of mathematics performance within a network of academic and demographic variables?

RQ3: Do digital competencies form a distinct cluster in the network, and how do they interact with other variables?

RQ4: How do school-level factors (typology, macroregion) and student background (ESCS, gender) influence mathematics performance when accounting for academic competencies?

The present study is a secondary data analysis employing a quantitative, non-experimental, descriptive research design for causal investigation.

The sample used in this study was retrieved from the INVALSI official webpage (https://serviziostatistico.invalsi.it/invalsi_ss_data/microdati-campione-g10-2024-25/). All measures of student performance in mathematics, Italian, and digital competencies are standardized INVALSI test scores. On the official webpage, microdata for grade 10 students who took the INVALSI national assessment in the school year 2024/25 is present. Information about their performance in mathematics, Italian, and digital competencies is presented as three different databases. There were 19,008 students included in the INVALSI mathematics database, 18,876 students in the Italian database, and 19,020 students in the Digital competencies database. There were 17,491 students in the intersection of all three databases. These students were included in the final database that was considered for future analysis. No data was missing.

The sample comprised 17,491 Grade-10 Italian students. Among them, 8,222 (47.0%) were male and 9,269 (53.0%) were female. Regarding birth year, 34 students (0.2%) were born in 2006 or earlier, 293 (1.7%) in 2007, 1,528 (8.7%) in 2008, 14,194 (81.2%) in 2009, and 1,442 (8.2%) in 2010. In terms of school type, 8,294 students (47.4%) attended a scientific, classical, or linguistic lyceum; 2,988 (17.1%) attended another type of lyceum; 4,139 (23.7%) attended a technical school; and 2,070 (11.8%) attended a vocational school. Geographically, 3,707 students (21.2%) were from North-Western Italy, 3,629 (20.8%) from North-Eastern Italy, 3,469 (19.8%) from Central Italy, 3,451 (19.7%) from Southern Italy, and 3,235 (18.5%) from Southern Italy and the Isles. In terms of citizenship, 15,226 students (87.0%) were native Italians, 471 (2.8%) were first-generation immigrants, and 1,411 (8.2%) were second-generation immigrants.

In all analyses, students’ mathematics proficiency (INVALSI mathematics score) was specified as the dependent variable, while Italian language proficiency, digital competencies, and demographic characteristics were treated as predictors. The variables that were available in the official microdata database and that were used in the study are (those indicated by * are continuous variables using the Rash model, where the mean of the population is set to M = 200, and the standard deviation to SD = 40):

Data was analyzed using descriptive statistics and multiple regression to estimate the unique contribution of each predictor to mathematics performance. To validate the robustness of the regression findings against potential non-linearities, machine learning techniques (Boosting and Random Forest regression) were also run. Network analysis was used to explore the structural relationships and interdependencies among all variables, providing a holistic view of how competencies and background factors interact. All analyses were performed with JASP v. 0.17.1.0.

Table 1 presents descriptive statistics of the continuous variables and the Pearson's correlation coefficients between the variables. Mathematics performance showed strong positive correlations with Italian proficiency (r = .635) and DigComp competencies (r = .531), and a weaker positive correlation with ESCS (r = .230). The DigComp subskills and overall score were highly intercorrelated (r > .65).

To identify the strongest independent predictors, a multiple regression analysis was conducted (Table 2). The final, fully adjusted model (Model 4) explained 51.5% of the variance in mathematics scores. Italian language proficiency was the strongest predictor (β = .420, p < .001). Overall digital competence was the second strongest predictor (β = .181, p < .001). Among demographic and contextual factors, school typology showed substantial negative effects, with students in vocational (β = −.537) and other lyceums (β = −.435) scoring significantly lower than those in academic lyceums. Gender (β = −.339, p < .001), indicating lower scores for female students, and school macroregion, with students from Southern Italy and the Isles scoring lowest (β = −.360), were also significant predictors. The effect of ESCS was positive but very small (β = .022, p < .001). The specific DigComp subskills did not retain significant independent predictive power in the full model. This answers RQ1 by establishing a clear hierarchy: language proficiency is the dominant predictor, followed by general digital competence, with school type, gender, and region also exerting significant independent influence.

To assess the robustness of the regression findings against non-linearities and complex interactions, we employed two ensemble machine learning methods: Boosting Regression and Random Forest regression. Critically, both models replicated the rank order of predictor importance identified by linear regression: Italian proficiency was the strongest predictor, followed by overall DigComp competence, and then school typology. The detailed specifications, performance metrics, and variable importance scores for both models are provided in the electronic Supplemental material.

