Prediction of math achievements by executive functions and math self-efficacy among grade 12 students in three study levels

Abstract

Introduction:

Extensive research has established strong connections between both general and specific executive functions (EFs) and students' mathematics achievement. However, less is known about whether different components of EFs – specifically metacognitive skills and behavioral regulation – contribute uniquely to math performance across varying academic levels, and whether math self-efficacy (MSE) serves as a mediating mechanism. This study examined the differential predictive roles of metacognitive and behavioral regulation EFs on math achievement across three study levels and investigated whether MSE mediates these relationships.

Methods:

The sample included 409 12th-grade students representing low, medium, and high study levels. Participants completed the Behavior Rating Inventory of Executive Function-Self Report (BRIEF-SR) and a MSE measure. Path analyses and Structural Equation Modeling (SEM) were conducted separately for each study-level group to assess direct and mediated relationships among EFs, MSE, and mathematics achievement.

Results:

SEM revealed distinct patterns across the study levels. In the low study level (LSL) group, metacognitive EFs – specifically working memory and planning/organizing - significantly predicted mathematics achievement, while behavioral regulation EFs showed no predictive value for this group. In the high study level (HSL) group, behavioral regulation EFs – particularly response inhibition - were the primary predictors. In the medium study level (MSL) group, both EF components contributed to math performance. SEM further showed that MSE directly predicted math achievement for all groups. Additionally, MSE mediated the relationships between both EF components and math achievement in the MSL and HSL groups, but no mediation effect was observed in the LSL group.

Discussion:

The findings demonstrate that the influence of EFs on mathematics achievement varies by students' study level, and that MSE plays a critical role, particularly for students in the MSL and HSL. The absence of mediation in the LSL group may reflect long-standing academic challenges and persistent feelings of failure among these students. The results highlight the need for differentiated instructional approaches and targeted teacher training programs that align math teaching practices with students' EF profiles and study levels. Such alignment may help bridge the gap between students' cognitive needs and the demands of mathematical tasks, ultimately supporting more effective and equitable math learning.

Introduction

Mathematics accompanies people throughout their lives and is an essential tool for observing and understanding the world. It is a significant language element implemented in daily activities, such as telling time, describing quantities and measurements, and comparing and assessing various scenarios. In modern society, a good understanding of math is crucial for achieving success and enjoying a better quality of life (Gross et al., 2009; OECD, 2017, 2021; Parsons and Bynner, 2005) and is considered vital to exact sciences that are based on mathematics (Aharoni, 2004; Quaye and Pomeroy, 2022).

Given this fundamental importance, educational systems worldwide have prioritized mathematics education. In the Israeli education system, high school students study mathematics at one of three levels: basic (low), intermediate, or advanced (high). The distinction among these study levels reflects not only the depth and complexity of mathematical content but also serves as a key determinant of future academic opportunities. A student's study level selection is determined by their mathematical ability, academic aspirations, and future fields of interest.

To support this tiered educational approach and ensure student success across all levels, professional development tracks for math teachers and diverse teaching and learning materials, especially for students who experience difficulties in this discipline, have been created. The mathematics matriculation exam is administered at three levels (low, medium, and high) at the end of Grades 11 and 12 and serves as the final math assessment in Israel's public schools. Accordingly, the high school math curriculum (Ministry of Education, 2011) is carefully structured to accommodate these three distinct study levels.

Executive functions and math ability

Various models offer different perspectives on executive functions (EFs) (Burgess and Simons, 2005). Researchers do not agree on a single model to explain EFs. However, there appears to be a consensus that EFs constitute a multidimensional framework of cognitive and behavioral abilities (Tirapu-Ustárroz et al., 2008, 2017). The EFs allow a person to define goals purposefully, develop plans to achieve them, and regulate cognitive and emotional behaviors (Grieve et al., 2014). In this study, we used the multidimensional framework proposed by Gioia and Isquith (2004). They defined EFs as a set of distinct yet related cognitive and behavioral abilities that support problem-solving and goal-directed actions. We chose Gioia and Isquiths (2004) multidimensional framework for the following reasons: (a) their model and questionnaire are widely validated and used in the field of EF research, (b) the questionnaires serve professionals, such as occupational therapists and psychologists, in diagnosing students to advance them within the educational system, and (c) the range of EFs presented in this model are congruent with the skills desired by educational systems, as well as with the skills required in the 21st century. These skills are critical in rapidly changing digital demands that necessitate lifelong learning and effective problem-solving.

