Advancing Conceptual Understanding: A Meta-Analysis on the Impact of Digital Technologies in Higher Education Mathematics

Abstract

The integration of digital technologies in mathematics is becoming increasingly significant, particularly in promoting conceptual understanding and student engagement. This study systematically reviews the literature on applications of Computer Algebra Systems, Artificial Intelligence, Visualisation Tools, augmented-reality technologies, Statistical Software, game-based learning and cloud-based learning in higher education mathematics. This meta-analysis synthesises findings from 88 empirical studies conducted between 1990 and 2025 to evaluate the impact of these technologies. The included studies encompass diverse geographical regions, providing a comprehensive global perspective on the integration of digital technologies in higher mathematics education. Using the PRISMA framework and quantitative effect size calculations, the results indicate that all interventions had a statistically significant impact on student performance. Among them, Visualisation Tools demonstrated the highest average percentage improvement in academic performance (39%), whereas cloud-based learning and game-based approaches, while beneficial, showed comparatively modest gains. The findings highlight the effectiveness of an interactive environment in fostering a deeper understanding of mathematical concepts. This study provides insights for educators and policymakers seeking to improve the quality and equity of mathematics education in the digital era.

1. Introduction

In today’s technology-driven world, digital tools are reshaping the way mathematics is taught and learned; this is particularly the case in higher education, where advanced conceptual understanding is essential (Haleem et al., 2022; Suchdava, 2023). Mathematics is often perceived by students as abstract and overly focused on the memorisation of formulas and procedures for examinations (Dowling, 2008). Yet, mathematics is fundamentally a discipline of problem-solving, logical reasoning and critical thinking (Ali & Reid, 2012). Students frequently struggle with conceptual understanding, relying on rote memorisation rather than recognising underlying principles or applying knowledge to real-world contexts.

This gap between abstract knowledge and authentic application is a persistent challenge in mathematics education. Many students fail to connect mathematical concepts with practical scenarios, which hinders deeper learning (Grehan et al., 2011). Developing conceptual understanding enables learners to apply their knowledge flexibly, transfer skills to novel problems and strengthen their reasoning abilities (Rittle-Johnson et al., 2001).

Digital technologies can help bridge this gap. Tools such as Computer Algebra Systems (CASs), dynamic geometry software and interactive simulations allow students to visualise and manipulate abstract concepts in engaging and accessible ways (Hoyles, 2018; Sedig & Sumner, 2006). Cloud-Based Platforms and graphing software promote collaboration and problem-solving, while AI-driven applications such as ChatGPT, MathGPT and PhotoMath personalise learning and provide immediate feedback (Wardat et al., 2023; Paliwal & Patel, 2025). These technologies also support inclusive practices: AI-based concept mapping, for instance, helps English Language Learner students overcome language barriers by providing visual representations of mathematical ideas (Bashir et al., 2025). However, technology adoption is not without challenges. AI-generated outputs may be inaccurate (Xiong, 2024) and structural barriers such as limited access to devices, technical skills, or internet connectivity restrict effective use in many contexts.

The COVID-19 pandemic further accelerated the adoption of educational technologies, making digital integration not optional but essential in mathematics instruction (Sofroniou & Premnath, 2022). Despite this surge, the existing research remains fragmented. Studies differ in scope, methodology and focus and their findings often provide inconsistent evidence regarding the effectiveness of tools. As a result, it remains unclear which technologies are most effective in improving student achievement, conceptual understanding and retention in higher mathematics and under what conditions they provide the greatest benefit.

Previous Meta-Analysis of Using Technology in Mathematics Education

Several studies have been conducted on the impact of digital technology in mathematics education. One notable study by (Tokac et al., 2019) reviewed 24 articles to analyse the effects of video games on mathematics education for PreK to grade 12 students. The study utilised a random model effect size, revealing that, overall, game-based learning had a small but significant effect (0.13) on mathematics achievement. Over the years, the demand for game-based learning has increased, resulting in more recent studies showing a higher effect size compared to older ones. It was also found that the duration of the intervention may influence the impact of game-based learning in mathematics education; longer interventions tend to have a greater effect than shorter ones. However, there were no significant differences observed across various group levels or types of interventions.

Another study conducted by (Rahma & Nurlaelah, 2024) reviewed 10 articles to examine the effects of digital technology on mathematics achievement. The review showed a moderate effect of digital technology on mathematics achievement, with a g value of 0.417. Contrary to the study by (Tokac et al., 2019), it found that different grade levels were influenced differently by digital technology. Specifically, junior high school students exhibited greater effects than senior high school students. Additionally, the topic of “Set Theory” showed the highest effect, while “Algebraic Functions” had the lowest impact. The article concluded that the influence of digital technology varies depending on the types of technologies used and the context of their implementation.

In a broader meta-analysis, (Higgins et al., 2019) examined the impact of technology on mathematics achievement, motivation and attitudes. The study found positive effects of technology on all three aspects of learning. The analysis of 24 articles reported a moderate effect size on mathematics achievement (0.68) and attitudes (0.59), while the influence on motivation was lower (0.30). However, these results may vary based on the different aspects of interventions examined. It also revealed that the topic of Numbers and Operations had the highest influence from technology, while algebra had the lowest. Interestingly, studies with a control group exhibited less effect than studies without one.

Focusing on primary education, (Akçay et al., 2021) reviewed studies from 2013 to 2019 and found a medium overall effect size (0.483) for technology-based learning. Differences emerged across grade levels, with Grade 5 students showing higher gains (0.481) compared to Grade 4 (0.408). GeoGebra and web-based platforms were identified as the most used and effective tools.

