2.1 The Multi-Dimensionality of Teacher Beliefs and Their Relevance to Technology Use

The integration of DT into mathematics teaching is shaped by a complex interplay of practical constraints, teacher competencies, and belief systems (e.g., Thomas & Palmer, 2014). While infrastructural limitations — such as inconsistent access to reliable technology in schools — remain a persistent barrier (Noyes et al., 2023), research increasingly highlights the pivotal role of teachers’ self-efficacy in determining the success of technology adoption (Geraniou & Misfeldt, 2022). Ertmer et al. (2015) argue that effective technology integration requires a multifaceted support system, encompassing adequate resources, a collaborative school culture, opportunities for professional learning, and pedagogical beliefs aligned with contemporary educational goals.

Early qualitative research, such as Leatham (2007), revealed that pre-service mathematics teachers hold nuanced beliefs about the timing, accessibility, and pedagogical alignment (in terms of mathematical content) of technology use. These findings stress the deeply held convictions that shape teachers’ decisions regarding technology use, a point reinforced by Hegedus et al. (2017), who contend that altering such beliefs is inherently challenging. Thurm and Barzel (2020) further note the scarcity of studies focused on belief change about technology use in mathematics education, prompting calls from scholars like Speer and Eichler (2022) for targeted interventions during teacher training. Their study, centred on the intelligent tutoring system STACK, demonstrated that belief transformation is possible through sustained engagement, involving phases of initial enthusiasm, disillusionment, and eventual differentiation. This developmental trajectory illustrates the need for structured, reflective experiences to foster meaningful change.

The relationship between teachers’ epistemological beliefs and their use of DT has also received attention. Misfeldt et al. (2016) found that Danish secondary mathematics teachers’ beliefs about the nature of mathematics — ranging from instrumentalist to Platonist — significantly influenced their attitudes toward technology. Teachers with performance-oriented views tended to restrict technology use, while those embracing mathematics as a problem-solving discipline were more open to exploratory, student-centred applications. Similarly, Belbase (2015) documented the evolving beliefs of a pre-service teacher in the US, whose engagement with tools like JavaBars and Geometer’s Sketchpad led to a shift from reliance on manipulatives to valuing digital tools for making abstract concepts explicit. These studies collectively suggest that epistemological beliefs are not static but can be reshaped through experiential learning and reflective practice.

Thurm and Barzel’s (2020) quasi-experimental study in Germany further demonstrated that professional development can positively influence teachers’ beliefs about the pedagogical value of DT, particularly in supporting multiple representations and discovery learning. However, beliefs related to self-efficacy and epistemology remained largely unchanged, indicating their relative resistance to short-term interventions. Their findings emphasise the importance of early support for novice teachers to prevent the entrenchment of negative beliefs and advocate for professional development that explicitly addresses self-efficacy through mastery experiences.

In their 2022 study, on which this paper is focusing, Thurm and Barzel looked at in-service mathematics teachers’ beliefs and practices related to technology use in education, specifically by examining the three key dimensions: “i) beliefs about teaching with technology, ii) self-efficacy beliefs, and iii) epistemological beliefs” (p. 42) at a finer-grained level. In fact, they claimed that these three key dimensions are “multidimensional constructs with distinct sub-dimensions” (p. 42) and therefore used multidimensional scales to explore the associations between the three above mentioned key dimensions and teachers’ self-reported “modes of technology use” on a finer-grained level.

Regarding common modes of technology use (M) in mathematics education, Thurm and Barzel (2022) reviewed relevant literature and referred to the following five modes of use. The first one was about supporting discovery learning (M1), where digital tools enable students to explore patterns, generate examples, and investigate mathematical regularities independently. This promotes mathematics as a constructive and exploratory activity (e.g., Hoyles et al., 2013). The second one was about supporting multiple representations (M2), involving the use of technology to facilitate switching between graphical, algebraic, and numerical representations. This helps students understand mathematical concepts more deeply by linking different forms of representation (e.g., Hegedus & Roschelle, 2013). The third mode was about supporting practice (M3), for which technology is useful not only for learning new concepts but also for reinforcing and practicing previously acquired skills. This is especially valuable for consolidating foundational mathematical principles (e.g., Drijvers, 2015). The fourth one was about supporting individual learning (M4), for which technology allows for personalised learning paths. Students can choose their own solution strategies, self-check their work, and compare different approaches, fostering autonomy and deeper engagement. The fifth mode of use was about supporting reflection (M5), where technology can prompt critical reflection, especially when outputs are misleading or incorrect. Discussing when and how to use technology appropriately can enhance students’ mathematical reasoning and understanding (e.g., Jankvist et al., 2019).

Teachers’ beliefs about teaching with technology (T) encompass their views on its role in learning, ranging from its potential benefits to possible drawbacks (e.g., Pierce & Ball, 2009). These beliefs significantly influence how and whether teachers integrate technology into their practice. Positive beliefs — such as recognising technology’s educational value and transformative potential — are linked to more frequent and effective use. However, research highlights several sub-dimensions of these beliefs, including views on technology’s ability to support discovery learning and multiple representations, concerns about the time required to teach with technology, fears of diminishing students’ by-hand skills, worries about mindless use, and differing opinions on the appropriate timing for technology integration, as indicated in the list of beliefs, also referred in Thurm and Barzel’s 2022 paper:

• (1) (T1) Beliefs about the role of technology to support discovery learning refer to teachers’ views on how technology can facilitate student exploration of mathematical concepts, such as through generating and investigating multiple examples (Doerr & Zangor, 2000).