EFs have wide-ranging effects, spanning cognitive, motor, social-emotional, and motivational-personality domains (Eslinger, 1996). Effective EFs are recognized as crucial contributors to achievement in educational settings and society (Miller and Marcovitch, 2011). In recent years, the role of EFs in math achievements has been the focus of much research (e.g., Bull and Lee, 2014; Duncan et al., 2016; Geary, 2004; Hawes et al., 2019; Lenes et al, 2020; Tanami, 2021; Tanami and Eilam, 2021a, 2021b; Ten Braak et al., 2022).

There is considerable evidence of a relationship between EFs and math achievements (e.g., Bull and Lee, 2014; Lenes et al, 2020; Ten Braak et al., 2022). This relationship has been investigated at the level of a general EF factor (e.g., Kahl et al., 2021; Tanami, 2021; Tanami and Eilam, 2021a, 2021b; Ten Braak et al., 2022) and found consistent throughout all developmental stages (Duncan et al., 2016; Cragg et al., 2017; Kahl et al., 2021). Recent research involving high school students (Tanami, 2021; Tanami and Eilam, 2021a, 2021b) revealed that a higher total EF score becomes necessary as mathematics study levels increase.

This relationship was investigated on specific EFs (e.g., Bull and Scerif, 2001; Cragg et al., 2017; Georgiou et al., 2020). Several researchers have highlighted that WM, inhibition of distracting information, and the ability to shift attention flexibly between tasks are more closely associated with mathematical abilities than other EFs (e.g., Bull and Scerif, 2001; Cragg et al., 2017; Živković et al., 2022). However, no consistent dominance for a particular EF emerges when examining the relationship between these three EFs and mathematics across different age groups (e.g., Cheung and Chan, 2022; Georgiou et al., 2020). It should be noted that some studies found a more consistent relationship between WM and math achievements as compared to the relationships between inhibition and shifting and math achievements (e.g., Blair and Razza, 2007; Clark et al., 2010; Cragg et al., 2017; Georgiou et al, 2020; Rose et al., 2011; Thorell, 2007; Yeniad et al., 2013; Živković et al. 2022). These disparities underscore the need for an analytic assessment of the relationship between EFs and math achievements. The main goal of the current study is to address gaps by investigating which specific EFs predict math achievement. In other words, our goal is to underline specific EFs that affect math performance in classroom learning, beyond the specific EFs of WM, cognitive flexibility (shifting), and inhibition. The specific EFs which are the focus of our study are based on the BRIEF - Behavioral Rating Inventory of Executive Functions (Guy et al., 2004), which include inhibition, emotional control, shifting, monitoring, working memory, planning/organizing, organization of materials, and task completion factors.

Math self-efficacy and math achievements

A variety of factors contribute to mathematics achievement. While EFs represent a cognitive component, students' math self-efficacy (MSE) represents a critical affective component that plays a significant role in mathematics learning outcomes. Bandura's social cognitive theory is the most prominent learning theory, and self-efficacy is an important component of the theory (Sakellariou, 2022; Yesuf et al., 2023). Following Bandura's (1977) theory, Hackett and Betz (1989) suggested that “mathematics self-efficacy can be distinguished from other measures of attitudes toward mathematics in that mathematics self-efficacy is a situational or problem-specific assessment of an individual's confidence in her or her ability to perform or accomplish a particular task or problem (p. 262).”

Various studies have shown that mathematics self-efficacy (MSE) significantly and positively affects math achievement (Aksu and Guzeller, 2016; Arifin et al., 2021; Delioglu, 2017; Duran and Bekdemir, 2013; Erkek and Isiksal-Bostan, 2015; Ozkal, 2019; Shone et al., 2024; Tasdemir, 2016; Yildirim and Yildirim, 2019; Zakariya, 2022). MSE was found as a significant predictor of math performance (Kalaycioglu, 2015; Ozkal, 2019; Skaalvik et al., 2015) and math achievement in TIMSS 1999, 2007, 2011, and 2015 among Turkish students (Doğan and Barış, 2010; Sari et al., 2017; Yavuz et al., 2017). In examining the predictability of math achievements among 12th-grade students, Tanami and Eilam (2021b) and Shone et al. (2024) found MSE to be a strong predictor of math achievements. Furthermore, MSE was found to have a stronger prediction of math achievements than a total EF score, student's attitude towards mathematics, and gender.