Network analysis was used to examine the structural relationships among all variables. The resulting network (Figure 1) was relatively dense, with 44 of 55 possible connections present. To identify influential variables and potential clusters, we computed centrality and clustering measures (Tables 3 and 4). The results reveal a clear structure: digital competence (DigComp competencies) was the most central variable in the network, exhibiting the highest strength and betweenness. This indicates it acts as a key hub connecting other factors. In contrast, the four DigComp subskills (Information and data literacy, Communication and collaboration, Digital content creation, Digital safety) formed a tightly interconnected cluster (high positive clustering coefficients across all measures), confirming they represent a cohesive construct.

Mathematics performance showed moderate centrality but negative strength, consistent with its role as a central outcome variable that is influenced by the network rather than a driver of it. Italian proficiency showed a positive expected influence, underscoring its supportive role. Demographic and contextual variables (ESCS, gender, macroregion, school type) generally occupied peripheral positions with low or negative centrality.

The partial correlation matrix (weights matrix, Table 5) clarified these relationships. The strongest edge was a positive link between Mathematics performance and Italian proficiency (.387), highlighting their unique association. Mathematics performance also had direct negative connections with School typology (−.278) and School macroregion (−.195), pointing to structural inequalities. Meanwhile, the DigComp subskills showed very strong mutual positive connections (>.72) but only weak direct links to mathematics performance, suggesting their influence may be indirect.

Overall, the network analysis reveals: (1) language proficiency is the primary direct correlate of math scores; (2) digital competence is a central, cohesive cluster of skills that may support achievement indirectly; and (3) demographic and school-context factors maintain direct negative associations with outcomes, indicating persistent structural effects.

Therefore, mathematics performance had moderate betweenness and closeness but negative strength, confirming its structural role as a central outcome variable that is influenced by the network rather than a driver of it (RQ2). Mathematics performance is, hence, a central, dependent node in the network. Additionally, DigComp subskills formed a tightly interconnected cluster, as evidenced by consistently high positive clustering coefficients across all measures. The overall DigComp competencies variable acted as a central hub for this cluster, exhibiting the highest strength and betweenness in the entire network. It answers RQ3 by demonstrating that digital competencies form a highly cohesive, distinct cluster, with the overall score serving as its central hub.

Furthermore, mathematics performance retained a strong direct positive link with Italian proficiency and weak direct links to digital skills. Crucially, it also maintained direct negative connections with School typology and School macroregion. The centrality measures showed that these demographic and contextual variables (ESCS, gender, macroregion, school type) occupied peripheral positions with low or negative centrality, indicating their influence is not mediated through the central competency variables. This answers RQ4 by showing that even after accounting for academic competencies (language and digital skills), school-level factors (type, region) and student gender maintain significant direct negative associations with mathematics performance, highlighting persistent structural inequalities.

In the multiple linear regression models, Italian proficiency emerged as the most consistent and strongest predictor of mathematics achievement across all model specifications. This result supports previous findings (Ding & Homer, 2020; Thien et al., 2015; Wang et al., 2023). In particular, language skills and proficiency are key elements to understand mathematics problems and effectively solve them (cf. Mercer & Sams, 2006; Ufer & Bochnik, 2020). This finding was further confirmed by the machine learning analyses. Both Boosting and Random Forest regression models identified Italian proficiency as the dominant predictor. This consistency across modeling techniques underscores the critical role of language proficiency in mathematics achievement. These results reinforce the international consensus that mathematics performance in large-scale assessments is inherently language-mediated, regardless of national curriculum differences.

DigComp competencies were also statistically significant predictors in the first two models, whereas the specific DigComp subcomponents did not retain statistical significance in the fully adjusted model. Therefore, these results are partly consistent with findings on general performance (Chaw & Tang, 2024). Since digital competencies are related to several skills that are central to mathematical literacy, such as algorithmic thinking, problem-solving, critical thinking, and reasoning (cf. Csernoch & Biró, 2015; Moylan & Code, 2024), and students’ learning (Chaw & Tang, 2024), it is plausible that reinforcing these cognitive skills may also support mathematics proficiency. In particular, strengthening algorithmic thinking may have a beneficial effect on mathematics proficiency, especially with regard to procedural knowledge. Similarly, digital problem-solving skills may contribute to more effective mathematics problem-solving strategies, thereby potentially enhancing students’ mathematics performance (cf. Jonsson et al., 2014).