• (2) (T2) Beliefs about the role of technology to support multiple representations concern the perceived value of technology in dynamically linking various representations — like tables, graphs, and algebraic expressions — to enhance understanding (Patterson & Norwood, 2004).

• (3) (T3) Beliefs about time needed to teach with technology reflect concerns that integrating technology into instruction demands additional time, particularly for teaching students how to use the software (Pierce & Ball, 2009;).

• (4) (T4) Beliefs about the loss of by-hand skills express apprehension that technology use may negatively impact students’ ability to perform basic mathematical procedures manually, such as graphing or solving equations (Erens & Eichler, 2015).

• (5) (T5) Beliefs about mindless working when teaching with technology suggest that technology might lead to superficial engagement, where students rely on “button pushing” rather than engaging in meaningful mathematical thinking (Pierce et al., 2009).

• (6) (T6) Beliefs about the time point of technology use involve differing opinions on when technology should be introduced — whether only after students have achieved conceptual mastery without it, or also at the beginning of the learning process (Fleener, 1995).

While these sub-dimensions are consistently identified in the literature, their relative importance and impact on teaching practices remain underexplored, with some — like beliefs about discovery learning — showing stronger associations with actual technology use than others. And this is what Thurm and Barzel (2022) aimed to address with their research study.

Another key dimension of their work involved self-efficacy beliefs about teaching with technology (S). Self-efficacy beliefs about teaching with technology — defined as beliefs in one’s capabilities to organise and execute actions to achieve desired outcomes (Bandura, 1997) — play a significant role in shaping how teachers use technology in mathematics education. These beliefs do not reflect actual ability but rather perceived competence. Research has shown that low self-efficacy beliefs can lead to teacher-centred and rigid uses of technology (Doerr & Zangor, 2000) and may prevent teachers from implementing their intended technology-rich lesson plans (Clark-Wilson & Hoyles, 2019). Despite their importance, there is limited research on the distinct sub-dimensions of self-efficacy beliefs. Philippou and Pantziara (2015) emphasised that self-efficacy is a multidimensional construct that varies across tasks and domains, urging more nuanced research. Scherer and Siddiq (2015) demonstrated that breaking down general computer self-efficacy into three factors yields a more detailed understanding. In mathematics education, two consistently identified domains of functioning are: (S1) Task design and selection, which involves the ability to choose or create tasks that leverage technology effectively (Leung & Baccaglini-Frank, 2016), and (S2) Lesson design and implementation, which refers to the confidence in orchestrating learning through appropriate didactical configurations (Drijvers et al., 2010; Thomas & Palmer, 2014). Although these domains are not exhaustive, they highlight key areas where self-efficacy beliefs influence teaching practices, and further research is needed to explore their differential relevance.

Epistemological beliefs — defined as beliefs about the nature of knowledge and learning (e.g., Lunn et al., 2015) — play a significant role in how mathematics teachers integrate technology. These beliefs are typically divided into beliefs about the nature of mathematics and beliefs about the acquisition of mathematical knowledge (Felbrich et al., 2008). Regarding the nature of mathematics, two orientations are commonly identified: the (E1) Static perspective (rules and procedures), which views mathematics as a formal, axiomatic system built on rules and formulae (Felbrich et al., 2008), and the (E2) Dynamic perspective (inquiry), which sees mathematics as a process of problem-solving and discovering structures and regularities. Beliefs about learning mathematics are similarly categorised into the (E3) Instructivist perspective (teacher direction), where learning is teacher-centered and knowledge is transmitted (Barkatsas & Malone, 2005; Felbrich et al., 2008), and the (E4) Constructivist perspective (active learning), which emphasises student-centered environments that support learners in constructing their own mathematical meanings. Research shows that these epistemological beliefs influence technology use: teachers with stronger constructivist beliefs and a dynamic perspective tend to use technology in more student-centered ways (Erens & Eichler, 2015; Misfeldt et al., 2016), while those with instructivist beliefs often have a limited view of technology’s potential. Despite these insights, there is a need for more nuanced research into the specific sub-dimensions of epistemological beliefs and their differential impact on technology integration.

Taken together, this body of literature emphasises that while practical barriers persist, it is teachers’ beliefs — particularly those related to pedagogy, self-efficacy, and epistemology — that critically mediate the integration of digital tools in mathematics education. These beliefs are shaped by context, experience, and professional learning, and their transformation requires sustained, reflective, and context-sensitive interventions. As mentioned above, Thurm and Barzel’s study found that multiple representations are central to teachers’ beliefs regarding the use of technology in mathematics education, while self-efficacy beliefs were found to play a central factor in constructivist technology use. Also, epistemological beliefs were found to hold a more peripheral position in technology use, revealing little or no association to technology use. Our aim is to investigate whether their findings are ‘robust’ to changes in context by replicating their study in England, which has significant contextual differences from the original study. In the next sections, we set out the country contexts before identifying why these contextual differences might provide challenges for replication.

2.2 Teacher Beliefs and Technology Use in England

In the English context, teacher beliefs about DT in mathematics education have been explored through various empirical and policy-oriented studies, revealing a complex and evolving landscape. One notable project (Clark-Wilson & Hoyles, 2017), conducted between 2014 and 2016, investigated the implications of dynamic DT on mathematics teachers’ knowledge and practice. A key finding was that teachers, initially apprehensive, reported increased motivation and professional value when engaging in collaborative discussions supported by targeted professional development resources. This suggests that teacher confidence and willingness to integrate DT can be positively influenced through structured, collegial learning environments.

