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	Revista Ensayos Pedagógicos Vol. 20, Nº 2. Julio-diciembre, 2025 e-ISNN: 2215-3330 / ISSN: 1659-0104 LICENCIA: (CC BY NC ND)

Recibido: 28 de julio de 2025. Aprobado: 15 de octubre de 2025

http://doi.org/10.15359/rep.20-2.15

Celia Gallardo Herrerías2

Universidad de Almería

Almería, España

cgh188@inlumine.ual.es

Introduction

The rising incidence of neurodevelopmental conditions such as Autism Spectrum Disorder (ASD) and Attention Deficit Hyperactivity Disorder (ADHD) is severely undermining the education system across the world. These social communication impairments, restricted behaviors (ASD), and enduring inattention patterns and/or hyperactivity-impulsivity (ADHD) interfere with children’s schooling, particularly in fundamental subjects such as mathematics. Arithmetic in this context refers to the set of early number procedures and solution methods acquired in elementary and early secondary school—i.e., number sense, basic addition, subtraction, multiplication, division, mental computation, paper-and-pencil algorithms, and basic one- or two-step word problems. The measure does not confuse arithmetic with more complicated math courses such as algebra, geometry, or statistics that put other cognitive demands (Blanco et al., 2024).

While such issues have been reported, a wide gap remains between systematic adoption and evaluation of arithmetic instructional accommodations to benefit such students across many educational contexts. More recent research (Lopez, 2024) points out that arithmetic accommodations per se—i.e., sequential scaffolding, multisensory assistance, and direct executive-function teaching—are crucial to ASD and ADHD students but relatively under-studied.

Much attention has been devoted to inclusive education models that are pedagogical in scope, while Evidence-Based Interventions (EBIs) targeting cognitive and behavioral student profiles of ASD and ADHD have only come under more and more attention. A very stringent review of the literature, however, offers little insight into comparative in-depth analysis of how countries teach instruction in arithmetic to such groups. Education-practice and policy at the classroom level differ across nations in conformity with socio-economic, institutional, and cultural settings. Such differences create global variations not only in access to post-secondary education but also in research informing such an education (Hendea & Răcășan, 2023).

There is no leading paradigm field necessitating effective arithmetic teaching reform for ASD and ADHD children and discussing their implementation across different school systems. While special curricula and modules for teacher training are common in the majority of high-income nations, in the middle- and low-income countries, resources are limited, and therefore, inadequate or non-existent support systems are the outcome. These children become more and more at risk of social exclusion and poor learning, contributing to exclusion cycles, and reducing possible pathways (Fernández-Cobos & Polo-Blanco, 2024).

The research reported on this article employs a cross-national comparative, mixed-methods strategy to this pressing issue through examination of mathematical pedagogic adaptations to students with ASD and ADHD. Triangulation and more nuanced interpretation of system- and classroom-level practice are provided through combination of qualitative (survey, observation, document analysis) and quantitative (survey data, statistical comparison) evidence. With comparisons between countries of varying quality of educational resources, the study aims to inform best practice, identify gaps, and provide policy and practice suggestions (Acker et al., 2009; Wolf et al., 2012).

Despite growing awareness of inclusive education, students with ASD and ADHD still struggle with an equal math education. These are consequences of pedagogical approaches not so well tailored to the cognitive and behavioral characteristics of these disorders. Although interventions at the individual level work, their adoption in large school systems is not consistent (Berry et al., 2014). Then, follow-up studies (Fauziyah et al., 2022) confirm that mathematical ability is especially susceptible to disruption in working memory, attentional control, and executive function, with a critical grasp of the necessity to establish expert accommodations rather than inclusive general practices.

Also of most concern is comorbidity of ASD and ADHD. For example, impairment of behavior and cognition is greater in the comorbid students, but nearly all educational research has separated these disorders into their constituent elements. Treatment of these constituent elements of the disorders has a splintered and worse intervention plan from this viewpoint. There has been a documented shortage of mathematics research aimed at double-diagnosed students despite calls for integrative pedagogic models in the works.