The current study: objective and questions

Recognizing and addressing EF requirements in learning tasks is essential for developing 21st-century learning skills. To teach effectively, teachers must understand the cognitive and emotional processes involved in learning and adapt their methods accordingly (Daniels and Shumow, 2003; Dubinsky et al., 2013; Lederman and Torff, 2016). A deeper understanding of EFs at various levels of knowledge enables teachers to design targeted interventions that support students’ mathematical development.

The present study seeks to expand previous research by focusing on two core aspects with theoretical and practical implications. First, while earlier studies examined the relationship between math achievement and a limited set of EF components—primarily working memory, inhibition, and cognitive flexibility (e.g., Bull and Scerif, 2001; Cragg et al., 2017; Živković et al., 2022);—the current research broadens this scope. It includes additional EF dimensions such as emotional control, impulse control, planning and organization, material organization, and task completion, thereby capturing a wider range of learning-related functions.

Second, this study investigates whether the relationship between EF and math achievement is mediated by students' math self-efficacy (MSE) and their level of math study. By adopting an analytical and integrative perspective, this research aims to provide insights that may support the development of precise, differentiated intervention strategies tailored to each study level.

Hypotheses

A differential positive and significant correlation between specific EF and math achievement in each study level will be found.

MSE will mediate the relationship between specific EF and math achievement in each study level.

Method

Participants

The sample included 409 12th-grade students from six schools in central regions in Israel. The students were recruited from classes of three math matriculation levels (low, medium, and high; see Instruments). The mathematics matriculation exam is administered nationwide at grades 11 and 12. The assignment of math levels is a dynamic process that starts in Grade 10 and is finalized at the end of Grade 11. The matriculation exam is nationwide administered, so all students at each study level on the same day and at the same time. The mean age of the students was 17.4 (SD = 0.45) years (range: 16–18 years). The sample was composed of 152 males (Low = 75; Medium = 28; High = 53) and 275 females (Low = 103; Medium = 61; High = 93). The student characteristics are summarized in Table 1.

Students' placement into mathematics study levels in high school is determined by subject coordinators, based on pedagogical judgment that draws on prior academic achievement, evaluations of students' ability and perseverance, and teachers' recommendations, in alignment with the requirements of the Ministry of Education curriculum. Initial placement occurs in Grade 10 and may be adjusted during Grades 10–11 based on students' progress. This process is dynamic and aims to support the optimal development of students' mathematical potential. Despite its dynamic nature, transitions between study levels are limited in scope and generally reflect consistent and well-founded professional judgments by the teaching staff.

The mathematics matriculation examination is administered nationwide in Grades 11 and 12. Assignment to mathematics study levels is finalized by the end of Grade 11, and all students within each study level take the matriculation examination on the same day and at the same time under standardized national conditions.

Instruments

Behavior rating inventory of executive function–self report (BRIEF-SR)

The executive functions were examined using the BRIEF-SR (Guy et al., 2004), a self-report questionnaire for assessing EFs of teenagers aged 11–18. The BRIEF-SR includes 80 statements representing eight different clinical components of EF. The eight components are divided into two scales: Behavioral regulation, which includes inhibition, shift, emotional control, and monitoring, and Metacognition, which includes task completion, WM, organization of materials, and planning/organizing. Respondents are asked to use a three-point Likert-type scale to mark the frequency in which the behaviors described in each statement occur: (1) “never”, (2) “sometimes”, or (3) “often or always”. An achievement score is calculated for each clinical component. Based on these scores, three indices are obtained: BRI, MI, and a global executive composite. In the context of this study, only the Behavioral Regulation Index (BRI) and the Metacognition Index (MI) serve as latent variables to investigate the link between EF and math achievements.

Studies in the United States support the reliability and validity of various BRIEF questionnaires (Gioia et al., 2000). The Cronbach alpha reliability of the BRIEF-SR achievement scores determined for the current sample was high for all scales (Table 2). The validity of the BRIEF-SR was tested by calculating the inter-correlations between the functions belonging to each field. The BRI correlation range was 0.28–0.69, and the MI range was 0.52–0.70. These findings indicate that while there is a link between the various functions in each field, they are still distinct—a significant positive correlation of 0.60 (p < .001) between BRI and MI was found.