As reported by Chaw and Tang (2024), students’ safety competencies are not associated with learning performance, a finding consistent with our results. This may be because protecting data and navigating the web safely does not require higher-order mathematical competencies or reasoning. However, a notable divergence from Chaw and Tang's (2024) findings emerges when considering the other variables, that is, information and data literacy, communication and collaboration, and digital content creation, which did not have statistically significant predictive power for students’ mathematics achievement in our models. One plausible explanation is that the overall DigComp index subsumes these competencies, reducing their individual statistical contribution when modeled simultaneously.

It may also be that information and data literacy competencies are more closely linked to how digital information is obtained and how data are presented, skills that align more with statistical literacy than with mathematical literacy per se. Communication and collaboration skills, while important in a socially connected world, might exert limited influence on mathematics performance due to the relatively marginal role of collaboration in mathematics instruction (although communication is recognized as an important element of mathematics education; Morgan et al., 2014). Furthermore, digital content creation may involve creativity and digital skills that, despite their importance in mathematics (particularly creativity; Leikin & Pitta-Pantazi, 2013), manifest in forms that differ from domain-general creativity (although the two are positively correlated; Schoevers et al., 2020). These findings contribute to the international debate on digital competence by showing that digital skills matter for mathematics performance, but their influence may be indirect, mediated by broader cognitive and linguistic abilities. This nuance is relevant for countries adopting DigComp-aligned frameworks or similar digital literacy standards.

Complementing these findings, network analysis revealed that DigComp competencies hold the highest betweenness and strength centrality within the network, indicating that digital competence acts as a critical structural bridge connecting other variables, including mathematics performance and Italian proficiency. The strong clustering of digital subskills further highlights that these competencies form a cohesive cluster, suggesting that improvements in one digital skill are likely to positively influence others.

Interestingly, the network also shows relatively weak direct partial correlations between DigComp subskills and mathematics performance, suggesting their influence may be indirect or mediated via other variables such as language proficiency. This nuance may explain why individual DigComp subcomponents did not independently predict math scores in fully adjusted regression models, even though the overall digital competence score was important. This structural insight is valuable beyond the Italian context, as it suggests that digital competence may function as a transversal mediator in educational systems where digital assessments and digital learning environments are increasingly prevalent.

Among the demographic variables, school typology was significantly associated with mathematics performance, indicating differences in achievement across school types. These results align with previous research (Argentin & Triventi, 2015), which found that students from lyceums tend to achieve higher scores than those from technical and vocational schools. This finding should also be interpreted from a curricular perspective. Since these three school typologies have different focuses: lyceums providing a broad general education across all subjects, while technical and vocational schools emphasize professional development and practical knowledge, the mathematics curriculum reflects these distinctions. Lyceum students receive more general, theoretical mathematical instruction, whereas students in technical and vocational schools experience a more specialized, practice-oriented curriculum. Additionally, students’ motivation to learn mathematics may differ across these school types, which could partly explain lower INVALSI test scores among technical and vocational school students due to reduced motivation and effort.

Gender showed a statistically significant negative coefficient, suggesting that, on average, females had lower predicted scores in the sample. This result aligns with a substantial body of national (Contini et al., 2017; Giofrè et al., 2020; INVALSI, 2022, 2025) and international research (Else-Quest et al., 2010; Lu et al., 2023) on gender differences in mathematics. One theoretical explanation for these differences is the gender stereotype model (Cvencek et al., 2011), which posits that mathematics (and science) are perceived as “male domains,” whereas reading (and the humanities) are viewed as “female domains.” This stereotype has been repeatedly documented in Italian schools, where evidence suggests that the gender gap in mathematics tends to widen in higher grades (Muzzatti & Agnoli, 2007; Passolunghi et al., 2014).

ESCS was also a statistically significant, though relatively small, positive predictor. On one hand, this result corroborates findings from national and international literature (cf. Agasisti & Longobardi, 2014; Cornoldi et al., 2013; Giofrè et al., 2020; INVALSI, 2022, 2025; OECD, 2019); however, the effect size is smaller than expected. This may be because other factors, such as students’ macroregion, capture some of the variance that ESCS would otherwise explain. In particular, literature consistently shows that students from southern Italian regions generally have lower ESCS compared to those from northern regions (Daniele, 2015; Giofrè et al., 2020). Therefore, while international studies emphasize ESCS as a strong predictor of mathematics performance on standardized tests, in the Italian context, macroregion may serve as a proxy for ESCS to some extent. It is important to interpret this finding cautiously, as generalization is limited; hence, future research should aim to better understand the complex relationship between these two variables.