The general aim of this research is to compare and analyze arithmetic adaptations for teaching ASD and ADHD students in various global contexts. Some specific goals are the identification and categorization of available strategies, institutional and cultural adaptation evaluation, national policy facilitation evaluation, training of teachers’ role evaluation, and focus on the degree to which dual-diagnosed students (ASD+ADHD) are individually addressed in pedagogy.

Methodology

The study being described here was a cross-national comparative qualitative design study with mixed methods for data collection, analysis, and interpretation of math accommodations for ASD and ADHD students. The mixed methods employed a triangulation design, where qualitative (document analysis, teacher interview, classroom observation) and quantitative (stakeholder questionnaire, descriptive and inferential statistics) strands were collected concurrently and combined at interpretation for complementarity and confirmation of findings.

The data were collected through four main sources: document analysis, scheduled interviews of the teachers, routine observation procedures of the classrooms, and a complex questionnaire for education stakeholders. The research was conducted in ten countries selected on geographical, economic, and educational terms, namely, Finland, the USA, Japan, Brazil, Kenya, India, Mexico, Germany, South Africa, and Indonesia. Among the variables used in their selection, displayed dedication to inclusive education, diversity of special education policy trajectory, and coexistence of high- and low-income environments were titled.

The participants included 100 mathematics teachers (10 from each country), 50 educational policymakers or curriculum planners (5 from each country), and 100 students (10 from each country) with ASD, ADHD, or ASD + ADHD diagnosed. Sampling was intentional: active inclusive education schools were recruited, and among them, students were selected based on official clinical diagnoses by trained staff. Distribution was in the following numbers: 42 with ASD, 38 with ADHD, and 20 with dual diagnoses, evenly spread over the ten participating countries (±2 cases per diagnosis per country). Teachers were selected if they had at least three years of experience with teaching inclusive classrooms, and policymakers if they had personally been involved in curriculum development or policy implementation in the last five years.

Measures were developed and pilot-tested in three languages (English, Spanish, and Japanese), professionally translated and back-translated and validated by a panel of specialist special education researchers. In addition to pilot reliability (Cronbach’s α > 0.85), reliability was also retest in the final dataset: teacher interview coding achieved intercoder agreement κ = 0.89, classroom observation rubric showed internal consistency α = 0.83 of items, and stakeholder questionnaire included subscale reliabilities of α = 0.81–0.89 for five thematic domains. Construct validity was ensured through expert validation and exploratory factor analysis of the questionnaire (five factors, KMO = 0.86, Bartlett’s test p < 0.001).

Teacher interview protocol was 15 ordered questions regarding types of arithmetic adaptations taken, perceived effect, barriers, and facilitatory mechanisms. Interviews were face-to-face or via secure videoconferencing, audio-recorded, and transcribed verbatim. A class observation tool was adapted from Universal Design for Learning (UDL) Look-For protocol with minimal adaptation for assessing arithmetic activity. It was measured on a 5-point Likert scale in terms of clarity of instructions, visual support, personal support, student interest, and behavior control.

The stakeholder questionnaire contained 40 items in five theme areas of awareness of the policy, implementation problems, teachers’ readiness, resources availability, and role of students. Items were made balanced in relation to positively and negatively worded items to minimize response bias, and versions to country were made available to adapt to culture through translation, expert review, and pilot check. Document analysis included teaching materials, national curricula, teacher training syllabuses, and inclusive education policy documents. Documents were theme-coded for policy congruence, mapping arithmetic adaptation patterns, and systemic loopholes.

Data collection took ten months. Interviews and in-class observations were collected in two-week intervals per country and anonymized and coded by trained, bilingual qualitative content analysis research assistants. Transcripts and fieldnotes were all brought into NVivo 14 and thematically coded according to a grounded theory approach. Codes were iteratively built and inductively developed by constant comparison, and emergent themes were allowed to develop. Synthesis between qualitative and quantitative findings was at the interpretive level: questionnaire results were cross-checked against coded interview themes and classroom observation results to identify convergences, divergences, and complementarities.