Math achievement test

The Math Achievement Test, composed by the Ministry of Education, is a two-stages test administered in Grade 11 and Grade 12. The students are assigned to math levels based on their achievements in Grade 11. Some math topics are taught in all three study levels (i.e., algebraic technique, verbal questions, analytical geometry, series, trigonometry, probability, growth and decay, differential, and integral calculus). In contrast, other topics are taught separately in each level. The common topics are taught in different degrees of depth and complexity (Ministry of Education, 2011). We chose the math matriculation test as the focus of our study as it signifies the culmination of 14 years of formal math studies (including pre-K and K learning) and every high school graduate in Israel is required to pass it. Because of its centrality, it determines future academic learning. The education system makes great efforts to enable various students to succeed in these tests, each according to his/her ability. As aforementioned, there are three study tracks leading to the math matriculation exam: high, medium, and low levels.

Math self efficacy (MSE)

The MSE, designed specifically for the current study, is composed of five questions that refer to the student's self-evaluation of math ability. Students were asked to mark the degree to which they agree with each statement, using a 5-point Likert-type scale. For example: “How do I evaluate myself in math learning—weak, medium, good, very good, excellent”. Based on the current sample, the Cronbach-alpha coefficient of the MSE was .76.

Analytic strategy

Prior to the main analyses, the distributional properties of the study variables were examined by inspecting skewness and kurtosis values as well as graphical distributions. Visual inspection of the violin plots (Supplementary Appendix C) was complemented by assessment of these distributional indices, which supported the assumption of approximate normality. Although minor departures from normality were observed in mathematics achievement scores at the lower study level, distributions at the medium and high study levels were approximately normal. Given the relatively large sample size (N = 409), these slight deviations were considered acceptable for structural equation modeling (SEM) analyses (Kline, 2016). To maintain high statistical power while examining group-specific patterns, a multi-group path analysis was employed. This approach allows for the estimation of distinct path coefficients for each study level while evaluating the fit of the single overarching model (as depicted in Figure 1) to the data across all groups simultaneously.

Figure 1

Procedure

The BRIEF-SR and the MSE questionnaires were administered in that order during a 30-minute session. Students with special needs were accommodated by providing them with more time to complete tests and questionnaires. Students were told that all measures were anonymous and unrelated to their regular school studies. The math matriculation scores were aggregated from the school system. The Chief Scientist of Ministry of Education approved the study.

Results

No data were missing, and all students completed all questionnaires. All analyses were performed in SPSS version 25. Data were analyzed using path and structural equation modeling (SEM). Supplementary Appendix A presents means and standard deviations of the study variables, Supplementary Appendix B displays correlations among variables, and Supplementary Appendix C shows distributions of EF (Supplementary Figure 1), Math (Supplementary Figure 2), and MSE (Supplementary Figure 3).

Structural equation modeling (SEM) analysis: prediction of math achievements by executive functions (EFs) and math self-efficacy (MSE)

The SEM analysis examined how behavioral regulation, metacognition, and MSE affect math achievements at each study level. Figure 1 presents a schematic model of the SEM analysis. The predicted criterion variable was the math achievement score, and the exogenic variables were the EF of BRI and the MI index.

The SEM analysis is estimated using the measurement error and path coefficients obtained from the maximum likelihood (ML) method. Testing the fitting the theoretical model to the data using a procedure suggested by Steiger (1990) and Kline (2011). Testing the fitness of a model to empirical findings is usually carried out by several indices of ML measures: Goodness of Fit Index (GFI), Comparative Fitness Index (CFI, Bentler, 1990), Root Mean Square Error of Approximation (RMSEA), the statistic of χ², and the ratio of χ²/df. The model chi-square is the most basic fit statistic and is reported in virtually all SEM analyses. The model is considered fit when the χ²/df < 3 and is not significant. A model is also considered fit to the data when the GFI and CFI exceed .95 and the RMSEA is below .05 (Bollen and Curran, 2006).