However, the relationship between technology use and pedagogical orientation is not straightforward. Bretscher’s (2021) survey of English secondary mathematics teachers challenged the assumption that specific technologies inherently align with particular pedagogical styles. Tools, such as spreadsheets, dynamic geometry, graphing software which are known for their transformative potential (e.g. Pierce & Stacey, 2010) are often assumed to require a student-centred approach, while Presentation and CAI tools (e.g., PowerPoint, MyMaths, Khan Academy) are often assumed by academics and mathematics educators to reinforce teacher-centred approaches. There is evidence that shows teachers with student-centred orientations may frequently use teacher-centred software, and vice versa. In addition, in England, a “discovery orientation” (Askew et al., 1997) has an alternative meaning, indicating a laissez-faire approach towards mathematics pedagogy, associated with less effective teaching. These findings highlight the need to move beyond binary classifications of pedagogy and recognise the nuanced ways in which teachers adopt DT based on their individual goals, constraints, and interpretations of effective practice.

Recent policy reports further illuminate the systemic dimensions of technology integration in mathematics education in England. The Joint Mathematical Council (JMC) report (Noyes et al., 2023) and the Royal Society report (Crisan et al., 2023) both emphasise that the transformative potential of DT in mathematics education hinges not merely on access, but on its strategic integration into curriculum, assessment, and teacher development. While the JMC report advocates embedding DT within high-stakes assessments and curriculum reform to encourage adoption, the Royal Society complements this by proposing a long-term Maths EdTech Strategy focused on infrastructure, pedagogical innovation, and sustained professional learning — also recognising the importance of aligning technology use with assessment practices. Crucially, both reports highlight the importance of developing teachers’ mathematical digital competencies — not only to enhance presentation, but to foster inquiry, reasoning, and conceptual understanding.

Collectively, these studies and reports suggest that while English mathematics teachers may vary in their beliefs and practices regarding DT, meaningful integration requires more than individual initiative. It demands systemic support, nuanced pedagogical understanding, and sustained professional engagement. The literature points to a shift from viewing technology as a neutral tool to recognising it as a pedagogical resource whose impact is mediated by teacher beliefs, institutional structures, and the broader educational ecosystem.

2.3 Teacher Beliefs and Technology Use in Germany

In the German educational context, the integration of DT into mathematics teaching is shaped by a decentralised schooling system, where each federal state determines its own educational policies. Despite national initiatives promoting technology use, consistent and widespread implementation remains limited (Noyes et al., 2023). This fragmented policy landscape contributes to variability in teachers’ experiences and beliefs about DT across regions.

Empirical research in Germany has begun to explore these beliefs in greater depth. As also mentioned earlier, Thurm and Barzel (2020) examined the impact of a professional development programme on mathematics teachers’ beliefs, particularly regarding multi-representational tools. Their findings showcased the importance of early intervention for novice teachers, recommending hands-on, confidence-building experiences to foster self-efficacy and prevent the development of technology-resistant attitudes. This aligns with broader literature emphasising the role of sustained professional learning in belief transformation about technology use in teaching practice. Expanding on this work, Thurm et al. (2022) investigated pre-service teachers’ beliefs about mathematical digital competency — a construct that integrates mathematical competency with digital fluency (Geraniou & Jankvist, 2019). Their study revealed a tension in teacher beliefs: while participants acknowledged the value of DT in enhancing mathematical learning, they maintained that students should be able to engage with mathematics independently of digital tools. This suggests a persistent view of DT as supplementary rather than integral, reflecting a cautious stance toward its epistemological role in mathematics education.

The most comprehensive study in this domain, and the focus of our replication, is Thurm and Barzel’s (2022) large-scale quantitative investigation involving 198 German secondary mathematics teachers. Their research conceptualised teacher beliefs as multidimensional, encompassing pedagogical beliefs about DT, self-efficacy, and epistemological orientations. Through cluster analysis, they identified three distinct belief profiles: a constructivist-integrated cluster, where high self-efficacy — particularly in lesson design — was linked to the use of DT for discovery and individual learning; a distinct cluster, centred on the use of DT for multiple representations, which appeared more autonomous and less dependent on broader pedagogical beliefs; a peripheral cluster, characterised by concerns about skill erosion and passive learning, which had minimal influence on actual technology use. These findings suggest that positive beliefs about DT and confidence in its implementation are more predictive of classroom integration than concerns about its limitations. Importantly, the study advocates for differentiated professional development tailored to these belief structures, recognising that teachers engage with DT in varied and complex ways.

In sum, research in Germany highlights the nuanced and context-sensitive nature of teacher beliefs about DT. While professional development can foster more favourable attitudes, deeply held epistemological views and systemic constraints continue to shape how technology is perceived and used. These insights highlight the need for targeted, belief-informed interventions that address both pedagogical and structural dimensions of technology integration in mathematics education.

2.4 Potential Challenges for a Replication Study in England

Exploring the educational contexts of Germany and England reveals significant structural, curricular, and policy-related differences that shape the integration of DT in mathematics education. These differences span teacher training programmes, national curricula, and assessment practices, all of which influence teachers’ beliefs and behaviours regarding technology use. Such contextual variations present potential challenges for replicating findings from Thurm and Barzel’s (2022) study in Germany, within the English context.