Ethical considerations were of highest priority. Institutional Review Board of the lead institution and respective educational authorities in the participating nations provided ethics approval. Informed written consent was obtained from all adult participants, and assent of minors with guardian permission. All data were anonymized through coded identifiers, protected by encrypted servers, and processed under GDPR compliance to add further robustness to transnational data protection. Results release to schools or local authorities was in aggregated, non-identifiable format. A feedback system was also included in the research process for reporting of results to participants and local education authorities to attempt to provide transparency and policy effectiveness.

Results

Findings of this cross-country comparative research indicate congruence and incongruence regarding arithmetic instructional provision for students with Autism Spectrum Disorder (ASD), Attention Deficit Hyperactivity Disorder (ADHD), and co-morbidities. The results give direct answers to the research questions and the research objectives. Evidences were derived from qualitative interviews, classroom observation, policy documents, and stakeholders’ questionnaires.

Mathematical accommodations were applied pervasively across settings but differed substantially in frequency, quality, and student responsiveness. Where resource availability levels were high in nations such as Finland, Germany, and the United States, teachers applied high levels of scaffolded visual aid, manipulatives, task reduction, and pacing accommodation. These accommodations were typically incorporated within broader inclusive systems by multidisciplinary teams and extensive teacher preparation. Adaptive computer software —especially in the United States and Japan— was utilized routinely to complement arithmetic instruction, providing additional practice and differentiation. One teacher from Finland commented: “Using visual scaffolding and computer manipulatives keeps my students with ADHD engaged longer than pencil-and-paper activities.”

Middle- and low-resource settings such as Kenya, India, and Indonesia had uneven adaptations. Staff noted highly limited access to specialist services, training, and organizational support. Peer-aided learning, oral rehearsal, simplified arithmetic exercises, and behavioral cues were typical practices. Although helpful, they were often ad hoc and lacking pedagogical models. As one Kenyan teacher described: “I do what I can with chalk and some colored sticks, but we have no formal training on how to support arithmetic for ASD children.”

Cultural and institutional pressures defined adaptation development. In collectivist nations such as Indonesia and Japan, instructors signaled tensions between class practices emphasizing homogeneity and differentiated instruction. National policy in Germany and Finland specifically mandated differentiated instruction, reinforced through finance and expertise.

Figure 1 captures cross-nationally five patterns in five rubrics: policy support, teacher preparation, resource availability, classroom practices, and dual-diagnosis accommodations. High-resource nations (Finland, U.S., Germany, Japan) possessed organized policies, committed teacher preparation, and use of technology. Middle-income nations (Brazil, Mexico, South Africa) depicted regional heterogeneity with dispersed innovations but irregular policy implementation. Low-resource environments (Indonesia, India, Kenya) had disorganized methods, inadequate training, and no or little dual-diagnosis use.

Figure 1

Teacher preparation level by country

Dual diagnosis findings were particularly insightful. Most difficulty was reported by teachers in every country with co-morbid issues. The shockingly low rate of 14% of teachers who self-reported employing differentiated strategies for those with co-morbid conditions is surprising. As a complaining American teacher said: “I can manage strategies for ADHD or ASD separately, but when both are enmeshed together, the system does not provide me with an evident model to apply.”

Quantitative analysis also verified these distinctions. Fewer than twice as many high-resource school teachers reported offering arithmetic-focused resources as their low-resource peers. Extremely strong relationships between teacher training and use of visual support (χ²(2, N=100) = 39.82, p < 0.001, Cramer’s V = 0.63, 95% CI [0.42, 0.78]), and between awareness of policy and consistency of adaptation (χ²(2, N=150) = 45.67, p < 0.001, Cramer’s V = 0.55, 95% CI [0.34, 0.70]) existed. Trained teachers were significantly more confident teaching neurodivergent students (M = 4.2, SD = 0.6) compared to untrained teachers (M = 2.7, SD = 0.9), t(98) = 8.64, p < 0.001, Cohen’s d = 1.23, 95% CI [0.85, 1.60].

