Open research questions in Cognitive and developmental aspects of mathematical skills

What the literature leaves open

• However, further research is necessary to fully determine which general cognitive abilities should be targeted in training to support children as they learn mathematical skills. Another limitation of this study is the lack of a measure of visuospatial ability (e. One limitation in our study is the general processing speed task we used.

  Exploring cognitive predictors: Examining varied impact on early number skills in a longitudinal study · 2026 · DOI

• Moreover, inconsistent results from simple techniques underscore the need for more individualized, flexible, and targeted CAI products for disabled pupils.

  Computer-Aided Instruction in Mathematics to Mentally Challenge Learners · 2026 · DOI

• Fourth, the study did not control for background variables such as socioeconomic status (SES), parental education, or school context, which may influence cognitive and academic outcomes.

  A comparative assessment of mathematical vocabulary, operations, and problem-solving in 5th grade children with ADHD and SLD: Cognitive profiles and implications for educational approaches to instruction and task design · 2026 · DOI

• The study is limited to the 2025–2026 academic year, a single public school, and a relatively small sample of 6th-grade students. Furthermore, the scope of the intervention is limited to a single unit within the mathematics curriculum, specifically the theme Numbers and Quantities 1.

  The Effect of a Curriculum Based on Dienes’ Theory of Mathematical Learning on Students’ Academic Achievement, Attitudes Toward Mathematics and Arithmetic Skills · 2026 · DOI

• Based on these findings, it remains unclear to what extent the identified task selection strategies reflect deliberate and effective engagement in SRL.

  Exploring shared control in upper primary school learners working with an adaptive learning technology · 2026 · DOI

• Overall, these findings are consistent with prior research on combined interventions, but provide some important extensions to guide future research in this area. The con- sistent impact of the math only and combined interven- tions on mathematics outcomes suggests that changing the content of the word problems did not hamper the impact of this intervention and was consistent with prior research on schema instruction to address word prob- lem-solving (Jitendra et al., 2007). As such, in addition to reading combined intervention from prior research, mathematics interventions may be modified to incor- porate SEL content to address dual competency areas (Cook et al., 2016, 2017). However, the impact on SEL outcomes of the combined intervention is less clear. In this study, SEL gains were positive for content quizzes, but generally inconsistent across the GAS and DESSA- Mini, and less clear than the gains made on measures of mathematics word problem-solving. This may suggest that as implemented here, the combined intervention may be effective in increasing awareness and knowledge, but not necessarily engagement in SEL skills for these at-risk students. Future research might (a) evaluate the impact of combined intervention as implemented here as part of Tier 1 SEL skill development, or (b) incorporate more Contemporary School Psychology (2026) 30:260–2791 3 274 deliberate intervention time on explicitly practicing and generalizing SEL skills to enhance the impact of this Tier 2 intervention. Combined interventions reflect a prom- ising area of future practice to address math and other skills (Codding et al., 2023). On behalf of all authors, the corresponding author states that there is no conflict of interest.

  Impact of a Math Problem-Solving Intervention Alone and with Embedded Socio-Emotional Learning · 2026 · DOI

• To continue supporting the differentiated instruction teaching approach in Mathematics especially in mathematical fractions and other difficult competencies, it is advised that Math- ematics teachers keep on incorporating differ- entiated instruction as part of their teaching method. Teachers can employ techniques such as flexible grouping, creating scaffolded learn- ing tasks, using manipulatives and visual mod- els, offering guided practice sessions, conduct- ing problem-solving activities that are contex- tualized, and preparing technology-supported lessons that match the diverse readiness levels, learning needs, and pace of understanding of the learners. Besides giving support to teachers, school administrators can play a role by ensuring that there are enough instructional materials, that teachers have access to learning technologies, and by creating teacher collaboration opportu- nities for lesson planning. They can also advo- cate the diagnosing of students' learning needs through assessments and continuous monitor- ing and encourage remediation and enrich- ment activities. The suggested intervention scheme, Pro- ject DIFF-MATH FRACTIONS, can be taken up and developed as a school-based Mathematics intervention program. It may act as an organ- ised reference for detecting learner deficien- cies, sorting learners into groups based on instruction, readiness, offering scaffolded tracking learner progress, and maintaining fractional concepts and operational skills. The program can also be a part of school enhance- ment projects, Mathematics remedial plans, and learner assistance programs.