The current model assesses the relationships between the variables in two ways. The first is to use a measurement model to assess the latent variables (i.e., the relationships between the EFs' observational variables and the latent variables, BRI and MI). The second is a mediating model assessing the indirect relationship between independent and dependent variables. The endogenic variable was MSE because it was conceptualized and empirically found as affected by EF on the one hand (e.g., Bandura et al., 2001; Gambin and Święcicka, 2015; Zimmerman and Cleary, 2006), and because it was found empirically as significantly predicting math achievements (e.g., Ozkal, 2019; Skaalvik et al., 2015; Tanami and Eilam, 2021b). The model was tested on the entire sample.

A path analysis was conducted using structural equation modeling to investigate how the primary executive indices (i.e., BRI and MI) affect math achievements through MSE. MSE was used as a mediator between EF and Math Achievements. The findings demonstrated good goodness of fit, meaning that the data matched the following expected model.

Predicting math achievements in the LSL group

The SEM analysis (Figure 2) shows that MSE and MI directly predicted math achievements. MSE was not found to mediate the relationship between the BRI and MI indices and math achievement. The analysis also revealed that all MI components were significantly involved in predicting math achievement; WM and plan/organize contributed more to math achievement than organization of materials and task completion.

Figure 2

Predicting math achievements in the MSL group

The SEM analysis (Figure 3) shows that MSE, MI, and BRI directly and significantly predicted math achievements. In addition, MSE was found to mediate the relationships between MI (β = .17, p < .05) and BRI (β = .12, p < .05) indices and math achievement. It is interesting that MSE directly predicts positive math achievements and is a mediating variable between BRI and MI indices and math achievements. It should also be noted that all BRI and MI components were found to be significantly involved in predicting math achievements; all components have a substantial contribution to mathematics achievement, except for shifting and monitoring.

Figure 3

Predicting math achievements in the HSL group

The SEM analysis (Figure 4) shows that BRI and MSE directly and positively predicted math achievements. In addition, MSE was found to mediate positively the relationship between the BRI (β = .13, p < .05) and math achievements. The analysis also shows that all BRI components were significantly involved in predicting math achievement; inhibition made the largest contribution, followed by shifting, emotional control, and monitoring.

Figure 4

Discussion

The current study aimed to investigate the relationships between specific EFs and math achievement among 12th-grade students and to examine the mediating role of MSE in these relationships. The SEM demonstrated good overall fit, supporting the hypothesized relations among EFs, MSE, and math achievement. It should be emphasized that MSE serves as a mediating variable between EFs and math achievements only in the high and medium study levels. Although the chi-square statistic was significant, χ₍₉₃₎² = 240.19, p < .001, this is expected, given the sensitivity of χ² to sample size and does not, on its own, indicate poor model fit. More importantly, multiple fit indices met or exceeded widely accepted criteria: GFI (.91), NFI (.93), and CFI (.92) surpassed the conventional .90 threshold for acceptable fit (Hu and Bentler, 1999). The RMSEA value of .06 aligned with recommended standards for close model–data approximation, and the SRMR value of .04 fell below the common .08 guideline, further supporting model adequacy (Hu and Bentler, 1999). Taken together, these indices demonstrate that the model accurately reproduced the observed covariance structure with minimal residual error and adhered to established SEM benchmarks. The model's robustness across the three study-level groups further supports the stability of the associations among EFs (as measured by the BRIEF), MSE, and math achievement. Consistent with cognitive–motivational theoretical frameworks, the significant mediation paths confirm that MSE partially mediates the influence of specific EFs on math achievement, highlighting the interplay between students' cognitive capacities and their math self-beliefs.

Across study levels, several consistent trends emerged. First, significant relationships were found between specific EFs and math achievement at each level, supporting prior research positioning executive functioning as a core contributor to academic outcomes (Bull and Lee, 2014; Ten Braak et al., 2022). Second, MSE emerged as a motivational factor strongly linked to math achievement, aligning with previous findings showing that students' confidence in their mathematical abilities is a key determinant of academic success (Quaye and Pomeroy, 2022; Shone et al., 2024; Tanami and Eilam, 2021b). However, the mediating role of MSE differed by study level: MSE mediated the EF–achievement relationship in the High Study Level (HSL) and Medium Study Level (MSL) groups, but no mediation effect was observed in the Low Study Level (LSL) group. This absence of mediation may reflect the long-standing academic difficulties experienced by LSL students, contributing to persistent feelings of failure and diminished self-efficacy. These findings underscore the developmental and contextual nuances inherent in the links between cognitive processes and motivational beliefs, reinforcing the need for level-sensitive instructional and psychological interventions.