Classroom observations validated these findings. ASD students were best supported by routine consistency, visual sequencing cues, and clear directions. ADHD students were supported by breaking tasks, planned breaks, and prompt feedback. When combined strategies were used with dual-diagnosed students, observers noted improvement in time-on-task by 25–30% over single-condition adaptations (95% CI [18%, 37%]).

Stakeholder feedback validated gaps in implementation. While inclusive education was constitutionally grounded in all ten nations, only Finland, Germany, and the United States had policy documents that specifically delineated arithmetic education for neurodivergent children. In Kenya and India, fewer than 30% of interviewees said they knew about such policies, while more than 80% did in Finland and Germany.

Teacher preparation was the single best predictor of successful practice. Seventy to eighty percent of teachers in Germany, Finland, and the United States were professionally prepared, while fewer than 20% in India, Mexico, and Kenya were. As one German teacher put it: “Our training modules in arithmetic adaptations are absolutely central—without them I wouldn’t have any idea how to differentiate pacing or scaffolding for my students.”

Scalability and sustainability also varied. Finland and the United States had system-level drivers for inclusive mathematics education like national funding, accountability, and incorporation into teacher training programs. Brazil and India had regional variation, too, but South Africa and Indonesia suffered from infrastructural limitations that prevented them from implementing it on a uniform basis.

Discussion

The findings of the study paint a multi-faceted portrait of how mathematics instruction is designed for students with ASD, ADHD, and dual diagnosis in international schools. Contrary to single-country-focused earlier studies, the research confirms concurrent developments and context specificity, presenting a more differentiated account of international inclusive educational practice.

At the classroom level, evidence has been found for the application of working memory support, visual scaffolding, and breaking down tasks in facilitating the increased arithmetic engagement and accuracy of neurodivergent students. Quantitative data indicated large effect sizes for adaptation usage and teacher training (Cramer’s V = 0.63), while qualitative data gave insight into how interventions such as timed breaks or visual manipulatives helped to increase time-on-task for children. This synthesis boosts validity to the hypothesis that systematic, evidence-based instruction is integratable into everyday arithmetic pedagogy (Tonizzi & Usai, 2023).

School achievement was fueled by changes in training and resource utilization. Structured professional preparation was connected with teachers who were more self-confident (Cohen’s d = 1.23) and enjoyed more effective arsenals of arithmetic accommodations. Finland and Germany used training pathways to implement uniformity of practice room to room, while Indian and Kenyan teachers were forced to improvise. These are results consistent with recent studies (Cohen & Sukenik, 2024) that have found coherent, context-sensitive teacher training as one of the most inclusive drivers.

System level budgeting and policy design best predicted sustainability. Only nations with precise policy directions for arithmetic reforms (Germany, Finland, United States) showed greater convergence between legislation, teacher training, and classroom practice. In contrast, cryptic but inspirational policy statements in Kenya, India, and Mexico produced gaps in implementation as well as teacher disorientation, with very low policy awareness levels (<30%). The trend supports previous arguments (Lopez, 2024) that policy designs must be intricate in operation design specifics if they are to perform well. One such under-studied case in the published literature is the dual-diagnosed student (ASD+ADHD). Our research indicates the lack of systematic pedagogical models for such learners, in addition to overtures of more cognitive and behavioral complexities. Integrated dual-diagnosis procedures were employed by just 14% of the sample teachers, but observational data reported 25–30% time-on-task improvement where such procedures were being applied. Such quantitative assessment of effect points to the imperative of facilitation of specific interventions in excess of individual-condition modifications (Karal & Riccomini, 2024).

The study further reveals the general imperative for sensitivity to cultures. South African and Brazilian educators adapted to utilize local visual resources and peer social networks under conditions of resource scarcity in line with González-López et al. (2025). Stigma and parental alienation in India and Kenya, on the other hand, imposed limitations on possible inclusive action. Such diversity will ensure that universal adaptation models will be culturally adjusted if they are to become institutionalized and legitimized in specific contexts.

Practice implications are triple:

•Educators need to have access to a variety of arithmetic accommodations (structuring with pacing, multisensory manipulatives, visual sequencing) and be encouraged to use them adaptively according to students’ profiles.