Collectively, these findings underscore the positive, albeit varied, impact of digital technologies on mathematics achievement. Factors such as content area, educational stage, intervention duration and technology type play a critical role in shaping learning outcomes. This body of evidence supports the strategic integration of digital tools in mathematics education, tailored to specific learning contexts.

Despite the growing body of research on digital technology in mathematics education, most existing meta-analyses and systematic reviews have predominantly focused on primary and secondary education (Li & Ma, 2010; Tokac et al., 2019; Rahma & Nurlaelah, 2024; Higgins et al., 2019; Akçay et al., 2021); this has left higher education—a context characterised by abstraction, disciplinary specialisation and diverse student populations—underexplored, with a significant gap in our understanding of how digital tools influence learning outcomes in higher mathematics education. A focused synthesis in this domain is therefore needed to identify which technologies most effectively support learning in Advanced Mathematics and to provide clarity where the literature has been inconsistent.

Accordingly, this study addresses three critical gaps: (1) the absence of a large-scale synthesis of digital technologies in higher mathematics; (2) limited understanding of how technology impacts distinct learning outcomes in this context; (3) lack of comparative evidence across technology categories. By addressing these gaps, this meta-analysis aims to provide actionable insights for educators, policymakers and curriculum designers in making informed decisions about technology adoption in higher mathematics education.

In line with this focus, the study investigates four constructs frequently reported in mathematics education research: conceptual understanding, student performance, retention and broader learning outcomes. Conceptual understanding refers to the ability to grasp mathematical principles and relationships in ways that allow flexible transfer to unfamiliar problems (Rittle-Johnson et al., 2001). Student performance denotes measurable academic achievement such as examination results, course grades, or standardised test scores (Kunter et al., 2013). Retention refers to the persistence of learning over time, typically measured through delayed post-tests or longitudinal assessment (Ebinghaus, 1915). Learning outcomes serve as an umbrella term encompassing these and related indicators such as problem-solving and academic persistence (Biggs & Tang, 2011). These constructs were selected because they were the most consistently reported across the 88 studies included in our analysis and are widely recognised in educational evaluation frameworks (OECD, 2019). Accordingly, they were incorporated into our hypotheses as the central outcomes through which the effectiveness of technology integration in higher mathematics can be assessed.

Among the various dimensions of mathematical proficiency, conceptual understanding represents a central focus of this study, as it underpins students’ ability to connect ideas, reason mathematically and transfer knowledge across contexts (Kilpatrick et al., 2001; Hiebert & Lefevre, 2013). It enables flexible reasoning, the ability to link different representations and the application of knowledge in novel situations (Hiebert & Carpenter, 1992). Within higher mathematics, conceptual understanding serves as the foundation for advanced problem solving and abstraction. Recent research (e.g., Rittle-Johnson et al., 2001; Mudaly & Rampersad, 2010) highlights how digital tools and visualisation environments can enhance conceptual understanding by supporting relational reasoning, multiple representations and deeper cognitive engagement. This framework underpins the present study’s focus on technology’s role in developing conceptual understanding within higher mathematics.

This study, therefore, investigates the following research questions:

• To what extent does the integration of digital technologies in higher mathematics education influence student achievement in mathematics?
• Which digital technologies are most effective in enhancing learning outcomes in higher mathematics education?

This paper is organised as follows. Section 2 reviews relevant literature on digital technologies in mathematics education. Section 3 outlines the methodology, including the search strategy, inclusion criteria and moderator variables. Section 4 presents the results of the meta-analysis, followed by a discussion in Section 5 that interprets the findings. Section 6 highlights areas for future research and Section 7 concludes with key takeaways and implications for practice and policy.

2. Literature Review

Research on digital technologies in higher education mathematics presents mixed findings. In the United States, most university students (92.3%) reported that technology positively influenced their learning, with 84.6% appreciating its use and a similar percentage intending to continue using it (Oates et al., 2014). In contrast, a South African study found that 75% of students had never used digital tools in their mathematics classes (Saal et al., 2020). This disparity highlights substantial differences in technology adoption across contexts, shaped by national policy, teacher training, institutional infrastructure and attitudes towards digital integration. These inconsistencies underscore the need for systematic synthesis to determine how and when digital tools effectively enhance mathematics learning in higher education.

The technologies included in this review were chosen because they appeared most frequently in the empirical studies retrieved during our systematic search and because they represent categories consistently examined in mathematics education: Statistical Software, Computer Algebra Systems (CASs), Artificial Intelligence (AI), AI-driven Learning Management Systems (AI-driven LMSs), Visualisation Tools, Cloud-Based Technologies and Game-Based Technologies. Each has been the subject of empirical study in higher education mathematics and together they represent the breadth of contemporary digital approaches to learning.

Augmented reality refers to digital tools that overlay virtual objects or information onto real-world environments, enabling learners to visualise and interact with abstract concepts in real life situation. A systematic review of 88 studies found that AR enhances students’ spatial reasoning, conceptual understanding and engagement, particularly among undergraduates in early mathematics courses (Palanci & Turan, 2021). Other research has highlighted AR’s capacity to promote collaboration and peer discussion by creating dynamic opportunities for shared exploration (Cirneanu & Moldoveanu, 2024). Studies in calculus and geometry contexts also suggest that AR improves comprehension and retention by making otherwise abstract material more tangible (Akçayır & Akçayır, 2017; Martín-Gutiérrez et al., 2015). However, successful implementation depends heavily on teacher readiness and institutional support, as inadequate training can result in superficial or ineffective use (Cirneanu & Moldoveanu, 2024).