Group differences: the differential role of EFs and MSE

The unique contribution of this study is to identify how the relationship between EFs and math achievement differs across study levels.

The Medium Study Level (MSL) group

In the MSL group, both BRI and MI executive functions predicted math achievements directly and indirectly through MSE. This dual influence may reflect the cognitive demands placed on students at this level. These students are expected to both regulate their behavior and engage in structured planning to solve moderately complex problems. These findings are consistent with prior work showing significant correlations between BRI, MI, global EF scores, and math outcomes among MSL students (Tanami and Eilam, 2021a). In line with this interpretation, Carriedo et al. (2024) found differential combinations of EFs across grade levels, with Grade 10 students showing reliance on prepotent response inhibition and WM - a pattern similar to our findings in the MSL group.

Pedagogical implications for MSL

Teachers of students with medium levels of ability should implement differentiated instruction that simultaneously addresses both behavioral self-regulation (e.g., managing impulsivity, maintaining focus during multi-step problems) and metacognitive skills (e.g., planning solution strategies, monitoring progress). This dual approach is supported by evidence showing that interventions combining cognitive and metacognitive training with self-regulation strategies can enhance mathematics performance in secondary students (Cueli et al., 2025; Gunzenhauser and Nückles, 2021; Tzuriel, 2021).

The High Study Level (HSL) group

In the HSL group, only BR, particularly response inhibition, predicted math achievements, and MSE mediated its effect. This finding suggests that high-achieving students rely more on behavioral regulation to navigate complex mathematical problems that require flexible thinking and frequent strategy shifts. The tasks at this level require careful analysis, inhibition of impulsive responses, and dynamic adjustment of strategies, all of which are hallmarks of strong behavioral regulation. Behavioral regulation functions are a condition for effective metacognitive functioning (Gioia et al., 2000; Guy et al., 2004). Metacognitive functions, while important, were not significant predictors in this context, perhaps because such students have already automatized many of the planning and WM processes.

This finding resonates with recent international studies (e.g., Shone et al., 2024; Carriedo et al., 2024). For example, Shone et al. (2024) reported strong correlations between mathematics self-efficacy and achievement (r = 0.797, p < .001), demonstrating that self-efficacy plays a particularly prominent role among higher-achieving students. The emphasis on response inhibition in our HSL group parallels findings showing that inhibitory control becomes increasingly critical in secondary education. As mathematical tasks become more complex careful analysis and dynamic strategy adjustment are required (Carriedo et al., 2024).

Pedagogical implications for HSL

For high-achieving students, instruction should emphasize the development of strategic inhibitory control through tasks requiring: (a) suppression of automatic responses in favor of deeper analysis, (b) flexible shifting between solution approaches when initial strategies prove ineffective, and (c) sustained attention during complex, multi-stage problem-solving. These recommendations align with recent evidence that interventions targeting self-competence beliefs, alongside cognitive skills, yield the strongest effects on mathematics outcomes among high-school students (Cueli et al., 2025).

The Low Study Level (LSL) group

In the LSL group, metacognitive functions, specifically working memory (WM) and planning/organizing, were the main predictors of math achievements. This finding aligns with past research identifying WM as fundamental to mathematical performance (e.g., Blair and Razza, 2007; Cragg et al., 2017; Georgiou et al., 2020; Živković et al., 2022; Breit et al., 2025). Behavioral regulation, in contrast, had no predictive value in this group. These students may rely heavily on familiar routines and cognitive scaffolds, requiring less regulation and more structured task support. This is consistent with Dawson and Guare’s (2018) claim that EFs are needed primarily to manage novel tasks rather than habitual routines. These findings align with broader international evidence indicating that EF skills function as compensatory mechanisms for students with lower mathematical abilities, with WM and planning behavior playing central roles (Ribner et al., 2023). The absence of MSE mediation in the LSL group may reflect achievement-level differences in the reciprocal relationship between self-efficacy and performance, as the development of stable self-efficacy beliefs depends on mastery experiences that LSL students may lack (Liu et al., 2024; Usher and Pajares, 2008). In such contexts, instructional support must reduce cognitive load and provide structured scaffolding that enables successful task completion.

