The ABN approach, originated in Spain as an alternative approach to traditional algorithm-based mathematics instruction, represents a paradigm shift from traditional, rigid pedagogical models by advocating for open, flexible, and adaptive instruction. Since its development, the method has progressively expanded beyond its initial context, being adopted in various educational settings across Latin America and several Northern European countries (Canto-López, 2017; Montero & Cortés, 2023). The ABN methodology is typically implemented as a whole-school instructional approach rather than as an individual pedagogical choice of a single teacher. In schools adopting this methodology, the approach is introduced during Early Childhood Education and continues throughout primary education as part of a structured learning trajectory. This progression allows students to gradually develop number sense, flexible calculation strategies, and conceptual understanding of numerical relationships through activities that increase in complexity across educational stages (Aragón et al., 2017).

This methodology centrally focuses on the use of meaningful quantities, concrete manipulation, and contextualized problem-solving. Key characteristics include the prioritization of whole-number cognition (in contrast to decontextualized digit processing), the establishment of mental computation as a fundamental mathematical tool, and the encouragement of procedural variability, allowing students to solve the same operation via multiple pathways tailored to their individual pace and learning style (Martínez-Montero, 2018; Valero-Rodrigo & González-Fernández, 2020). Furthermore, this approach is hypothesized to foster a positive affective disposition toward mathematics by facilitating conceptual understanding from a more accessible, manipulative, and comprehensible perspective, particularly during the early childhood education stage (Canto-López et al., 2022).

More specifically, the ABN method is based in a sequence of didactic principles that are clearly distinct from traditional algorithmic instruction. These include: (a) the progressive construction of number sense through the use of concrete materials and real-life contexts; (b) the decomposition and recomposition of numbers as a central strategy for calculation; (c) the use of open algorithms that allow multiple solution paths instead of a single fixed procedure; and (d) the continuous connection between symbolic and non-symbolic representations of quantity (Canto-López, 2017; Montero & Cortés, 2023). In practical terms, this involves activities such as manipulating objects to represent quantities, using number lines in a flexible manner, and solving arithmetic problems through partial sums or transformations adapted to the child’s level of understanding.

Furthermore, unlike traditional approaches that often introduce symbolic notation early, the ABN method prioritizes the development of quantitative meaning before formal symbolization. This pedagogical sequence aligns with developmental models suggesting that children first acquire non-symbolic representations of quantity before mastering symbolic numerical systems (Dehaene, 2011). By delaying rigid symbolic procedures and emphasizing conceptual understanding, the ABN approach aims to reduce cognitive demands and support a more gradual and meaningful transition to formal mathematical operations.

Empirical evidence suggests that ABN can positively impact early mathematical competence, although results are not always consistent. Differences are often attributed to developmental variability and contextual factors. Some studies report advantages in estimation, number sense, and numerical reasoning (Aragón et al., 2017; Canto-López et al., 2021; Cerda et al., 2018), suggesting that ABN may support foundational skills that become more evident over time.

Beyond teaching methodology, mathematical performance is influenced by both domain-general and domain-specific cognitive factors (Costa et al., 2018). Domain-general predictors include intelligence, processing speed, working memory, and phonological awareness, which support learning across domains. Domain-specific predictors involve numerical abilities such as subitizing, number line estimation, and magnitude comparison (Clements et al., 2019; De Smedt et al., 2009; Zhu et al., 2017).

One of the most robust domain-general predictors of mathematical achievement is working memory (WM), defined as the capacity to temporarily store and manipulate information (Cowan, 2017). During early childhood education, the main components of Baddeley’s model (1986)—the central executive, the phonological loop, and the visuospatial sketchpad—gradually develop and support mathematical tasks such as counting or number line representation, which require the manipulation of quantitative and spatial information (Menon, 2016). Consistent longitudinal evidence shows that higher WM capacity is associated with better arithmetic fluency and calculation performance across schooling (Zhang et al., 2023).

Another notable general cognitive factor is fluid intelligence (Gf), defined as the capacity to solve novel problems and draw logical inferences without reliance on pre-existing knowledge (Cattell, 1971; Ramírez-Benítez et al., 2016). Research involving preschool-aged children has consistently identified a significant predictive relationship between Gf and early mathematical competence (Chuderski, 2022). This robust association suggests that fluid intelligence equips children with the necessary cognitive flexibility to adapt to and master novel challenges—such as initial exposure to symbolic number representation, advanced counting strategies, or basic arithmetic problem-solving—thereby facilitating mathematical knowledge acquisition from an early developmental stage.