In addition to AR, CAS tools such as Mathematica (Wolfram Research, 2003), Maple (Maplesoft, 2024) and MATLAB (MathWorks, 2022) are widely used in undergraduate mathematics to facilitate symbolic computation, algebraic manipulation and dynamic visualisation. Evidence suggests these systems can boost student confidence and support deeper problem-solving (Cretchley et al., 2000; Hiyam et al., 2019). In calculus, Mathematica has been shown to enhance students’ problem-solving ability (Hiyam et al., 2019), while Maple has been associated with improved conceptual and procedural understanding in integration tasks (Majid et al., 2012; Awang & Zakaria, 2013). MATLAB has also been reported to improve exam performance in engineering mathematics courses (Kumar & Kumaresan, 2008). However, without appropriate pedagogical frameworks and teacher training, CAS tools may not reach their potential (Kumar & Kumaresan, 2008; Aruvee & Vintere, 2022). Overall, the literature suggests CASs can transform mathematics learning from procedural computation to active exploration when effectively integrated.

More recently, Artificial Intelligence (AI) platforms, including ChatGPT, MathGPT and SOWISO, represent a newer class of technologies providing personalised and adaptive support for mathematics learning. These systems offer step-by-step guidance, real-time feedback and opportunities for self-paced learning. Studies report improvements in both procedural and conceptual understanding (Joel et al., 2024; Sahar et al., 2025), while AI use has also been linked to reductions in mathematics anxiety and increased motivation (Yavich, 2025). However, cultural differences in adoption highlight variations in student motivation and trust in AI systems (Mohamed et al., 2024). Accuracy and overreliance remain concerns, with calls for greater teacher involvement to verify AI-generated solutions (Xiong, 2024). Despite such challenges, AI’s adaptability and inclusivity position it as a promising innovation in higher mathematics education.

Visualisation Tools such as graphing calculators, GeoGebra (Hohenwarter & Preiner, 2007) and dynamic geometry software help learners explore mathematical relationships graphically. In college algebra, graphing calculators have been found to enhance motivation and engagement (Rodriguez, 2019), while GeoGebra use in calculus has been shown to improve conceptual understanding and problem-solving (Diković, 2009). Earlier work by Caldwell (1995) also reported gains in procedural understanding with the use of TI calculators. Such tools make abstract mathematical structures more accessible, though their effectiveness depends on sufficient instructional time and orientation for students.

Alongside visualisation, Cloud-Based Platforms, such as Google Jamboard and collaborative mathematics software, enable flexible, interactive and collaborative engagement with mathematical content. Chimmalee and Anupan (2022) found a 60% improvement in conceptual understanding among students using cloud-based tools compared to traditional methods, with significant increases in engagement and self-direction. Iji et al. (2018) similarly reported benefits for differentiated instruction and formative assessment. However, outcomes are highly dependent on the availability of digital infrastructure and students’ digital literacy. With appropriate scaffolding, cloud-based tools can bridge formal instruction and independent learning in higher education contexts.

Finally, game-based learning strategies integrate mathematical content into interactive, play-based environments. Studies have shown significant gains in mathematics achievement and motivation among undergraduates using game-based approaches (Chan et al., 2021; Christopoulos et al., 2024). Games promote persistence, problem-solving and collaboration by creating low-stakes environments where learners can test strategies and reflect on errors (Lee et al., 2023). However, games must be carefully aligned with curricular objectives and supported by reflective discussion to maximise pedagogical value (Foster & Shah, 2015).

Taken together, these strands of literature reveal both the promise and the challenges of digital technologies in higher mathematics education. Yet, findings across individual studies remain fragmented, vary in methodological quality and are often limited in scope. By systematically synthesising these results, the present meta-analysis contributes a more robust evidence base for understanding the role of technology in supporting conceptual understanding, performance and retention in higher education mathematics.

3. Materials and Methods

3.1. Literature Search

A systematic literature search was conducted in accordance with the PRISMA 2020 guidelines. The following academic databases were searched: Scopus, ERIC, Web of Science, APA PsycArticles, Academic Research Complete, ProQuest, SPORTDiscus and Humanities International Complete. In addition, Google Scholar was manually searched to capture grey literature and studies not indexed in major databases. Reference lists of eligible studies and existing meta-analyses on technology in mathematics education were also reviewed to identify additional publications.

The database search was carried out between December 2024 and June 2025 and included all records indexed from inception. The process was undertaken by three reviewers working collaboratively to ensure a comprehensive search. The Boolean search strategy was developed using combinations of primary and secondary keywords, targeting interventions involving digital technologies in mathematics education at the tertiary level.

Primary search terms included the following: “Mathematics” AND (“Technology” OR “Digital tools”) AND “Higher education” AND (“Mathematical understanding” OR “Learning outcomes”). Synonyms such as “Digital learning”, “Math learning”, “University”, “Learning achievement”, “Conceptual understanding”, “Procedural understanding” and “Student engagement” were also incorporated.

Specific technologies were included in the string, such as “Artificial Intelligence” (e.g., ChatGPT, SOWISO, MathAI), Computer Algebra Systems (e.g., MATLAB, Mathematica, Maple), Visualisation Tools (e.g., GeoGebra, Desmos, Dynamic Geometry Software), Learning Management Systems (e.g., Moodle (Dougiamas, 2002), ALEKS (ALEKS Corporation, 2024)), cloud-based learning, blended learning, Statistical Software (e.g., SPSS, R) and game-based learning (e.g., GBL, gamification).