  Enhancing Grade 6 Learners’ Performance in Mathematical Fractions through Differentiated Instruction · 2026 · DOI

• Based on the results of this study, the following recommendations are proposed: 1. To support the development of problem-solving and problem-posing skills among hearing loss students, it is recommended to integrate a greater number of problem-posing activities into instructional processes. 2. It is suggested that fill-in-the-blank and semi-structured problem-posing tasks, which have been observed to enhance students’ motivation and yield higher levels of success, be incorporated into classroom practices more frequently. 3. Considering that students experienced particular difficulties in expressing ideas related to division while posing problems, it is recommended to develop instructional activities that will emphasise the conceptual differences between multiplication and division. 4. Given the relationship between students’ language skills and their problem-solving abilities, it is recommended to implement reading comprehension-based practices aimed at improving mathematical literacy. 5. Additionally, to enable students to employ more diverse strategies during problem–solving, it is recommended that explicit instruction on a variety of problem-solving strategies be included in the curriculum. 6. For future research, it is suggested to make comparisons using tasks that involve solving and posing reallife problems rather than standard word problems, and to include classroom observations to provide a more comprehensive analysis of students’ behaviours.

  Problem Solving and Posing Processes of Middle School Students with Hearing Loss in Inclusive Education · 2026 · DOI

• Future studies could investigate if, and to what extent, students make gains when given high, minimal, or no prompting. Future studies should consider the criteria for moving between phases and determine a priori if and when refresher sessions will be utilized. Though the sample size used is consistent with single-case design, additional research needs to be replicated with students from different demographic groups to increase generalizability of findings. Additional implementation of the CRA-VM could be explored with other age groups, with students of varying disability status and racial/ ethnic backgrounds, targeting other mathematical skills, and in different settings such as the general education classroom, the special education classroom, at home, or virtually.

  Combining the Concrete Representational Abstract Approach and Video Modeling to Increase Basic Addition Skills for First Grade Students · 2026 · DOI

• Future research could focus on Highlighting the strengths of regional and rural children in early…1 3 targeting further interventions to better support rural and regional children, leverag- ing their unique strengths to ensure equitable access to quality education, and to inform policy that addresses geographic disparities in educational outcomes.

  Highlighting the strengths of regional and rural children in early mathematics education: exploring the role of spatial reasoning · 2026 · DOI

• Therefore, that we cannot draw conclusions about the potential impact of geography on traditional, large-scale measures is a limitation of this study and important avenue for future research. In this study we chose to focus on the understudied aspect of geography with the sample intentionally drawn across economic groups.

  Highlighting the strengths of regional and rural children in early mathematics education: exploring the role of spatial reasoning · 2026 · DOI

• taking *** p <.001, ** p <.01; partial η2 only reported for significant comparisons 9.63*** 4.77** 10.34 0.04 1,487 1,487 1,487 1,487 1,487 1,487 1,487 1,487 0.19 0.29 0.19 0.05 0.04 0.02 - - 0.67 2.83 1.27 0.09 2,487 2,487 2,487 2,487 par- tial η 2 - - - - Highlighting the strengths of regional and rural children in early…1 3 Fig. 5 Changes in learning from the start to end of the program on the four measures, based on Geog- raphy. All graphs use percentages for ease of comparison that reflect the general lower performance for rural children on these measures. How- ever, although not statistically significant, there is a trend on the patterning measure that shows gaps between the groups that are smaller at the end of the program as compared to the start. There were no discernible differences between the data lines for spatial language and perspective taking, and this is consistent with the lack of significant differences in performance on the measures. Notably, although not signifi- cantly different between the geographic groups at the start of the program, the gaps at the end of the program for spatial language are negligible. An Analysis of Covariance (ANCOVA) was also conducted as a secondary means of examining differences between the geographic groups (IV) on performance at the end of the program (DV), with scores at the start of the program used as the covari- ate. No measure showed differences based on geography at the end of the program; numeracy, F(2, 523) = 3.00, p =.05, patterning, F(2, 664) = 2.92, p =.06; language, F(2, 713) = 0.91, p =.40; perspective taking, F(2, 679) = 0.15, p =.86. This result reinforces that when we account for baseline scores at the start of the program, geo- graphic location did not significantly impact performance at the end of the program.