Finally, among the domain-specific predictors of mathematical achievement, magnitude comparison is particularly salient (De Smedt et al., 2009; Rodic et al., 2018). This ability, typically expressed through non-symbolic comparison of numericities in early childhood, is considered a fundamental component of number sense and a precursor to formal mathematical competence (He et al., 2016). It is closely linked to the Approximate Number System (ANS), an innate mechanism that allows the estimation and comparison of quantities without counting. Research indicates that higher ANS precision is associated with both basic arithmetic skills and more advanced numerical reasoning (Chen & Li, 2014), highlighting its importance in early mathematics education.

The ANS is characterized by its approximate and proportional nature, meaning that discrimination between quantities depends on their relative difference (Dehaene, 2011; Piazza, 2010). Evidence suggests that early ANS precision is related to later mathematical achievement, particularly in estimation and reasoning tasks (Chen & Li, 2014; Schneider et al., 2017). However, its role remains debated, as symbolic numerical knowledge appears to be a stronger predictor of formal mathematics performance in later stages (Fazio et al., 2014; Lyons et al., 2012).

Current perspectives propose that both systems interact during development: the ANS provides an initial intuitive foundation, while symbolic representations support precise calculation and formal reasoning (De Smedt et al., 2013). This highlights the importance of educational approaches that connect non-symbolic and symbolic representations, as emphasized in methodologies such as ABN.

From a cognitive developmental perspective, the ABN method has been associated with the systematic practice of several domain-specific skills related to mathematical performance, including subitizing, number line estimation, numerical grouping and decomposition, and non-symbolic magnitude comparison (Valero-Rodrigo & González-Fernández, 2020). In addition, the frequent use of mental calculation and flexible strategies may also engage domain-general processes such as short-term and working memory (Aragón et al., 2017).

Previous research has suggested that instructional approaches may influence the relative contribution of different cognitive variables to mathematical achievement. In particular, Aragón et al. (2017) reported that although fluid intelligence predicted performance across instructional contexts, students taught using the ABN method showed stronger associations between mathematical achievement and memory-related processes. This pattern suggests that differences in instructional practices may be associated with distinct patterns in the cognitive factors supporting mathematical learning. In this sense, approaches that emphasize manipulation, flexible calculation, and conceptual understanding—such as the ABN method—may foster the development and use of specific numerical skills while reducing reliance on broader domain-general abilities.

In line with this body of literature, the primary objective of the present research is to examine how different cognitive variables associated with early mathematical learning relate to the instructional methodology implemented in schools. Particularly, this study aims to analyse whether the type of instructional approach (ABN vs. non-ABN) is associated with differences in early mathematical competence and with distinct patterns in the cognitive factors underlying mathematical performance.

More specifically, the study pursues three main aims. First, it analyzes potential differences between the two instructional groups in mathematical performance, working memory, processing speed, fluid intelligence, and magnitude comparison abilities. These variables are also considered to ensure initial comparability between groups and to control for potential confounding effects. Second, it examines the relationships between these cognitive variables and overall mathematical performance, as well as with the two subtests of the instrument (relational and numerical). This analysis is intended to provide a descriptive characterization of the cognitive profile associated with mathematical performance. Finally, it compares the relative contribution of these cognitive variables to mathematical performance in each instructional group in order to identify the factors most strongly associated with achievement depending on the methodology used. Based on these objectives, the following hypotheses are proposed:

H1: It is hypothesized that students instructed through the ABN method will demonstrate higher levels of early mathematical competence compared to those receiving traditional instruction.

To address H1, group differences in early mathematical competence were examined as a function of instructional methodology (ABN vs. non-ABN). Table 1 presents the descriptive statistics for all measures, including means, standard deviations, and the results of the Mann-Whitney U tests. Contrary to Hypothesis 1, inferential analyses indicated no statistically significant intergroup differences between the ABN group and the non-ABN group in early mathematical competence (TEMT total score and subtests). Similarly, no significant differences were observed in the cognitive variables analysed, supporting the comparability of both groups at the cognitive level. Given the absence of differences in performance, subsequent analyses focused on examining whether the cognitive processes underlying mathematical competence differed between instructional contexts.