Some variation in results is expected, as the search in our study was further refined beyond the listed keywords. Specifically, in addition to using those terms, we applied filters to restrict the scope to mathematics education and to university or college students and we limited the results to publications in English. These additional parameters, as well as potential differences in the timing of the search, indexing updates, or database settings (e.g., “All Fields” vs. “Title/Abstract/Keywords”), can account for the discrepancy between other retrieved counts and those reported in our study.

3.2. Manual Screening and Eligibility

The systematic search yielded 241 documents. After removing duplicates and inspecting titles and abstracts, 223 full-text studies were read and assessed for eligibility. A total of 88 meta-analyses were eligible for inclusion in this umbrella review as shown in Figure 1. All included studies were published in peer-reviewed journals.

Inclusion Criteria

To identify relevant research articles for our study, we established a set of seven inclusion criteria to ensure the selection of appropriate literature. The specific criteria were the following:

• Requirement: Studies must be publicly available and published in English.
• Target Population: Participants must be in higher mathematics education (undergraduate or postgraduate).
• Research Methodology: The study must employ quantitative research methods with analysable numeric data.
• Comparative Design: Studies should include pre-test/post-test results or data from control and experimental groups to assess technology effectiveness.
• Discipline Focus: The research must explicitly address mathematics education.
• Technology Specification: The technologies investigated must be clearly escribed to evaluate their relevance to mathematical learning.
• Learning Outcomes: Studies must report outcomes related to conceptual understanding, procedural understanding, problem-solving skills, or overall mathematical achievement. Studies providing effect size data, or sufficient statistical information to calculate it, were prioritised.

While studies without effect sizes did not contribute to the pooled estimates, they consistently reported positive outcomes associated with educational technologies. As such, their inclusion helps to contextualise the meta-analytic findings, reduces the risk of bias due to selective reporting and provides a more comprehensive picture of the literature.

By adhering to these rigorous inclusion criteria, we aimed to compile a robust and relevant body of literature that reflects the intersection of technology and mathematics education among higher education students.

3.3. Moderator Variables

In meta-analysis research, it is common to investigate the presence of moderating variables, study-level characteristics that may account for variations in reported effect size (Hall & Rosenthal, 1991; Rosenthal & DiMatteo, 2001). In the context of this study, moderators refer to specific attributes of the included studies that may influence the effectiveness of digital technologies in mathematics education. The moderator analysis conducted in this review focused on three key variables: the type of digital technology implemented (e.g., AI, CAS, cloud-based tools), the mathematical subject or course involved (e.g., calculus, statistics, algebra) and the year in which the study was conducted.

These moderators were selected based on theoretical relevance and prior research suggesting that contextual and pedagogical factors can influence the impact of educational technologies (Sofroniou et al., 2024). The analysis of these variables enabled a more nuanced understanding of how different technologies perform across subjects and sample sizes, offering insights into the conditions under which technology integration in higher mathematics education is most effective.

The analysis of 88 studies reveals distinct patterns in the utilisation of technologies and subject areas. As shown in

Table 1. Technologies and software used in higher education mathematics courses (frequency of mentions across studies).

Course Area	CAS	AI	Visualisation Tools	AI-Driven Systems	Statistical Software	Games	Cloud-Based Technology	Total
Calculus	13	5	3	3	-	1	1	23
Statistics	-	1	4	4	8	-	-	17
Algebra/Linear Algebra	-	2	6	4	-	-	-	12
Geometry	-	-	2	-	-	-	-	2
Set Theory	-	-	-	1	-	-	1	2
Number Theory	-	-	-	-	-	-	2	2
Numerical Analysis	-	-	-	-	-	-	1	1
Financial Mathematics	-	-	-	1	-	-	-	1
Engineering Mathematics	-	4	-	-	-	-	-	4
Total (specified courses)	13	12	15	13	8	1	5	67
Not specified in studies1	7	7	4	2	3	5	0	24
Overall Total	20	19	19	15	11	6	5	88

, the distribution of technologies employed in these studies indicates that Computer Algebra Systems were the most common, followed closely by Artificial Intelligence and Visualisation Tools. Notably, AI-driven systems were featured in 11 studies, while Statistical Software and Games- and Cloud-Based Technologies were less frequently employed, with 8, 6 and 5 studies, respectively.

Our dataset covered a wide range of mathematical subdomains, including Calculus, Algebra/Linear Algebra, Statistics, Geometry, Set Theory, Number Theory, Numerical Analysis, Financial Mathematics and Engineering Mathematics. Among these, Calculus was the most frequently represented, with 23 studies. This was followed by Statistics (17 studies) and Algebra/Linear Algebra (12 studies). Engineering Mathematics appeared in four studies, while Geometry was represented in two studies. The remaining subdomains, Set Theory, Number Theory, Numerical Analysis and Financial Mathematics, were each represented by a single study.

To examine whether sample size influenced the reported effects, the included studies were categorised according to their sample sizes. Following common practice in educational meta-analyses, four groups were created: small (N < 50), medium (50 ≤ N < 100), large (100 ≤ N < 300) and very large (N ≥ 300). This categorisation allowed for meaningful distinctions between studies with limited participants and those with more robust samples. As shown in Figure 2, most studies fell into the medium (n = 40) and large (n = 22) categories, with fewer studies in the small (n = 20) and very large (n = 6) groups. This distribution provided sufficient variation to examine potential moderating effects of sample size on the outcomes.

To strengthen coding reliability, two reviewers independently coded all studies and an inter-rater reliability coefficient (Cohen’s κ) of 0.86 was obtained, indicating high agreement. Discrepancies were resolved through discussion with the third reviewer.

3.4. Operational Definitions

To ensure consistency in data coding and interpretation, the key constructs examined in this meta-analysis were operationalised based on established definitions in mathematics education research.