  Highlighting the strengths of regional and rural children in early mathematics education: exploring the role of spatial reasoning · 2026 · DOI

• Future research can extend in at least two directions. Replacing the cross-sectional design with a longitudinal one would enable the exploration of causal relationships and the transformation of internal cognitive structures. Additionally, enhancing the study’s variables—such as by expanding the views on number facts scale and including a more comprehensive range of basic arithmetic operations on the number facts scale—could yield further insights. Integrating additional psychological constructs, like those measured by Pittalis et al. (2018) or Gilmore et al. (2018), may also help clarify their contributions to arithmetic skill development. Author contributions: CC: conceptualization, formal analysis, funding acquisition, investigation, methodology, writing – original draft, writing – review & editing; IB & FB: methodology, writing – review & editing. All authors approved the final version of the article.

  The changing role of number facts in the development of arithmetic skills: A cross-sectional study on students’ views and performance · 2026 · DOI

• We have asked participants about their parents’ qualifications; however, we did not get any usable answers; students simply didn’t possess information about their parents’ background. Therefore, we could not to use this for our analysis. Another issue we need to address is that there was no question 100 PETER FEHÉR – DÓRA ORSOLYA AKNAI: SOME RESULTS OF LARGE-SCALE NET GENERATION 2022 STUDY IN HUNGARY about foreign language competences, although they play an important role in the future of learners. Apart from self-reported data, no reliable source exists today. We must also mention that problematic Internet use also became an intensively researched topic, but it was out of scope for our investigation. After the first stage of the research, we are planning further analysis of data and complementary interviews with students to get in-depth information about their motivations, habits, and opinions. This paper provides teachers and researchers with a better overview of this generation and presents detailed empirical evidence that students' requirements for learning have significantly changed. LITERATURE BENNETT, S. – MATON, K. – KERVIN, L. (2008): The ‘digital natives’ debate: A critical review of the evidence. British Journal of Educational Technology, Vol. 39. Issue 5. 775-786. https://doi.org/10.1111/j.1467-8535.2007.00793.x [21 May 2023] BENNETT, S. – MATON, K. (2010): Beyond the ‘Digital Natives’ Debate: Towards a More Nuanced Understanding of Students' Technology Experiences. Journal of Computer Assisted Learning, Vol. 26, Issue 5. 321-331. https://doi.org/10.1111/j.1365-2729.2010.00360.x [21 May 2023] BESSENYEI, István (2009): A net-generáció új tudása. Élet és Irodalom, Vol. 53. Issue 6. 15. BESSENYEI, István (2010): A digitális bennszülöttek új tudása és az iskola. Oktatás-Informatika, Vol. 2, Issue 1-2. 24-31. CALVANI, A. – FINI, A. – RAINERI, M. – PICCI, P. (2012): Are young generations in secondary school digitally competent? A study on Italian teenagers. Computers & Education, Vol. 58, Issue 2. 797-807. https://doi.org/10.1016/j.compedu.2011.10.004 [21 May 2023] CARR, N. (2010): The Shallows: What the Internet is Doing to Our Brains. W. W. Norton and Co., New York. CILLIERS, E. J. (2017): The challenge of teaching Generation Z, International Journal of Social Sciences, Vol. 3, Issue 1. 188-198. https://doi.org/10.20319/pijss.2017.31.188198 [21 May 2023] DASTANE, O. – HABA, H. F. (2023): The Landscape of Digital Natives Research: A Bibliometric and Science Mapping Analysis, FIIB Business Review. https://doi.org/10.1177/23197145221137960 [21 May 2023] ECDL Foundation (2014): The Fallacy of the ‘Digital Native’: Why Young People Need to Develop their Digital Skills.