Pedagogical implications for LSL

Teachers working with lower-achieving students should prioritize: (a) explicit instruction in WM strategies, such as chunking information and using visual organizers; (b) structured planning protocols that break complex problems into manageable steps; and (c) scaffolded practice that builds mastery experiences to gradually develop mathematics self-efficacy.

Educational implications

The findings highlight the importance of level-sensitive instructional design in secondary mathematics education. Strengthening students' mathematics self-efficacy should remain a central goal across all study levels, as mastery experiences and structured feedback play a critical role in fostering sustained engagement and achievement (Özcan and Kültür, 2021).

At the same time, instructional strategies should be differentiated according to the dominant executive demands at each study level. For medium-level students, integrated support targeting both behavioral and metacognitive regulation appears essential. For high-level students, emphasis on strategic inhibitory control may optimize performance on complex and unfamiliar tasks. For low-level students, structured cognitive scaffolding that supports working memory and planning is likely to be most beneficial. These differentiated strategies may be implemented through carefully designed classroom practices and, where appropriate, technology-enhanced learning environments that support adaptive feedback and self-regulation.

The differentiated patterns identified in this study also carry implications for teacher professional development. Implementing level-sensitive executive and motivational supports requires that teachers possess a nuanced understanding of the cognitive and self-regulatory mechanisms underlying mathematical learning. Without such conceptual grounding, instructional adaptations may remain superficial or inconsistent. Professional development programs should therefore incorporate knowledge of executive functions, working memory demands, inhibitory control, and the developmental formation of self-efficacy beliefs, enabling teachers to make informed and context-sensitive pedagogical decisions.

Ultimately, the findings suggest that improving mathematics achievement is a combination of strengthening students’ executive and motivational capacities, alongside equipping teachers with the conceptual tools needed to accurately recognize and respond to the differentiated cognitive demands characteristic of each study level, as reflected in the dominant executive functions within each group.

Research contribution

The theoretical contribution clarifies the cognitive processes linking EFs to math achievement across different levels, reinforcing the distinction between behavioral and metacognitive EFs. The findings highlight the importance of training teachers to recognize and support students' in the classroom (Gioia and Isquith, 2004; Klenberg et al., 2010).

The findings expand previous research into three main aspects: First, the range of EFs related to math achievements extends beyond global indices or specific commonly studied functions such as shifting, WM, and inhibition. Second, this study reveals that the relationship between EFs and math achievements exists at all study levels—not only in the MSL, as previously found—with each level showing a distinct pattern. Third, while MSE contributes at all levels, it mediates the EF-achievement link only in the MSL and HSL groups.

The findings of the present study extend existing literature by highlighting the differential role of MSE across study levels. Students in the medium and high study levels typically develop relatively stable self-efficacy beliefs grounded in cumulative mastery and an awareness that effort and self-regulation lead to success (Bandura, 1997; Zimmerman, 2000). In contrast, students at the low study level often represent a population for whom mathematics has been a persistent challenge. Under such conditions, self-efficacy beliefs may be weaker or less closely linked to actual performance (Usher and Pajares, 2008). Moreover, instructional practices at lower levels may emphasize procedural learning, potentially reducing the functional role of self-efficacy as a mediator between EFs and achievement (Boekaerts and Corno, 2005).

Limitations of the study

The evaluation of math achievement in this study relied on the results of a single exam taken at a single point in time, without considering the student's mathematical skills across multiple tests or over an extended period. Moreover, it does not have differential references to test components such as different subjects or levels of thinking. In this study, the population examined was only 12th-grade students. This limits the generalizability of the findings to other populations.

Suggestions for future research

The assessment of math achievement in this study relies on the matriculation test results as a single factor, without distinguishing among specific math subjects (e.g., algebra, geometry). Because there is evidence that specific EFs may have differential effects across math subjects, it is advisable to examine the effects of specific EFs on specific math subjects using different participant groups, such as age and clinical groups.

In addition, future studies may benefit from employing longitudinal designs to explore the developmental dynamics among EFs, MSE, and achievement over time. Intervention-based research could further investigate whether targeted training in EFs, MSE, or their integration leads to differential improvements in mathematics achievement across study levels. Finally, extending this line of research to diverse educational and cultural contexts may help to establish the generalizability of the proposed model.

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