A key distinction lies in the role of DT in national mathematics assessments. Both the Royal Society report (Crisan et al., 2023) and the Joint Mathematical Council (JMC) report (Noyes et al., 2023) argue that embedding DT into high-stakes assessments could incentivise its classroom use. In Germany, particularly in North Rhine-Westphalia (NRW), this shift has already begun. Prior to the 2014–2015 school year, DT was included in curriculum standards but excluded from final state examinations (Zentralabitur), resulting in fragmented and largely voluntary adoption. The inclusion of DT in these high-stakes exams from 2014 onwards compelled teachers to integrate technology into their practice to ensure student preparedness. This policy change catalysed a broader uptake of DT, although teacher readiness and experience varied considerably, as evidenced in Thurm and Barzel’s (2022) study. While professional development (PD) opportunities — such as those offered by state initiatives or the or networks like the Texas Instruments’ T³ (Teachers Teaching with Technology) network — were available, participation remained limited prior to the policy shift, and many teachers lacked prior exposure to DT in teaching.

At the time of Thurm and Barzel’s study, the NRW context was undergoing a transitional phase, with teachers demonstrating diverse levels of engagement with DT. The move toward digital assessment, both formative and summative, reflects a broader national trend in Germany, where external policy drivers increasingly shape classroom practices. These systemic changes have the potential to influence teacher beliefs, not only by necessitating DT use but also by reframing its pedagogical relevance.

The English context presents a markedly different picture. DT is not mandated within the mathematics curriculum or teacher standards, and national assessments remain predominantly paper-based. Consequently, technology use in mathematics classrooms is often limited to teacher-centred applications, such as presentation tools (Bretscher, 2021). The absence of formal requirements for DT integration contributes to its marginal presence in Initial Teacher Education (ITE) programmes, where training on digital pedagogy is frequently minimal or absent. Although PD opportunities exist, they are neither compulsory nor widely accessible, with financial constraints further limiting school-level support for teacher development in this area.

These contextual differences have profound implications for replicating Thurm and Barzel’s (2022) findings in the English context. In Germany, policy-driven integration has created a more structured pathway for DT adoption, albeit with challenges related to teacher preparedness and belief alignment. In England, the lack of systemic incentives and curricular mandates has resulted in a more individualised and inconsistent approach, where technology use is shaped by personal motivation rather than institutional expectation. Consequently, while German teachers may be influenced by external pressures to adopt DT, English teachers operate within a context that affords greater autonomy but less structural support. This highlights how national contexts may mediate the relationship between teacher beliefs and technology use, suggesting that belief change is not solely an individual process but one deeply embedded in broader educational structures. Such differences bring forward potential challenges for validating and generalising findings from the German context to the English educational landscape.

2.5 Our Research Question

Based on the reviewed literature and the contextual background presented above, it is evident that important gaps remain in understanding the robustness and generalisability of prior findings on teacher beliefs in relation to technology use. Consequently, the central research question for our replication study is formulated to rigorously test whether the original results hold under comparable conditions, while accounting for potential contextual variations and challenges. Our main research question (RQ) is: To what extent are Thurm and Barzel’s (2022) findings about the associations between sub-dimensions of teacher beliefs and modes of technology use in Germany replicable in the context of England?

In light of the authors’ multi-dimensional approach and to further elaborate on the main research question, it is useful to examine the specific dimensions and sub-dimensions that may influence the robustness of the findings. Accordingly, the following sub-research question (SRQ) is proposed to provide a more nuanced understanding of the contextual factors underlying the overarching RQ: How are findings about the associations between sub-dimensions of teacher beliefs (i) about teaching with technology, (ii) self-efficacy, (iii) epistemology related to sub-dimensions of self-reported modes of technology use replicable in the context of England?

3.1 Instruments

We implemented the instrument employed in Thurm and Barzel (2022) in full. As set out in the original paper and mentioned earlier, the instrument is designed using a multi-dimensional approach to measure teachers’ (i) beliefs about teaching with technology (scales T1–T6), (ii) self-efficacy beliefs (scales S1–S2), (iii) epistemological beliefs (scales E1–E4), and self-reported (iv) modes of technology use (scales M1–M5). The complete instrument is located in Thurm (2020).

Table 1 summarises the number of items comprising each scale and provides sample items. Each T-scale item was rated using a 5-point Likert scale, scored as 1 = strongly disagree to 5 = strongly agree, to measure teachers’ beliefs about teaching with technology. For items comprising the self-efficacy scales, S1 and S2, teachers were asked to score their self-efficacy on a scale of 0–100. These self-efficacy scores were then re-scaled to a score between 0–5 for analysis in line with the original study. Scales E1–4 were measured using items with 6-point Likert scales, ranging from 1 = strongly disagree to 6 = strongly agree. Finally, for the M-scales, items in M2, M4 and M5 were rated on a 5-point Likert scales with response categories ‘almost never’, ‘once or twice a quarter’, ‘once or twice a month’, ‘once a week’ and ‘almost every lesson’. For the remaining M-scales (M1 and M3), items were also rated first on a 5-point Likert scale with respect to how often their teaching focussed on a particular aspect of mathematics (e.g. on practising content). Respondents were then asked to indicate on another 5-point Likert scale what proportion of this time involved technology use. These two ratings were then combined to provide an overall score for each item in M1 and M3.