Table 2. Operational definitions and measurement of key constructs.

Construct	Operational Definition	Measurement/Coding Example
Conceptual Understanding	Ability to relate and apply mathematical concepts across representations (Hiebert & Lefevre, 2013; Kilpatrick et al., 2001).	Studies employing tasks that required reasoning, conceptual explanation, or flexible application of mathematical ideas beyond procedural recall.
Student Performance	Quantitative achievement such as test/exam scores or grades.	Standardised tests, course marks.
Retention	Sustained learning measured through delayed post-tests or longitudinal outcomes.	Post-course assessments or follow-up tests.
Learning Outcomes	Composite indicators (e.g., problem-solving, reasoning, persistence).	Studies reporting composite measures of mathematical achievement encompassing problem-solving, reasoning and higher-order thinking skills.

summarises how each construct was defined and measured across the included studies.

3.5. Quality Appraisal

To assess the methodological quality of the 241 studies included in this meta-analysis, we utilised the Mixed-Methods Appraisal Tool (MMAT, Version 2018), which is specifically designed to evaluate qualitative, quantitative, mixed-methods and design-based research (Hong et al., 2018). The MMAT evaluates five key methodological dimensions: (1) representativeness of the study participants, (2) appropriateness of the measurement tools, (3) completeness of outcome data, (4) control for confounding variables and (5) implementation fidelity of the intervention.

Each study was rated on these five criteria using a three-point scale: “Yes”, “No”, or “Can’t tell”, based on the clarity and sufficiency of information provided in the article. An overall quality rating was then determined: studies meeting all five criteria were classified as high quality, those meeting three or four criteria were classified as moderate quality and those meeting fewer than three were considered low or unclear quality. Studies that were theoretical, conceptual, or review-based, for which MMAT was not applicable, were categorised as “Not applicable”.

Of the 241 studies appraised, 203 (84.2%) were rated as high quality, 22 (9.1%) as moderate quality and 16 (6.6%) were classified as not applicable. The high proportion of rigorous studies contributes to the overall validity and reliability of the conclusions drawn from this meta-analysis.

4. Results

4.1. Publication Bias

To assess potential publication bias, a funnel plot was constructed using the standard error of each study as the vertical axis and the corresponding effect size (Cohen’s d) as the horizontal axis (Sterne et al., 2005; Sofroniou et al., 2020). As shown in Figure 3, the data points are symmetrically distributed around the mean effect size. A 95% confidence region was plotted as a funnel-shaped boundary, represented by red dashed lines.

The overall shape of the plot does not indicate substantial asymmetry, suggesting a low likelihood of publication bias or small-study effects. Larger studies, characterised by smaller standard errors, appear near the top of the funnel and are tightly clustered around the mean, while smaller studies with larger standard errors are more widely scattered, as expected in a well-balanced meta-analysis. The visual symmetry of the plot supports the validity and robustness of the included studies and the absence of systematic bias in the reported effects.

4.2. Heterogeneity Test

To assess the variability of effect sizes across the seven categories of digital technologies, a heterogeneity analysis was conducted using Cochran’s Q test and the I² statistic (Deng & Yu, 2023). These tests evaluate whether the observed variance in effect sizes exceeds what would be expected due to random sampling error alone.

Cochran’s Q was calculated using the formula:

$$\mathit{Q}=\mathbf{\sum }_{\mathit{i}\mathbf{=}\mathbf{1}}^{\mathit{k}}{\mathit{w}}_{\mathit{i}}{\mathbf{(}{\mathit{d}}_{\mathit{i}}\mathbf{-}\overline{\mathit{d}}\mathbf{)}}^{\mathbf{2}}$$

where ${\mathit{w}}_{\mathit{i}}$ denotes the weight for each study, ${\mathit{d}}_{\mathit{i}}$ shows the individual effect size and $\overline{\mathit{d}}$ depicts the mean effect size across all categories. With k = 7 categories, the degrees of freedom (df) were 6. The critical value for the chi-square distribution at the 0.05 significance level was ${\mathit{\chi }}_{\mathbf{0.95}\mathbf{,}\mathbf{6}}^{\mathbf{2}}$ = 17.16, indicating meaningful heterogeneity. These results indicate that the variation in average effect sizes across the categories of digital technology was statistically significant, suggesting that the differences are unlikely to be due to random sampling error alone. The I² value of 65.03% further supports this, pointing to moderate to substantial heterogeneity among the included studies. Therefore, a random-effects model is more appropriate for this meta-analysis, as the assumption of homogeneity is not fully met.

4.3. Statistical Analysis Results

The statistical analysis aims to assess the efficacy of various digital technologies in higher education mathematics by scrutinising the data gathered from the chosen studies. The p values, effect sizes, confidence intervals and percentage improvements are just a few of the important statistical metrics that will be averaged for every teaching strategy in the analysis. This strategy will assist in determining the best methods for bridging the gaps in educational equity. Based on information from the pertinent studies, it was determined that the average p value, effect size, confidence interval and percentage improvement for each teaching strategy. The number of studies included in the analysis is also noted, ensuring that the averages reflect only those studies that provided the necessary data.

4.3.1. Overall Effect of Digital Technologies on Higher Mathematics Education

To examine the impact of digital technology on higher mathematics education, a total of 88 empirical studies that implemented various forms of digital technology in higher mathematics contexts were analysed. The complete list of included studies is provided in the Appendix A.

Of the 88 studies identified, 6 were excluded from the meta-analysis due to insufficient statistical data required for calculating effect sizes. Consequently, 82 studies were included in the computation of the mean effect size.