Machine learning results reinforced the importance of school typology. School macroregion, although less influential, emerged as a modest but consistent predictor, reflecting regional disparities highlighted in the literature. Gender and ESCS had relatively minor but statistically significant effects, with gender slightly more influential than ESCS in the models. Network analysis further illustrated that demographic variables such as ESCS, gender, and macroregion generally occupy peripheral positions with low or negative centrality measures, indicating they are less central in the network of predictors compared to cognitive and digital competencies. The negative partial correlations between these demographic factors and mathematics performance highlight potential structural inequalities influencing achievement.

Based on the findings, some practical recommendations emerge for educators and policymakers. Firstly, given the robust association between Italian proficiency and mathematics performance, integrating language development into mathematics teaching could improve comprehension and problem-solving. Strategies may include explicit vocabulary instruction and reading comprehension exercises contextualized in mathematical content. While this study draws on Italian data, the recommendation aligns with international research emphasizing the importance of mathematical language proficiency across diverse educational systems. Thus, rather than proposing system-specific reforms, we highlight the broader implication that mathematics instruction benefits from explicit attention to linguistic demands. We therefore suggest that educators develop specific laboratories or interdisciplinary classes to reinforce students’ language skills and interconnect them with mathematics problems.

Secondly, the central role of DigComp competencies highlights the importance of digital skills in supporting mathematical learning. Schools should prioritize fostering algorithmic thinking, digital problem-solving, and critical reasoning skills alongside traditional mathematics content. Although recent Italian initiatives (e.g., coding programs supported by PNRR) illustrate one possible approach, the broader implication is that educational systems worldwide may benefit from integrating digital competence development into mathematics curricula in ways that reflect their own policy contexts and technological infrastructures. This might help students to gain digital competencies, develop their critical thinking, algorithmic thinking, reasoning, and mathematical modeling, which would, in turn, result in better achievement in mathematics as well.

Thirdly, differences across lyceums, technical, and vocational schools reflect varied curricular emphases. Educational strategies should consider these differences, providing support that addresses both curriculum content and student engagement, particularly in technical and vocational settings. Tracked or stratified educational systems often produce differentiated mathematics outcomes, and targeted support for students in less academically oriented tracks may be necessary across many countries. Being mathematical literacy of great importance in today's society and labor market, specific interventions are needed to guarantee students from each school type comparable mathematical skills.

Despite its contributions, this study has some limitations that should be considered when interpreting the findings. First, the study relies on observational data from the 2024/25 INVALSI national assessment, which limits the ability to establish causal relationships among language proficiency, digital competencies, demographic variables, and mathematics performance. Second, while the dataset is large and nationally representative, some variables, such as ESCS and macroregion, may share overlapping variance, potentially complicating the interpretation of their unique effects. The finding that ESCS had a relatively smaller effect size than expected may reflect this issue, as macroregion might act as a proxy for socioeconomic status in the Italian context. Third, the study focuses on broad measures of digital competence using the DigComp framework; however, some subdomains showed limited independent predictive power, suggesting that further refinement or alternative conceptualizations of digital skills might be needed. This raises questions that extend beyond Italy, particularly for countries adopting or adapting DigComp-aligned frameworks, where the granularity and operationalization of digital competence remain active areas of debate. Additionally, motivation, attitudes, and other affective factors influencing mathematics performance and digital competence were not included, representing an important gap. Finally, the cross-sectional nature of the data precludes analysis of developmental trajectories or changes over time, such as the evolution of the gender gap in mathematics achievement.

Future research should address these limitations to deepen understanding of the complex factors influencing mathematics achievement. Longitudinal studies could clarify causal pathways and examine how language proficiency, digital competencies, and demographic factors interact over time, particularly across critical educational transitions. Further investigation into the role of affective and motivational variables, including students’ attitudes toward mathematics and digital learning, may offer additional explanatory power. Given the limited predictive power of certain DigComp subcomponents, qualitative or mixed-methods studies might explore how specific digital skills relate to mathematical problem-solving in classroom contexts. Moreover, research should unpack the intertwined roles of ESCS and regional factors within Italy, investigating how socioeconomic and geographic inequalities shape learning opportunities and outcomes. Finally, targeted research is needed to explore mechanisms underlying gender disparities in mathematics, particularly interventions that might reduce stereotype effects and promote equitable engagement in STEM subjects.