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Scales and sample items, adapted from Thurm & Barzel (2022)

Citation: Implementation and Replication Studies in Mathematics Education 5, 2 (2025) ; 10.1163/26670127-bja10030

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We used the online survey platform Gorilla (https://gorilla.sc/) to deliver the survey to participants. This mode of delivery had significant advantages for us over a pen-and-paper format used by Thurm and Barzel (2022) since data was immediately stored in a secure, digital environment without incurring the costs associated with transferring data from an analogue to digital format.

3.2 Sample

Our survey sample differs in important respects from the participants in the original study beyond the differences in national context discussed in the opening sections of this paper. We first describe the similarities and differences between the samples before setting out the characteristics of our sample in more detail.

Our participants had less teaching experience and more variable backgrounds in terms of their mathematical education at university-level than the sample in Thurm and Barzel (2022). These differences are important because less-experienced teachers or those with more varied mathematical backgrounds may have less settled or well-developed belief systems and modes of technology use and, as a result, we might expect more variance in their survey responses. The teachers in our sample had at most two years teaching experience, with a mean average age of approximately 25 years, whereas those in the original study had an average age of approximately 43 years. In addition, the teachers in Thurm and Barzel’s (2022) study were working in upper secondary schools, which require an undergraduate-level mathematics degree to teach at this level. By contrast, the teachers in our survey sample had more varied university-level backgrounds with undergraduate degrees which were either in mathematics or mathematics-related subjects, such as computer science, physics or engineering, or non-mathematics-related degrees. Of the participants in the replication study, 52% were female compared to 54% in Thurm and Barzel (2022).

Our sample consisted of 114 pre-service and early-career teachers, studying on three different Initial Teacher Education (ITE) programmes at a university in London, England (see Table 2). Of our sample, 49 pre-service teachers were studying on the one-year Post-graduate Certificate of Education (PGCE) Mathematics programme. These pre-service teachers typically have an undergraduate degree in mathematics or a mathematics-related subject. Ten pre-service teachers were studying on the PGCE Physics with Mathematics programme. These pre-service teachers primarily focus on teaching physics, but also receive input on teaching mathematics, and their undergraduate degrees are typically mathematics-related, either in physics or engineering. Finally, 55 early-career teachers were in the second year of the two-year Post-graduate Diploma in Education (PGDE) programme and were teaching mathematics nearly full-time in school during those 2 years of their programme. These early-career teachers therefore had at least an extra year of teaching experience compared to the pre-service teachers. Early-career teachers on the PGDE programme have a more varied undergraduate background: the majority (30 out of 55) had non-mathematics-related degrees; 14 had mathematics-related degrees; and 11 had mathematics degrees.

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The sample in our replication study

Citation: Implementation and Replication Studies in Mathematics Education 5, 2 (2025) ; 10.1163/26670127-bja10030

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3.3 Data Analysis

We used correlation analysis to investigate the associations between teacher beliefs and self-reported modes of technology use, following the methods adopted by Thurm and Barzel (2022), in line with our aim of carrying out a close replication of their study. As Thurm and Barzel (2022) argue, the advantage of correlation analysis is that the direction of the relationship between variables is not specified, as in regression analysis, for example. As a result, correlational analysis is appropriate for the investigation of associations between teacher beliefs and modes of technology since such relationships are under-theorised and there is likely to be mutual influence and reinforcement between the variables.

For each individual, we calculated the mean item score for each subscale and then produced descriptive statistics (mean and standard deviation) for each subscale. We calculated pairwise correlation coefficients between all subscales of (i) beliefs about teaching with technology, (ii) self-efficacy beliefs about teaching with technology, (iii) epistemological beliefs, and self-reported (iv) modes of technology use. Correlations were calculated and two-tailed tests for significance carried out with Holm adjustments (Holm, 1979) for multiple tests in R, using the corr.test() function in the psych package (Revelle, 2023). In line with our close replication, we followed Hemphill’s (2003, as cited by Thurm & Barzel, 2022) guidelines for interpreting correlation size in psychological research: small < 0.20; medium = 0.20 to 0.30, and large > 0.30.

We replicated the canonical correlation analysis using the cancor() function in the Canonical Correlation Analysis (CCA) package in R (González et al., 2008). CCA is an exploratory method for analysing correlations between two datasets. This method enables exploration of the relationships between the beliefs scales and self-reported modes of technology use without stating dependent or independent variables. Such an exploratory analysis is appropriate since the relationship between beliefs and modes of use is complex and likely to be bi-directional. In addition, we report the p-value from the Pillai–Bartlett test (Olson, 1976) for the canonical correlation analysis, which provides a robust approximation to the F-test, to test the number of canonical dimensions. Canonical dimensions are latent variables, analogous to the factors obtained in factor analysis, which explain the shared variance between the beliefs scales and modes of technology use. To support interpretation of these dimensions, we calculated canonical loadings which can be interpreted in a similar way to factor loadings (Hair et al., 2019). For ease of comparison, we adopt the same criteria as Thurm and Barzel (2022), namely, loadings greater than or equal to 0.45 indicate that the variable makes an important contribution to the canonical dimension. The greater the loading, the more important or dominant its contribution is to the canonical dimension.