The following null and alternate hypotheses were considered to analyse each digital technology separately at a 0.05 significance level:

H₀: 

The use of digital technology in higher mathematics education has no significant effects on academic success or retention.

H₁: 

The use of digital technology in higher mathematics education has a significant effect on academic success or retention.

The overall mean effect size of digital technologies on students’ mathematical achievement was 0.98. According to Cohen’s (2013) benchmarks for interpreting effect size (where d < 0.2 indicates a small effect, d = 0.5 a moderate effect and d > 0.8 a large effect), this value represents a large effect size.

These findings indicate that the integration of digital technologies in higher mathematics education has a substantial positive impact on students’ academic achievement. Therefore, the null hypothesis, that digital technology use has no positive effect on academic success, is rejected in favour of the alternative hypothesis across all digital technology categories at the 0.05 significance level, as shown in Table 2.

4.3.2. Results by Technology

This study synthesised findings from a total of 88 peer-reviewed articles to examine the impact of digital technologies on higher mathematics education.

To facilitate analysis, each study was first categorised according to the specific type of digital technology employed in its research context. These categories were defined based on the primary digital tools or platforms used, such as Statistical Software, Computer Algebra Systems, AI Technologies, Visualisation Tools, Game-Based Technologies, Cloud-Based Technologies and AI-Based LMS.

Following this classification, the average effect size was calculated for each technology category. This enabled a comparative evaluation of the relative effectiveness of different digital technologies in enhancing learning outcomes in higher mathematics education. The results highlight which types of technologies yielded the most significant positive impact, offering insights into best practices for integrating digital tools into mathematics curricula at the tertiary level.

Table 3. Comparison of educational technology categories with average p values, effect sizes and confidence intervals.

Technology	Average p Value	Average Effect Size	CI (95%)
Statistical Software	0.02	1.24	0.63–1.7
Cloud-Based Technologies	0	1.31	1.02–1.96
Visualisation Tools	0.04	1.63	1.07–2.15
AI Technologies	0.04	0.99	0.5–1.55
Computer Algebra Systems	0	0.67	0.24–1.19
Game-Based Technologies	0	0.2	0.37–1.16
AI-driven LMS	0.04	0.57	0.19–0.94
Cloud based Technologies	0	1.31	1.02–1.96

presents a comparative analysis of average p values, effect sizes and confidence intervals across seven categories of digital technologies applied in higher mathematics education. Among these, Cloud-Based Technologies and Visualisation Tools demonstrated the highest average effect sizes (d = 1.31 and d = 1.63, respectively), with narrow confidence intervals, suggesting both strong impact and consistency in outcomes. Statistical Software also performed notably well (d = 1.02), reflecting a substantial influence on student achievement with a relatively low p value.

AI Technologies yielded an effect size of d = 0.97, indicating positive but somewhat variable outcomes, while Computer Algebra Systems and AI-driven LMS technologies displayed moderate average effects (d = 0.67 and d = 0.57, respectively). The lowest average effect was observed in Game-Based Technologies (d = 0.20), which, although still statistically significant, reflect more limited gains in mathematics achievement. Importantly, all categories reported statistically significant p values (p < 0.05), confirming the overall positive impact of digital technologies on learning. These results support the conclusion that, while all technologies offer pedagogical value, Cloud-Based Technology and Visualisation Tools currently provide the most robust and consistent improvements in mathematics education.

As shown in Figure 4, Visualisation Tools led to the highest average learning gain (39%), followed closely by AI Technologies (32%) and Statistical Software (31%). These findings are consistent with the effect size results presented earlier, reinforcing the conclusion that technologies promoting dynamic interaction and conceptual modelling offer the greatest benefits in higher mathematics education.

Conversely, Cloud-Based Technologies and Game-Based Technologies exhibited the lowest gains (15% and 16%, respectively), suggesting that, while they may enhance engagement or accessibility, their direct impact on conceptual understanding may be more limited. These trends support the recommendation that educators prioritise technologies that actively support mathematical reasoning, visualisation and real-time feedback when designing digital learning environments.

Consequently, the findings are supported for all technologies examined, affirming that these digital interventions have a positive impact on academic success and retention in higher education mathematics. This conclusion is further reinforced by the consistently large effect sizes observed, particularly for Visualisation Tools. The alignment between statistical significance and substantial effect sizes strengthens the validity of these findings and highlights the pedagogical value of integrating targeted digital tools into mathematics education.

4.3.3. Results by Course Type

When the results were disaggregated by mathematics subject, notable differences emerged across course types. Although our dataset included studies on Calculus, Algebra/Linear Algebra, Geometry, Set Theory, Number Theory, Numerical Analysis, Financial Mathematics and Engineering Mathematics, the number of studies in each of these subdomains was too limited to permit reliable subgroup analysis. To ensure analytical robustness while still reflecting course-level distinctions, we grouped these domains into a single category of Advanced Mathematics, given their common emphasis on abstract reasoning and higher-level conceptual learning. In contrast, Statistics-related courses were retained as a distinct category due to their applied orientation toward data analysis and probabilistic reasoning. This categorisation enabled us to explore course-level differences in a meaningful way while avoiding underpowered analyses.

The subgroup analysis revealed an average effect size of d = 0.79 for Advanced Mathematics courses and a larger pooled effect size of d = 1.90 for Statistics courses. These results suggest that educational technologies may have a particularly strong impact in the teaching and learning of Statistics compared to other areas of mathematics.