Table 1 Table 1 Descriptive statistics and results of the Mann-Whitney U test for the ABN and non-ABN groups in the tests used

To explore the relationships between cognitive variables and mathematical performance, bivariate correlations were computed separately for each instructional group (Tables 2 and 3). These analyses were considered descriptive and aimed at characterizing the cognitive profile associated with mathematical performance in each group. Consistent across both groups, statistically significant positive correlations were observed between early mathematical competence and all analysed cognitive variables. This indicates that, regardless of the instructional approach, both domain-general and domain-specific cognitive abilities are positively associated with early mathematical achievement.

Table 2 Table 2 Correlations between mathematical performance and the cognitive variables studied for the ABN group Notes:

TEMT DS = Direct Score on the TEMT test; Rel. TEMT DS = Direct Score on the relational subscale of the TEMT; Num TEMT DS = Direct Score on the numerical subscale of the TEMT; WM DS= Direct Score on the Digit Test (Working Memory); PS DS =Direct Score on the Coding Test (Processing Speed); FI DS = Direct Score on the Raven test (Fluid Intelligence); SMC DS = Direct Score on the symbolic magnitude comparison test; NSMC DS = Direct Score on the non-symbolic magnitude comparison test. ** The correlation is significant at the 0.01 level (bilateral); * The correlation is significant at the 0.05 level (bilateral).

Table 3 Table 3 Correlations between mathematical performance and the cognitive variables studied for the non-ABN group Notes:

TEMT DS = Direct Score on the TEMT test; Rel. TEMT DS = Direct Score on the relational subscale of the TEMT; Num TEMT DS = Direct Score on the numerical subscale of the TEMT; WM DS= Direct Score on the Digit Test (Working Memory); PS DS =Direct Score on the Coding Test (Processing Speed); FI DS = Direct Score on the Raven test (Fluid Intelligence); SMC DS = Direct Score on the symbolic magnitude comparison test; NSMC DS = Direct Score on the non-symbolic magnitude comparison test. ** The correlation is significant at the 0.01 level (bilateral); * The correlation is significant at the 0.05 level (bilateral).

However, differences emerged when examining the relative contribution of these variables through regression analyses conducted separately for each group (Tables 4 and 5). A stepwise regression analysis was performed, taking as predictive variables all cognitive measures that were collected (working memory, processing speed, fluid intelligence, and quantity comparison) and as the dependent variable the total score on the TEMT test.

Table 4 Table 4 Results of the Linear Regression Analysis for the ABN Group Notes:

a. Predictor variables: (Constant): Comparison of symbolic magnitudes; b. Predictor variables (Constant): Comparison of symbolic magnitudes, Working memory. Dependent variable: General mathematical competence (TEMT DS).

The analysis for the ABN group resulted in two sequential models, with the final Model 2 exhibiting the strongest fit. As detailed in Table 4, Model 2 achieved a multiple correlation coefficient of R = 0.776 and accounted for a substantial proportion of the variance in mathematical performance, with a coefficient of determination of R²= 0.602 (Adjusted R² = 0.582). This indicates that the model explained 58.2 % of the variability in early mathematical competence as assessed by the TEMT. The Durbin-Watson statistic (D = 2.15) confirmed the independence of residuals, suggesting the model satisfied the assumption of no autocorrelation.

The two variables that showed a statistically significant and unique contribution to the model were Symbolic Magnitude Comparison (β = 0.479) and Working Memory (Digit Span) (β = 0.358). The remaining variables were excluded from the final stepwise regression model due to their lack of significant incremental contribution to model fit.

Table 5 Table 5 Results of the Linear Regression Analysis for the Non-ABN Group Notes:

a. Predictor variables: (Constant): Comparison of symbolic magnitudes; b. Predictor variables (Constant): Comparison of symbolic magnitudes, Fluid Intelligence. c. Predictor variables (Constant): Comparison of symbolic magnitudes, Fluid Intelligence, Working Memory. Dependent variable: General mathematical competence (TEMT DS).

The stepwise multiple linear regression analysis for the non-ABN Group yielded three sequential models, with the final Model 3 demonstrating the greatest predictive value. As presented in Table 5, Model 3 achieved a multiple correlation coefficient of R = 0.832 and accounted for a high percentage of the variance in mathematical performance, with a coefficient of determination of R² = 0.693 (Adjusted R²= 0.678). This finding indicates that the final model explained 67.8 % of the variability in early mathematical competence as assessed by the TEMT. The Durbin-Watson statistic (D = 1.82), which is sufficiently close to 2.0, confirmed the validity of the model by ensuring the independence of residuals and rejecting the assumption of autocorrelation.