4.1 Correlation Analysis for Teachers’ Beliefs about Teaching with Technology

The reliability coefficients of the M-scales, representing self-reported modes of technology use, ranged from 0.80 to 0.92 showing good internal consistency. The reliability coefficients of the T-scales, representing teachers’ beliefs about teaching with technology, were also sound and ranged from 0.73 to 0.84 with the exception of beliefs about the high time requirements of teaching with technology (T3, Cronbach’s alpha = 0.69) which falls just short of the benchmark value of 0.7 for acceptable internal consistency. Only one technology beliefs scale showed any statistically significant correlations with self-reported modes of technology use. The sub-dimension measuring teachers’ beliefs about the role of technology to support multiple representations (T2, ρ = 0.34, t = 3.89, p < 0.01) positively correlated with self-reported use technology to work with multiple representations (M2), perhaps unsurprisingly. Teachers’ beliefs about the role of technology to support multiple representations also showed correlations above 0.2 with the self-reported use of technology for discovery learning (T1, ρ = 0.20, t = 2.21, p = 1), however this result is not statistically significant at the 5% level after adjusting for multiple tests. Teachers’ beliefs about the role of technology to support multiple representations had the highest mean score (T2, mean = 4.05, SD = 0.61) of the technology beliefs sub-dimensions. Remarkably, there were no correlations of any meaningful size or significance between self-reported modes of technology use and beliefs about technology for discovery learning (T1), high-time requirements of technology (T3), the loss of skills (T4), the risk of mindless working (T5) or that mathematical concepts/procedures should be mastered prior to technology use (T6). These results are surprising given evidence from prior research that such beliefs about technology are important for teachers’ technology use in the classroom.

4.2 Correlation Analysis for Teachers’ Self-Efficacy Beliefs

The reliability coefficients for teachers’ self-efficacy beliefs showed good internal consistency, with 0.83 for task design and selection (S1) and 0.85 for lesson design and implementation (S2). Both sub-dimensions of self-efficacy were positively correlated with self-reported modes of technology use, as reported in Table 3. Self-efficacy for task-design and selection (S1) had relatively high correlations (ρ = 0.41–0.46, all t > 4, all p < 0.001) with all modes of self-reported technology use except practice (M3, ρ = 0.33, t = 3.65, p < 0.05).

Similarly, self-efficacy for lesson design and implementation (S2) showed relatively high correlations for discovery (M1, ρ = 0.48, t = 5.74, p < 0.001), multiple representations (M2, ρ = 0.43, t = 5.05, p < 0.001) and reflection (M5, ρ = 0.41, t = 4.76, p < 0.001). Correlations for lesson design and implementation with self-reported use of technology for practice (M3, ρ = 0.27, t = 3.02, p = 0.16) and individual learning (M4, ρ = 0.34, t = 3.77, p < 0.05) were somewhat lower and statistically significant for individual learning only at the 5% level, after correcting for multiple tests. Another way of saying this is that self-reported use of technology for practice was less strongly related to self-efficacy beliefs than other modes of technology use. Self-reported use of technology for individual learning was relatively strongly related to self-efficacy beliefs about task design and selection and somewhat less strongly related to self-efficacy beliefs about lesson design and implementation.

4.3 Correlation Analysis for Teachers’ Epistemological Beliefs

The reliability coefficients for teachers’ epistemological beliefs showed good internal consistency, ranging from 0.73 to 0.82, except for beliefs about learning mathematics through active learning (E4, Cronbach’s alpha = 0.68). No statistically significant correlations were found between beliefs about the nature of mathematics (E1, E2) and self-reported modes of technology use. Similarly, no statistically significant correlations were found between beliefs about the learning of mathematics (E3, E4) and self-reported modes of technology use. For sub-dimensions E1 and E3, some correlations rose above the 0.2 threshold, however they were not statistically significant after correcting for multiple tests. For example, beliefs that mathematics is a collection of rules and procedures (E1) showed a positive correlation above the 0.2 threshold for self-reported use of technology for discovery (M1, ρ = 0.24, t = 2.59, p = 0.49), practice (M3, ρ = 0.24, t = 2.61, p = 0.47) and reflection (M5, ρ = 0.23, t = 2.48, p = 0.64). Similarly, beliefs that learning mathematics is best achieved through direct instruction (E3) showed a positive correlation above the 0.2 threshold for self-reported use of technology for discovery (M1, ρ = 0.24, t = 2.65, p = 0.43), practice (M3, ρ = 0.28, t = 3.07, p = 0.13) and reflection (M5, ρ = 0.26, t = 2.86, p = 0.24). Remarkably, there were no correlations of any meaningful size or significance between self-reported modes of technology use for multiple representation and teachers’ beliefs about the nature of mathematics and the learning of mathematics. Similarly, there were no correlations of any meaningful size or significance between self-reported modes of technology use for individual learning and teachers’ beliefs about the nature of mathematics and the learning of mathematics.