4.3.4. Results by Sample Size

As shown in Figure 5, studies with medium sample sizes (50–100 participants) demonstrated the largest observed effect size (d = 1.24), suggesting that interventions in these studies were particularly impactful. Small studies (N < 50) followed with a moderate effect size (d = 0.84), while large studies (100–300 participants) showed a slightly lower effect (d = 0.79). Very large studies (N ≥ 300) exhibited the smallest effect size (d = 0.44), indicating a noticeable decline compared to smaller or medium-sized studies.

These findings suggest a somewhat non-linear relationship between sample size and the magnitude of observed effects: moderate-sized studies may capture stronger or more detectable effects, whereas very large studies might demonstrate lower effect sizes due to increased population heterogeneity, more stringent measurement precision or a dilution of the observed impact across a larger number of participants. Overall, this pattern highlights the importance of considering sample size when interpreting the effectiveness of technological interventions in higher mathematics education.

4.4. Sensitivity Analysis

To assess the robustness of the findings, a category-level sensitivity analysis was performed using the updated average effect sizes from each of the seven digital technology categories identified in the meta-analysis (Copas & Shi, 2000). These categories included the following: Statistical Software, Cloud-Based Technologies, Visualisation Tools, AI Technologies, CASs, Game-Based Technologies and AI-driven LMS.

Table 4. Leave-One-out sensitivity analysis: new weighted mean effect sizes.

Left-Out Category	New Weighted Mean Effect Size
Visualisation	0.88
Cloud-Based Technologies	0.91
Statistical Software	0.93
AI Technologies	0.95
Game-Based Technologies	1.01
CAS	1.01
LMS	1.07

shows the effect of ‘Leave-one-out’ for the sensitivity analysis. The pooled average effect size across all categories was calculated as Cohen’s d = 0.98, indicating a large overall effect. To test the sensitivity of this result, each category was excluded one at a time and the mean effect size was recalculated. The recalculated effect sizes ranged from d = 0.88 (when Visualisation Tools were excluded) to d = 1.07 (when LMS was excluded), showing a maximum deviation of 0.09 from the overall mean. This modest fluctuation suggests that no single technology category exerted a disproportionate influence on the aggregated outcome.

Despite the variation between the original average effect size and the weighted mean effect size, all categories demonstrated effect sizes indicative of meaningful educational benefits. These findings confirm the overall consistency of the meta-analytic results and reinforce the conclusion that digital technologies positively support conceptual understanding and performance in higher mathematics education.

5. Discussion

This meta-analysis examined the effectiveness of digital technologies in supporting students’ conceptual understanding, performance and retention in higher mathematics education. Across 82 studies, a substantial overall effect was identified (pooled effect size d = 1.06), with all categories of technology demonstrating statistically significant benefits. Visualisation Tools (d = 1.63) emerged as the most effective, while Game-Based Technologies (d = 0.20) showed more limited, though still positive, effects.

When comparing effect sizes and learning gains, it was observed that Visualisation Tools achieved both the highest effect size and the highest average learning gains. However, while AI Technologies ranked fourth in effect size, they produced the second-highest learning gains in students’ mathematics scores.

This discrepancy arises from the different statistical methods of the two measures. Learning gain is primarily based on the mean difference between post-test and pre-test scores and therefore depends directly on the group’s average performance levels. In contrast, effect size (such as Cohen’s d) is a standardised measure of improvement that incorporates both the mean difference and the variability (standard deviation) within the sample (Cohen, 2013). As a result, a group may exhibit a high average learning gain but a lower effect size if there is substantial variability among learners, whereas a group with smaller yet more consistent improvements can yield a higher effect size.

Another notable result of this study is that, while comparing the effect sizes by the courses, Statistics had a significantly large effect size than the Advanced Mathematics courses. One possible explanation for the comparatively higher effect size observed in Statistics is that most studies in this category involved the use of Statistical Software (e.g., SPSS, R, SAS, or similar platforms). Such technologies are often closely integrated with the curriculum and provide students with immediate opportunities to apply concepts to real datasets, which may amplify learning gains. By contrast, in Advanced Mathematics courses, technologies are often used more indirectly (e.g., as Visualisation Tools or Computer Algebra Systems), which may explain the relatively smaller, though still substantial, effect size.

Interestingly, studies with medium sample sizes (50–100 participants) demonstrated the largest observed effect size (d = 1.24). This may indicate that such studies achieve an optimal balance between statistical power and implementation of loyalty. In medium-scale interventions, researchers often maintain greater control over instructional consistency and participant engagement, which may enhance effectiveness.

These results highlight the value of tools that facilitate dynamic interaction, visual modelling and immediate feedback, such as GeoGebra and Desmos, in fostering conceptual reasoning. Prior studies have similarly found that dynamic geometry and visualisation software enhance both conceptual and procedural understanding in topics such as calculus and algebra (Diković, 2009; Majid et al., 2012; Radović et al., 2019; Fokuo et al., 2023). By enabling learners to manipulate representations and explore mathematical relationships graphically, such tools make abstract content more accessible. In contrast, platforms such as Learning Management Systems (LMSs) and gamified systems may contribute more to motivation and content delivery than to the development of deep conceptual reasoning, a trend noted in earlier work comparing motivational versus cognitive outcomes of technology adoption (Chan et al., 2021; Lee et al., 2023).

Importantly, our findings suggest that different technologies influence student achievement and retention in distinct ways. For example, Statistical Software and Cloud-Based Platforms showed notable gains in achievement (e.g., exam scores, course grades), consistent with research indicating their utility in supporting data analysis and collaborative tasks (Chimmalee & Anupan, 2022; Iji et al., 2018). However, these tools were less strongly associated with long-term retention, perhaps because they emphasise procedural understanding rather than sustained conceptual engagement. By contrast, Visualisation Tools and AI systems, with their interactive and personalised feedback, appear to promote not only immediate learning gains but also retention, as learners can revisit and apply concepts in varied contexts (Yavich, 2025; Sahar et al., 2025). This distinction underscores the importance of aligning technology choice with the intended learning outcome, whether the focus is short-term performance or longer-term persistence.