The final model identified three cognitive factors that made a statistically significant and unique contribution to predicting mathematical performance: Symbolic Magnitude Comparison (β = 0.442), Fluid Intelligence (Gf) (β = 0.346) and Working Memory (Digit Span) (β = 0.249). The remaining variables -processing speed and non-symbolic magnitude comparison-were excluded from the final stepwise regression model due to their lack of significant incremental contribution to the overall model fit.

To directly assess the effect of the type of intervention, a single linear regression model was estimated in which methodology (ABN vs. non-ABN group) was included as a predictor, along with its interaction with relevant variables. The model was globally significant, F (5,101) = 37.86, p < 0.001, and explained 65.2 % of the variance in early mathematical competence (R^² = 0.652; adjusted R^² = 0.635).

At a 90 % confidence level, verbal working memory (B = 0.592, p = 0.024), fluid intelligence (B = 0.672, p < 0.001), and symbolic comparison (B = 0.279, p < 0.001) showed positive and significant effects. The interaction between methodology and fluid intelligence was also significant at the 90 % level (B = −0.346, p = 0.094), indicating that the relationship between Raven scores and early mathematical competence differs depending on the type of intervention, being weaker in the ABN group than in the non-ABN group. Specifically, the effect of Raven was B = 0.672 in the non-ABN group and B = 0.326 in the ABN group. The main effect of methodology did not reach statistical significance (B = 5.691, p = 0.101), although it was retained in the model following the hierarchical principle.

Overall, these findings reveal a differentiated pattern of cognitive predictors depending on instructional methodology. While symbolic magnitude comparison and working memory were important in both groups, fluid intelligence emerged as a relevant predictor only in the non-ABN group.

The present study aimed to analyse differences in early mathematical competence and its associated cognitive predictors between students instructed through the ABN methodology and those following a traditional pedagogical approach during Early Childhood Education. Regarding the first hypothesis (H1), the inferential analyses revealed no statistically significant differences between groups in the cognitive and mathematical variables assessed; therefore, H1 must be rejected. These findings were further supported by the regression model including instructional group as a predictor, which also showed that methodology did not significantly explain variance in mathematical performance. Nevertheless, the descriptive results suggest a tendency toward slightly higher scores in the ABN group, particularly in the numerical subtest of the mathematical assessment as well as in measures of working memory and fluid intelligence. These differences were small and did not reach statistical significance, and should therefore be interpreted with caution. Nevertheless, they may reflect emerging tendencies that could become more evident with further instructional exposure and developmental maturation. This interpretation is consistent with previous research indicating that performance differences favouring the ABN methodology tend to emerge in slightly older samples (Aragón et al., 2023; Canto et al., 2025). At this early stage, some of the most distinctive elements of the ABN approach—particularly systematic training in flexible calculation strategies—may not yet be fully consolidated.

The most relevant finding of the present study concerns the different contribution of cognitive variables to mathematical performance depending on the instructional methodology (H3). Although both groups showed similar levels of mathematical competence at this stage, the regression analyses revealed notable differences in the variables most strongly associated with performance. In the ABN group, mathematical competence was primarily explained by symbolic magnitude comparison and working memory, whereas in the non-ABN group fluid intelligence also showed a significant association with performance. These findings provide support for accepting H3, as differences in the pattern of cognitive predictors were observed across instructional groups. Firs of all, regarding the relationships between cognitive variables and mathematical performance, the results showed that both domain-general and domain-specific cognitive variables were significantly associated with early mathematical competence across groups. These findings align with a growing body of literature suggesting that these cognitive abilities constitute foundational precursors of early mathematical development (Amland et al., 2024; Nogues & Dorneles, 2021).

Moreover, symbolic magnitude comparison emerged as one of the strongest predictors of mathematical competence across both groups, consistent with previous studies (Lau et al., 2021; Meloni et al., 2023; Outhwaite et al., 2024). This ability, which involves comparing numerical values represented by Arabic digits, has been widely recognised as a robust predictor of later mathematical achievement (Schneider et al., 2017). Its importance has often been interpreted within the framework of the Symbolic Access Deficit Hypothesis (Rousselle & Noël, 2007), according to which difficulties in early mathematics are primarily related to problems accessing the semantic meaning of symbolic numbers rather than to deficits in non-symbolic magnitude processing. The strong predictive role of symbolic comparison observed in the present study reinforces the relevance of early mastery of symbolic numerical representations for the development of formal mathematical skills.