4.4 Results of the Canonical Correlation Analysis

The canonical correlation analysis resulted in one significant dimension with a canonical correlation of 0.63 (p = 0.010), as reported in Table 4. A second dimension with a canonical correlation of 0.39 was not statistically significant (p = 0.616). Table 5 reports the loadings for the first, significant canonical dimension. Each of the scales of self-reported technology use have loadings of magnitude above 0.45, indicating they make an important contribution to the canonical dimension. Three modes of self-reported technology use have particularly high loadings above 0.8, including use of technology for discovery learning (M1 = −0.86), multiple representations (M2 = −0.87) and reflection (M5 = −0.85). The remaining two modes of self-reported technology have slightly lower loadings but nevertheless make an important contribution to the dimension: use of technology for practice (M3 = −0.61) and for individual learning (M4 = −0.72). Of the beliefs scales, only three make an important contribution to the canonical dimension. Both self-efficacy scales have high loadings above 0.8 (S1 = −0.83, S2 = −0.81). Of beliefs about teaching with technology, only the scale for beliefs that technology supports teaching with multiple representations (T2 = −0.48) was an important contributor to the canonical dimension. Finally, none of the epistemological beliefs about the teaching and learning of mathematics had loadings above 0.45. The results of the canonical correlation analysis seem to reflect the results of the pairwise correlation analysis between teacher beliefs and self-reported modes of technology use.

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Test of the number of canonical relationships — Pillai-Barlett test

Citation: Implementation and Replication Studies in Mathematics Education 5, 2 (2025) ; 10.1163/26670127-bja10030

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Canonical loadings for first two canonical relationships (note that only the first is significant)

Citation: Implementation and Replication Studies in Mathematics Education 5, 2 (2025) ; 10.1163/26670127-bja10030

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5.1 Multiple Representations Are Central to Teachers’ Beliefs and Use of Digital Technology across Contexts

Beliefs about the use of DT to support multiple representations (T2) emerged as the most strongly endorsed in England, recording the highest mean scores across all six T-scales, and therefore indicating the generalisability of this finding, which also holds true in Thurm and Barzel’s study. This finding aligns with existing literature on the pedagogical value of multiple representations in mathematics education (Clark-Wilson et al., 2020; Thurm & Barzel, 2020). In both studies, the use of DT for multiple representations (M3) was positively correlated with beliefs about its pedagogical role (T2) and with self-efficacy beliefs, while showing no significant correlation with other belief dimensions. This suggests that teachers perceive multiple representations not only as a core instructional strategy but also as a relatively autonomous construct within their broader belief systems. The apparent independence of multiple representations from other belief constructs — regardless of contextual variables such as teaching experience or curriculum mandates — supports Thurm and Barzel’s (2022) proposition that multiple representations offer a promising focal point for professional development, as they resonate with teachers across diverse background and levels of experience. This also echoes Ertmer et al.’s (2015) argument that effective technology integration depends on aligning pedagogical beliefs with 21st-century practices, including the use of DT to enhance conceptual understanding through varied representations.

While the centrality of multiple representations is evident in both contexts, canonical correlation analysis revealed structural differences in how this belief dimension is embedded within teachers’ broader belief systems. In the German study, beliefs about and use of multiple representations formed a distinct sub-dimension, largely separate from other belief constructs. This may reflect systemic influences, such as curriculum mandates and assessment policies that have increasingly embedded DT into mathematics education in Germany (Noyes et al., 2023). In the English context — where DT use is not mandated and professional development is less structured (Bretscher, 2021; Crisan et al., 2023) — teachers’ beliefs about multiple representations were embedded within the only statistically significant dimension, alongside self-efficacy and all modes of technology use. This suggests that in England, beliefs about multiple representations are more tightly interwoven with teachers’ confidence and broader pedagogical practices, possibly due to the absence of systemic structures that would otherwise isolate or elevate this belief domain. These findings resonate with Speer and Eichler’s (2022) study, which demonstrated that beliefs about DT can evolve through sustained engagement with digital tools, particularly when supported by opportunities to reflect on their pedagogical value. In this light, the centrality of multiple representations may serve as a gateway for broader belief transformation, especially in contexts like England, where DT is not yet fully embedded in curriculum or assessment. As Clark-Wilson et al. (2020) emphasise, effective technology use depends not only on access but on teachers’ ability to design meaningful tasks and orchestrate learning experiences that leverage DT’s representational affordances.

In sum, Thurm and Barzel’s (2022) findings highlight the importance of multiple representations, a finding replicated by our study. However, beyond this headline finding, the integration of multiple representations into teachers’ belief systems and practices is shaped by contextual factors. These insights support the validation and generalisability of the German findings to the English context, while also highlighting the need to address contextual challenges. Professional development that foregrounds multiple representations as a pedagogical anchor, while also supporting teacher self-efficacy and addressing systemic constraints, may offer a powerful strategy for fostering meaningful and sustained DT integration in mathematics education.

5.2 The Way Self-Efficacy Beliefs Are Related to Technology Varies According to Context

Self-efficacy is significantly correlated with all modes of technology use in both the German and English contexts, reinforcing its central role in shaping teachers’ engagement with DT, as highlighted in previous research (Ertmer et al., 2015; Geraniou & Misfeldt, 2022). However, the nature of this relationship is mediated by contextual factors such as teaching experience, curriculum mandates, and institutional support. This finding supports the generalisability of Thurm and Barzel’s (2022) conclusions, while also highlighting the need to account for contextual challenges when applying them to the English educational landscape.