•Schools need to be dedicated to built-in collaborative planning time, peer coaching, and parent involvement structures so that accommodations can be used systematically.

•National policy must include special arithmetic provisions, trainings with funds allocated provided, and monitoring schemes in ways that enable equitable implementation to occur within spaces made available.

Finally, the study contributes to evidence literature in that quantitative effectiveness patterns (statistical correlations, effect sizes) are integrated with qualitative teacher and student experience. The integration yields a more nuanced, more actionable evidence base for informing macro-level policy and micro-level instruction.

Limitations

Although this study has significant comments regarding cross-cultural arithmetic accommodations for pupils with ASD and ADHD, a number of limitations need to be considered:

First, the sampling design was convenience-oriented and purposive to a certain extent. Schools were recruited through available networks of inclusive education and, therefore, schools that had greater tendencies towards inclusion may have been overrepresented. Second, the distribution of student participants —42 with ASD, 38 with ADHD, and 20 with dual diagnoses— was uneven between countries, generating potential selection bias and limiting cross-national comparability.

Second, cultural and linguistic variation also create challenges of equivalence of measurement. Regardless of great care in translation, back-translation, and peer review by astute peers, subtle variations in interpretation of items and concepts can have infected responses. Additionally, cultural construction of disability and inclusion might also have affected teacher and policymaker accounts, limiting cross-contextual validity of findings.

Third, interview and observational data could have been subject to reactivity. Researchers could have changed the behavior of teachers and students during observation or interview, especially on class visitations. Even though all attempts were made to circumscribe this risk, there can be no complete risk elimination of performance bias.

Fourth, quantitative analysis was constrained by the fact that it was unable statistically to control for multiple comparisons. Statistical association was reported with effect sizes and confidence intervals but without statistical controls for multiple comparisons, thus leaving open the door to risk of Type I error. Second, the relatively small size of the sample of dual-diagnosed students (n = 20) constrains statistical power of inference for this group, although large effect sizes were obtained.

Finally, generalizability of findings is restricted. Findings are not to be assumed to represent all the schools within participating countries because contexts vary considerably by region, socioeconomic status, and implementation of policies. Results are therefore more an indication of trends and patterns than absolute fact.

These are such limitations for which subsequent research should: (a) use larger and more representative sampling frames; (b) use cross-cultural validation of measures with formally tested invariance; (c) include longitudinal designs for examining sustainability of accommodations; and (d) extend focus on dual-diagnosis learners with larger targeted subsamples.

Conclusions

This cross-nationally comparative research integrates evidence on the provision of arithmetic accommodations to students with Autism Spectrum Disorder (ASD), Attention Deficit Hyperactivity Disorder (ADHD), and double diagnoses across multiple school settings. Despite cross-country differences, several main conclusions can be made:

Above all, institutional and systemic support is the deciding factor. Nations with definitive policies, targeted teacher preparation, and multi-year funding (e. g., Finland, Germany, United States) evidenced coherent and effective arithmetic accommodations. In middle- and low-resource settings, by contrast, accommodations were incoherent, under-resourced, and dependent on teacher individual creativity.

Secondly, arithmetic needs to be considered as a discrete pedagogical challenge. Unlike more general mathematics, arithmetic is profoundly reliant on working memory, serial order, and attentional control—domains in which ASD and ADHD learners are most challenged. Policy and practice remain predominantly generic and not arithmetic-specific, hence the tension between provision and needs.

Third, dual-diagnosis students’ neglect is a critical omission. Since only 14% of instructors report combined methods, they remain neglected, nonetheless. Yet because, as the findings of this study show, dual-targeted assistance (e. g., combining visual scaffolding with attentional pacing accommodations) yielded measurable gain in time-on-task and engagement, there is an urgent need for differentiated models above the one-size-fits-all practice.

Finally, cultural sensitivity was crucial. Locally adapted materials, parent involvement, and responsiveness to social norms enabled or hindered implementation. Whatever is possible in Finland or Germany is not necessarily possible in Kenya or India, and this serves to underscore the difficulty of creating interventions that are scalable but context-sensitive.