In addition to magnitude comparison, working memory also emerged as a relevant factor associated with mathematical performance in both instructional groups. This finding is consistent with a substantial body of research indicating that working memory plays a crucial role in early mathematical development, as it supports the temporary storage and manipulation of numerical information required for tasks such as counting, calculation, and problem solving (Friso-van den Bos et al., 2013). Indeed, lower levels of working memory performance have been consistently linked to difficulties in early numeracy acquisition, highlighting its importance as a foundational cognitive resource in the development of mathematical skills (Shvartsman & Shaul, 2024). Taken together, these results indicate that both symbolic magnitude comparison and working memory represent common cognitive foundations of early mathematical competence, regardless of instructional methodology.

However, differences emerged when considering the role of fluid intelligence. This variable showed a significant association with mathematical performance only in the non-ABN group, suggesting a differential pattern of cognitive involvement across instructional contexts. These results should not be interpreted as evidence that instructional methodology directly causes these differences in cognitive predictors. Given the non-experimental design of the study, it is not possible to rule out the influence of pre-existing differences between groups or other contextual factors. Rather, the findings indicate that different patterns of association between cognitive variables and mathematical performance were observed across instructional contexts. In this sense, one possible interpretation is that instructional approaches may be associated with different cognitive demands during mathematical task performance. Along these lines, when instruction relies more heavily on abstract representations and closed algorithms, students may depend to a greater extent on general reasoning abilities to successfully solve mathematical tasks. In other words, the learning process may require greater reliance on domain-general cognitive resources to compensate for the higher level of abstraction involved in traditional approaches (González-Flórez, 2021; Torres & Calo, 2022).

From a theorical perspective, the reduced role of fluid intelligence observed in the ABN group may suggest that this methodology facilitates access to mathematical concepts by grounding learning in manipulation, flexible calculation strategies, and meaningful numerical relationships. In early childhood education, mathematical understanding develops primarily through concrete experiences and the progressive construction of numerical meaning rather than through purely symbolic or abstract representations (Clements & Sarama, 2014). Approaches that rely heavily on symbolic procedures and closed algorithms may therefore place greater demands on domain-general reasoning abilities, as children must interpret and apply abstract rules that are not yet fully connected to their underlying quantitative meaning. By contrast, more open instructional approaches such as ABN emphasize the decomposition of quantities, the use of manipulatives, and flexible calculation strategies, allowing students to construct numerical relationships through direct interaction with quantities. In this sense, mathematical processing may rely more on numerical skills than on broader abstract reasoning, which is consistent with previous research linking ABN performance to working memory and numerical processing abilities (Aragón et al., 2024).

However, alternative explanations must also be considered. For example, differences in teaching practices, classroom dynamics, or individual variability in students’ prior experiences could contribute to the observed patterns of association. Without experimental control, it is not possible to determine the extent to which these factors may account for the results.

In conclusion, the present study contributes to the understanding of the cognitive foundations of early mathematics learning. Although no significant differences in overall mathematical performance were observed between instructional groups, the results suggest that the cognitive variables associated with mathematical competence may differ depending on the instructional methodology. Symbolic magnitude comparison emerged as a common predictor across both groups, whereas fluid intelligence showed a stronger association with performance in the traditional instruction group, and working memory played a more prominent role in the ABN group.

Taken together, these findings suggest that, while the ABN methodology does not lead to higher levels of mathematical performance, it may be associated with differences in the pattern of cognitive variables linked to such performance. In particular, domain-specific numerical processing and working memory showed a stronger association in the ABN group, whereas fluid intelligence was more strongly associated with performance in the traditional instruction group.

Despite these contributions, the findings should be interpreted with caution due to certain limitations, including the sample size and the inherent constraints of research conducted in natural educational settings. Studies carried out in school contexts inevitably involve human and developmental factors, such as differences in teacher practices and the specific developmental stage of the students. Moreover, the present study was not designed as an experimental intervention; therefore, it did not aim to control or manipulate the specific classroom activities used in each instructional approach. Moreover, although differences in the pattern of cognitive predictors were observed across groups, it is not possible to determine whether these differences are attributable to the instructional approach itself or to pre-existing characteristics of the participants or their educational contexts. Both instructional groups operate within shared curricular frameworks and educational objectives, and therefore the study does not compare fundamentally different learning outcomes, but rather explores how similar competencies may be supported through different instructional pathways. In this sense, the interpretations proposed should be considered tentative and require further empirical verification through longitudinal or experimental designs that allow for a more precise examination of the directionality and causal nature of these relationships. Future research with larger samples would also contribute to clarifying how cognitive factors interact with instructional approaches during the early stages of mathematical learning.