  Should we draw, or should we work with numbers? Investigating proportional reasoning among 5th to 7th graders · 2026 · DOI

• Abstract Purpose Mathematical reasoning in adolescence relies on higher order language abilities, yet little is known about how specific language domains support mathematical performance in autistic adolescents, especially in morphologically rich languages such as Hebrew.

  Structure and Meaning in Mathematics: Divergent Roles of Syntax and Meaning-Based Language in Autism · 2026 · DOI

• Although finger sensorimotor skills, such as finger gnosia and fine motor skills (FMS), are crucial for arithmetic development, the processes underlying this relationship remain poorly understood.

  Linking sensorimotor skills and finger use to arithmetic development: A latent growth modeling approach · 2026 · DOI

• The principal limitations of this study include single-database coverage (Scopus only), English- language restriction, and the inability to conduct fully automated co-citation and bibliographic coupling analyses due to CSV format constraints; analyses recommended for future research using RIS exports processed through VOSviewer.

  From Behaviorism to Cognitive Neuroscience: An 83-Year Bibliometric Analysis of Mental Arithmetic Research in Educational Psychology (1942–2024) · 2026 · DOI

• Future research should explore how social media environments interact with our "hierarchical" brain processes, helping us design digital spaces that support, rather than overwhelm, the human spirit. We have a deep understanding of how 71 the mind processes information in a vacuum, but we lack evidence of how these "calculable processes" hold up when a young person is navigating the weight of "hustle culture" or the moral gray areas of modern society.

  Exploring Mathematical Psychology: A Systematic with Special Reference to Neurodiversity · 2026 · DOI

• Several limitations should be acknowledged when interpreting these findings. First, although adequate for exploratory analyses, the sample size was modest once stratified by age group and diagnostic subtypes, which likely reduced statistical power. Replication with larger samples is essential, particularly to validate subgroup differences and predictive models of diagnostic classification. Second, although the SLD subgroups were clinically meaningful, they remained heterogeneous. The subdivision into SLD-Dys and SLD-Mixed provided a more refined perspective; however, further differentiation, in accordance with diagnostic criteria from the ICD-10 and DSM-5, among isolated dyslexia, dysorthography, dyscalculia, and mixed profiles, would allow for a clearer delineation of their characteristic features and functioning profiles (American Psychiatric Association, 2013; World Health Organization, 1992). Previous evidence demonstrating heterogeneous cognitive profiles within these subtypes suggests that even more granular subgrouping could reveal more specific and informative error patterns (Cornoldi et al., 2019b; McGrath et al., 2019; Menghini et al., 2010; Pennington, 2006; Pennington et al., 2012; Poletti, 2016; Scorza et al., 2023; Toffalini et al., 2017; Willcutt et al., 2013). Third, the cross-sectional design limits conclusions about developmental trajectories. Longitudinal research is needed to determine whether error profiles change with age, whether the reduced differences observed in adolescence reflect true convergence or compensatory strategies, and whether early error patterns predict later academic outcomes. Such studies may help identify early cognitive markers of persistent versus remitting learning difficulties. Finally, the study focused exclusively on TD and SLD groups. Comparing error profiles across broader neurodevelopmental conditions (e.g., ADHD, ASD, Intellectual Disability) would help establish whether certain error types (e.g., R errors reflecting attentional dysregulation; WP errors reflecting difficulties in abstraction and rule extraction) are specific to SLD or represent transdiagnostic cognitive markers. Moreover, potential moderating variables such as socioeconomic background, linguistic experience, comorbidities, and prior intervention history should be examined to better understand individual variability in fluid reasoning performance. Furthermore, another aspect to consider is the possibility of extending the analysis of errors to include skipped responses, which may provide additional information on participants’ engagement, perceived task difficulty, or fatigue. Future studies could integrate these data to enhance the sensitivity of MatriKS in performance. individual differences in detecting In addition to these future directions, the current study opens up further lines of research. First, given that response times constitute a valuable source of information on cognitive performance, a systematic examination of the relationship between response times and error patterns would offer further insights into the underlying cognitive processes or individual characteristics (e.g., tendencies to impulsivity). Second, given that the matrices in MatriKS are generated according to different rules (e.g., logical and visuo-spatial rules; Brancaccio et al., 2025), it would be important to investigate potential interactions between error type and matrix characteristics, such as the type of rule required to answer an item, the number of rules involved, and the perceptual or logical complexity of the elements. For instance, some items require a single rule, such as a color change across cells, while others involve multiple rules, for example, a combination of color, shape, and orientation changes simultaneously. Items may also differ in perceptual complexity, such as figures with multiple visual features (color, shape, size), or in logical complexity, requiring deduction or integration of multiple conditional rules.