The results are consistent with prior meta-analytical work in education more broadly, which has shown that interactive technologies yield larger effects on conceptual learning than more passive or content-delivery approaches (Tamim et al., 2011). However, our study extends these findings specifically to higher mathematics, where the cognitive demands and abstraction are distinct from general education. CAS and AI systems also yielded promising results, though their effectiveness varied, possibly due to differences in user proficiency, instructional integration, or mathematical domain, echoing findings from Awang and Zakaria (2013) and Hwang and Tu (2021).

Although the pooled analysis demonstrated strong overall effects, heterogeneity was moderate–substantial (I² = 65%), indicating that study-level characteristics, such as technology type, mathematical domain, or regional context, account for some variability. Subgroup analysis revealed that Visualisation Tools and CAS were particularly impactful in calculus and algebra, while Statistical Software was more effective in statistics courses, aligning with their pedagogical affordances. The sensitivity analysis, however, showed that excluding any single technology category did not materially change the overall effect size, reinforcing the robustness of the conclusions.

Several limitations should be acknowledged. The included studies varied in quality, sample size and technology types. The review was restricted to published literature, which may overrepresent studies reporting positive results despite funnel plot analyses showing minimal publication bias. While technology type and subject domain were examined as moderators, the observed difference between Statistics and Advanced Mathematics should be interpreted with caution. The high effect size for Statistics may be partly attributable to the nature of the interventions, since most studies in this category employed Statistical Software as the instructional technology. This close alignment between the tool and the course content may have artificially inflated the observed effect, limiting the generalizability of the findings to other types of technologies or mathematical domains. Future research should investigate whether comparable gains can be observed when similar levels of technological integration are achieved in Advanced Mathematics courses.

The variation in effect sizes observed may be attributed to the diverse technologies utilised, along with the significant influence of instructional design factors on the outcomes across various studies. Although this meta-analysis did not extensively examine specific instructional design variables, many studies indicated that stronger outcomes were associated with the effective integration of digital tools into active, inquiry-based, or collaborative learning environments. It will be advantageous to focus on instructional design features as potential moderators of technology effectiveness, as this could yield valuable insights into the reasons behind the observed variations in effect sizes. By doing so, we can enhance our understanding and maximise the impact of technology in education.

Other potentially important factors, such as assessment type, instructional time and student background, were not consistently reported, limiting deeper subgroup analyses.

Overall, this study advances the field by demonstrating that, while all digital technologies positively support higher mathematics learning, the magnitude and nature of their effects vary by technology and by outcome measure. For practice, the findings underline the pedagogical value of integrating digital technologies that support active exploration and conceptual reasoning, particularly in challenging domains such as calculus and algebra. For research, future studies should expand the evidence base to underrepresented contexts, explore retention as a distinct outcome and investigate the long-term sustainability of learning gains from different technologies.

6. Future Research

While this meta-analysis highlights the positive impact of digital technologies on students’ academic success in higher mathematics education, further research is needed to deepen and extend these findings. Future studies should explore the long-term effects of technology use on mathematical reasoning, knowledge retention and problem-solving ability. Most existing studies focus on short-term academic performance, leaving questions about sustained learning and transfer of skills unanswered. Comparative studies that directly evaluate the effectiveness of different technologies, such as AI tools versus visualisation software, under controlled conditions would also offer valuable insights.

Additionally, future research should aim to address gaps in geographic and contextual representation. Expanding the scope to include underrepresented regions and diverse educational contexts would provide a more comprehensive understanding of how digital technologies function across different learning environments. Moreover, examining the role of educators’ digital literacy and instructional practices could help clarify how implementation quality influences student outcomes.

7. Conclusions

This meta-analysis provides compelling evidence that digital technologies have a significant positive impact on students’ conceptual understanding in higher mathematics education. Across 88 studies, all categories of technology examined, ranging from Statistical Software to AI-driven learning platforms, were found to improve learning outcomes, with varying degrees of effectiveness. The highest average effect sizes were observed for Statistical Tools, Cloud-Based Platforms and Visualisation Technologies, highlighting their value in facilitating abstract mathematical thinking.

The consistency of effect sizes across studies, reinforced by low heterogeneity and robust sensitivity analysis, strengthens the reliability of these findings. As educational institutions continue to integrate digital tools into teaching and learning, this study underscores the importance of choosing technologies that not only enhance delivery but also support deeper cognitive engagement. Future research should continue to explore comparative effectiveness, contextual factors and long-term impacts of technology-enhanced learning in mathematics to inform evidence-based practice and policy.

The findings of this study underscore important implications for teacher education and digital policy development in higher education. Strengthening educators’ digital pedagogical competence, guided by established frameworks such as TPACK (Mishra & Koehler, 2006) and DigCompEdu (Punie, 2017), is essential to maximise the potential of technology in fostering conceptual understanding. Professional development initiatives should extend beyond technical proficiency to include pedagogical strategies that promote critical thinking, visualisation and metacognitive engagement in Advanced Mathematics. Policymakers are encouraged to support sustained professional learning opportunities, ensure adequate technological infrastructure and promote the pedagogically sound integration of digital tools aligned with curricular objectives. Such efforts can contribute to a more dynamic and equitable learning environment that enhances students’ mathematical understanding and overall academic success.