In our study, canonical correlation analysis revealed that among English pre-service teachers, self-efficacy was closely associated with beliefs about multiple representations (M2) and all modes of technology use. This suggests that for novice teachers — who typically lack extensive classroom experience — self-efficacy serves as a critical driver of technology-related beliefs and practices. These findings align with Leatham’s (2007) and Belbase’s (2015) work, which emphasise the formative nature of pre-service teachers’ beliefs and the importance of early, hands-on experiences with DT in shaping their pedagogical orientations. Moreover, Speer and Eichler (2022) further demonstrate that belief transformation is possible through sustained engagement with digital tools, particularly when supported by structured reflection and design-based learning, further underscoring the importance of building confidence during initial teacher education. In contexts like England where DT use is not mandated, voluntary engagement with technology may reflect a self-selecting group of teachers who already possess strong self-efficacy and hold positive beliefs about its pedagogical value. This is consistent with Bretscher’s (2021) findings, which challenge assumptions about the alignment between technology use and pedagogical style, showing that teachers with high self-efficacy may adopt a range of tools for diverse instructional purposes. The absence of systemic incentives or curricular requirements in England likely amplifies the role of individual motivation and belief systems in shaping technology use.

Thurm and Barzel’s (2022) study in North Rhine-Westphalia, conducted after the introduction of DT into high-stakes exams, revealed that self-efficacy was more narrowly linked to student-centred modes of technology use. The widespread adoption of DT for multiple representations — driven by curriculum and assessment mandates — appeared to reduce the extent to which self-efficacy influenced this particular mode of use. This supports the argument that systemic mandates can standardise certain practices, thereby diminishing the variability introduced by individual beliefs (Clark-Wilson et al., 2020). Importantly, Thurm and Barzel (2020) found that while professional development can positively influence beliefs about the pedagogical value of DT, self-efficacy and epistemological beliefs are more resistant to change. This suggests that in contexts where DT use is externally driven, belief transformation may require deeper, sustained interventions beyond policy mandates. Ertmer et al. (2015) similarly argue that effective technology integration depends on a multifaceted support system, including opportunities for mastery experiences that build confidence and pedagogical alignment.

In summary, we successfully replicated the finding that self-efficacy is associated with technology use, however its influence is mediated by the broader educational context. In voluntary-use settings like England, self-efficacy plays a more prominent role in shaping engagement. In contexts like Germany, where DT integration is policy-driven, self-efficacy may exert a more nuanced and mode-specific influence. These findings validate the relevance of Thurm and Barzel’s (2022) framework in the English context, while also highlighting the importance of context-sensitive professional development that not only builds technical competence but also fosters pedagogical confidence and reflective practice.

5.3 Epistemological Beliefs Hold a More Peripheral Position in Technology Use across Both Contexts

A consistent pattern regarding epistemological beliefs emerged across both the German and English studies. None of the epistemological belief scales yielded loadings above 0.45, indicating that these beliefs did not significantly contribute to the canonical dimensions. Statistically significant associations between epistemological beliefs and modes of technology use were minimal or absent in both contexts, suggesting that such beliefs occupy a peripheral role in shaping technology integration. This finding supports the generalisability of Thurm and Barzel’s (2022) conclusions and highlights the need to interpret epistemological beliefs as a secondary factor in technology-related pedagogical decision-making.

This aligns with previous research that has questioned the direct influence of epistemological beliefs on technology use. For instance, Misfeldt et al. (2016) demonstrated that teachers’ conceptions of mathematics — ranging from instrumentalist to Platonist — can influence their attitudes toward DT, but these beliefs often manifest in complex and sometimes contradictory ways. Similarly, Belbase (2015) found that while pre-service teachers’ epistemological beliefs evolved through engagement with digital tools, their initial views were shaped more by practical experiences than by abstract conceptions of mathematics. These studies suggest that epistemological beliefs are not static, but their influence on technology use may be indirect and mediated by other factors such as self-efficacy and pedagogical orientation.

In our study, scores for inquiry-based learning (E2) and active learning (E4) were lower in Thurm and Barzel’s (2022) German sample, while teacher-centred beliefs (E3) were more pronounced among English pre-service teachers. These differences may reflect context-specific interpretations of epistemological beliefs, shaped by curriculum design, assessment practices, and teacher education programmes. The greater variability in epistemological belief scores in our English sample may also be attributed to the relative inexperience of participants, echoing Leatham’s (2007) observations that pre-service teachers often hold less established beliefs and Hegedus et al.’s (2017) observations that teachers are more susceptible to change through experiential learning.

In the German context, canonical correlation analysis indicated that epistemological beliefs fell outside the two main sub-dimensions, reinforcing their peripheral status. In England, none of the epistemological belief scales loaded highly on the sole significant dimension, further confirming their limited explanatory power in relation to technology use. This finding resonates with Bretscher’s (2021) study, which challenged the assumption that technology use is inherently aligned with student-centred pedagogies. Her work demonstrated that teachers with varying epistemological orientations may adopt similar digital tools for different purposes, suggesting that technology integration is not necessarily driven by epistemological stance. Moreover, Thurm and Barzel (2020) found that professional development had limited impact on epistemological beliefs, which remained largely unchanged despite targeted interventions. This supports Ertmer et al.’s (2015) assertion that belief change — particularly in epistemological domains — requires sustained, multifaceted support beyond short-term training. As Clark-Wilson et al. (2020) argue, effective technology integration depends not only on access and technical competence but also on teachers’ ability to design meaningful tasks and reflect critically on their pedagogical goals.

In summary, our findings replicate the peripheral role of epistemological beliefs observed in Thurm and Barzel’s (2022) study. Thus, while epistemological beliefs are theoretically relevant to instructional decision-making, their practical influence on technology use appears limited across contexts. This suggests that professional development efforts may be more effective when focused on building self-efficacy and pedagogical knowledge, with epistemological beliefs addressed through longer-term, reflective engagement.