  Error patterns on a computerized version of Raven’s progressive matrices in specific learning disorders · 2026 · DOI

• While the findings of this study are encouraging, several limitations should be acknowledged to contextualize the results. First, the sample was drawn from a single lower secondary school in Greece, which may limit the generalizability of the findings to different educational contexts, cultural settings, or age groups. The relatively small sample size also constrains the statistical power for detecting smaller effects and may limit the applicability of the conclusions to more diverse student populations. Second, the duration of the intervention was six weeks, which, while sufficient to detect short-term gains in conceptual understanding, procedural fluency, and engagement, did not allow for the examination of long- term retention, transfer of learning, or sustained changes in attitudes toward mathematics. Longer interventions might yield different patterns of improvement or reveal whether the observed benefits persist over time. Third, the study relied on teacher-managed AI tool usage records and self-reported engagement measures. While these approaches provide valuable insights, they may be subject to biases such as 352 European Journal of Science and Mathematics Education, 14(3), 337-358 European Journal of Science and Mathematics Education, 2026 overestimation of engagement or underreporting difficulties. More objective measures, such as automated log data analysis and direct observation, could provide richer and more precise evidence of how students interact with AI tools. Finally, the intervention was implemented under relatively favorable conditions, including adequate technological infrastructure and teacher familiarity with AI tools. Schools with limited resources, insufficient internet connectivity, or lower levels of teacher preparedness may face additional challenges in achieving similar outcomes.

  AI meets Piaget and Vygotsky: A theory-driven approach to fraction learning in Greek lower secondary mathematics · 2026 · DOI

• Building on the present findings, future research should adopt multi-site designs to test the model’s effectiveness across diverse geographical, cultural, and socio-economic contexts. Including schools with varying levels of technological infrastructure would provide a clearer picture of the scalability and adaptability of AI-enhanced mathematics instruction. Longitudinal studies are also warranted to examine whether the improvements in conceptual understanding, procedural fluency, and engagement are maintained over time and whether they transfer to other mathematical domains, such as algebra, geometry, or problem-solving in real-world contexts. Further work should also explore the role of teacher professional development in maximizing the pedagogical benefits of AI tools. Investigating how teachers integrate AI functionalities into lesson planning, classroom management, and assessment practices could offer practical strategies for sustainable implementation. Additionally, the study’s threshold analysis suggests that optimal learning gains are linked to specific usage benchmarks for each AI tool. Future studies could experimentally manipulate dosage levels to determine causal relationships between AI engagement and learning outcomes, potentially leading to more precise guidelines for effective tool integration. Lastly, given the ethical considerations surrounding AI in education—including data privacy, algorithmic transparency, and equitable access—future research should include explicit frameworks for ethical governance and evaluate their impact on teacher and student trust in AI systems. This would ensure that technological advancements are implemented in ways that promote inclusion, fairness, and responsible use.

  AI meets Piaget and Vygotsky: A theory-driven approach to fraction learning in Greek lower secondary mathematics · 2026 · DOI

• While EEG studies document correlations between sustained attention and automatic versus procedural arithmetic in developmental dyscalculia populations, neurocognitive investigations systematically comparing attention networks across dyscalculic, typically developing, and mathematically gifted populations using combined EEG-fMRI or high-density EEG protocols are notably absent from the literature.

  Systematic survey of neurocognitive studies that examine connections between domain-general cognitive characteristics and mathematical processing · 2026 · DOI

• Meta-analyses of fMRI studies identify brain areas associated with numbers and calculations in children, but the survey reveals insufficient neurocognitive research directly examining how working memory domain (visuospatial versus verbal) differentially affects neural activation during distinct mathematical skill types (single-digit arithmetic versus multi-digit computation versus word problems).

  Systematic survey of neurocognitive studies that examine connections between domain-general cognitive characteristics and mathematical processing · 2026 · DOI

• The survey references studies on neural correlates of symbolic number processing in children and adults, but lacks systematic neurocognitive investigation of how individual differences in mathematical competence modulate error-monitoring brain responses across development from childhood to adolescence. Longitudinal fMRI designs tracking error-related negativity and P300 components are needed across different age groups and proficiency levels.

  Systematic survey of neurocognitive studies that examine connections between domain-general cognitive characteristics and mathematical processing · 2026 · DOI

• The cited meta-analyses demonstrate relationships between executive function and mathematical achievement in primary education, but neurocognitive neuroimaging studies distinguishing automatic versus procedural arithmetic in gifted underachievers versus typical achievers remain sparse. Brain imaging protocols should specifically contrast neural activation patterns in these subgroups during automatic arithmetic versus complex calculation tasks.

  Systematic survey of neurocognitive studies that examine connections between domain-general cognitive characteristics and mathematical processing · 2026 · DOI

Most-cited papers in Cognitive and developmental aspects of mathematical skills

• Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis · Developmental Science · 2016 · 546 citations
• Preschool executive functioning abilities predict early mathematics achievement. · Developmental Psychology · 2010 · 495 citations
• Preschool acuity of the approximate number system correlates with school math ability · Developmental Science · 2011 · 386 citations
• Analogical transfer, problem similarity, and expertise. · Journal of Experimental Psychology Learning Memory and Cognition · 1988 · 329 citations
• Comorbidity Between Reading Disability and Math Disability · Journal of Learning Disabilities · 2013 · 290 citations
• The development of executive functions and early mathematics: A dynamic relationship · British Journal of Educational Psychology · 2011 · 205 citations
• How is phonological processing related to individual differences in children’s arithmetic skills? · Developmental Science · 2009 · 194 citations
• A Meta-Analysis of Working Memory Deficits in Children With Learning Difficulties · Journal of Learning Disabilities · 2014 · 192 citations
• Mathematics Learning and the Sexes: A Review · Journal for Research in Mathematics Education · 1974 · 152 citations
• Mathematics Anxiety Effects in Simple and Complex Addition · Mathematical Cognition · 1996 · 151 citations

Most recent work

• Brief Pre-Class Physical Exercise Selectively Enhances Mathematics-Specific Inhibitory Control: A Cluster-Randomized Trial in Authentic Classrooms · Educational Psychology Review · 2026
• Effects of the AMPPS One-on-One Mathematics Intervention on Students’ Complex Computation, Word-Problem Solving, and Math Self-Concept · Behavioral Sciences · 2026
• Playing with word problems: a digital gamified intervention to enhance word-problem-solving skills in primary education · Mathematics Education Research Journal · 2026
• Family socioeconomic status and young children’s mathematical process skills: chain mediating roles of parents’ mathematics education beliefs and parent–child mathematics activities · Early Child Development and Care · 2026
• Exploring the sustaining of mathematics interest: students navigating stuckness during online small-group activity · ZDM – Mathematics Education · 2026
• The SNARC effect is not a unitary phenomenon: Individual variation in space–magnitude associations across domains. · Journal of comparative psychology · 2026
• Don’t overthink! Round number expressions are interpreted sharp · Glossa Psycholinguistics · 2026
• The Links Between Spatial and Math Skills in Preterm and Full-Term Children · Journal of Cognition and Development · 2026
• The development of metacognition and its impact on mathematics academic achievement among junior high school students: A two-and-a-half-year longitudinal study · Metacognition and Learning · 2026
• The evolved system for conceptual understanding: Implications for mathematical development · Journal of Numerical Cognition · 2026

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