Factors Influencing the Usage of Interactive Action Technologies in Mathematics Education: Insights from Hungarian Teachers’ ICT Usage Patterns

1 Introduction

Some years ago, one of the first author’s math teacher students expressed a sentiment that struck the author. They said, “I do not know why a subject as beautiful as mathematics should be spoiled by technology. I kept my school math notebooks, and I want to teach math the way my math teacher taught me: with paper and pencil.” While not representative of all math teachers in Hungary, this statement highlights a crucial aspect of the challenge of integrating technology into mathematics education: teachers’ attitudes and approaches.

This anecdote reflects a broader hesitation among some teachers toward embracing digital tools in teaching despite the increasing emphasis on technology in educational curricula worldwide. Institutional culture, defined as the norms, values, and practices of an educational system, plays a significant role in teachers’ attitudes toward the integration of digital technologies in mathematics education (Artigue, 2002). Resistance to technology integration may emerge when traditional values and practices are stable.

The Hungarian National Curriculum (Government of Hungary, 2020) deals in detail with the role of digital tools in teaching mathematics. Based on the Hungarian curriculum, the learner should use digital tools as early as possible, even in the early grades, to practice operations and problem-solving using computer games. Mathematical development games, computers, and other digital tools can enhance learning. Additionally, educators should introduce students to mathematical software that enhances their mathematical knowledge and digital literacy. Finally, learners should reach a level where they can independently utilize calculators, computers, visualization aids, digital information sources, and mathematical software that facilitates the application of mathematics.

This ambitious objective raises several questions, first and foremost, about whether the use of digital tools has been shown to impact learning outcomes positively. The outlined answer is that the benefits of technology in mathematics education are modest, as evidenced by experimental studies. The OECD’s (2015) correlational study provides minimal evidence of the benefits of digital technology use. A thorough literature review (Drijvers, 2018) has revealed that some experimental studies, particularly review studies, have reported significant positive effects. However, they varied considerably, ranging from small to moderate effect sizes. Compared to other innovative interventions, evidence supporting the benefits of digital technology in mathematics teaching is not particularly strong. Drijvers also called for a closer examination of the problem and improved investigation methods.

One factor behind this disappointing fact may be teachers’ actual practice of using digital technology. With the growing capabilities of educational technology and adequate technological infrastructure in schools, integrating technology into mathematics teaching has not been as effective as anticipated.

The OECD Teaching and Learning International Survey (OECD, 2018) revealed that the ratio of teachers who frequently or consistently let students use info-communication tools for projects or class work is approximately 48% in Hungary. In addition, Eszenyiné (2019) has investigated several areas of digital competence of mathematics teachers, and digital content creation is relevant to our research. This includes the use of tools to produce and present information. According to this research, 42% of mathematics teachers have low levels of this competence, and there is no regular use of ICT tools among these teachers. 31% have a medium level and 27% have an advanced level. The relationship between curriculum goals and classroom practice forms the rationale of our research, which examines some possible factors contributing to the utilization of technology in mathematics education in Hungary, focusing on math teachers’ preparedness for the application of digital technology, their attitudes toward digital tools, and their beliefs about the effects of digital tools in mathematical problem-solving.

Our research question is as follows in a raw outlined form: What is the relationship between Hungarian math teachers’ digital tool use habits and their perceived ICT literacy, digital pedagogy knowledge, attitudes toward using technology, and beliefs about the role of digital tools in problem-solving?

Investigating beliefs about the role of digital tools in problem-solving is a novelty of our research, which specifically examined the use of technology by mathematics teachers in the context of problem-solving. Our approach investigates how teachers perceive the role of technology within the well-known problem-solving phases (understand the problem, devise a plan, carry out the plan, and look back) outlined by Polya (1945). This focus allows us to explore the integration of technology in mathematics education and how it can be strategically utilized to enhance the problem-solving process.

To answer the research question, we developed a questionnaire to evaluate Hungarian mathematics teachers’ self-assessed digital competencies and use of digital tools. A total of 349 mathematics teachers participated in this study.

2 Literature Review

The use of digital tools in mathematics education is a complex and evolving field with many potential applications. According to Santos-Trigo (2020), digital tools in mathematics education can be categorized into three main types: mathematical action technologies, conveyance technologies, and online resources. Mathematical action technologies, such as Dynamic Geometry Systems, Computer Algebraic Systems, and computer simulations, enable the representation, exploration, and solving of mathematical tasks. These tools allow for the dynamic modeling of mathematical concepts, enabling students to manipulate objects and observe changes, thus fostering a deeper understanding of mathematical relationships and invariances. Conveyance technologies, including communication applications and presentation tools, facilitate the sharing and discussing of mathematical ideas. Online platforms offer resources such as instructional videos, problem examples, and extensive information on mathematical concepts, thus enhancing the learning experience.

The concept of digital curriculum resources (DCR) further expands the role of digital tools in mathematics education. DCR is defined as organized systems of digital resources in electronic formats that articulate the curricular content (Drijvers, Stacey, & Trouche, 2024). DCRs include digital platforms, software, textbooks, and other materials that help with lesson planning and execution. They give teachers the tools to follow the curriculum in their classrooms, and thus, DCRs are the link between culture, policy, and teacher-curricular practice. In Hungary, the National Public Education Portal (NKP; see the website nkp.hu in Hungarian) is one of the leading educational platforms in Hungary, providing free digital curricular elements and services helpful in the teaching-learning process for public education stakeholders.

Many scientists have reported that the digital shift in mathematics education has also affected problem-solving. Artigue (2002) claims that technological knowledge is not just a supplementary skill but becomes an integral part of mathematical knowledge in digital learning environments. Her perspective anticipates later theoretical developments, such as Borba and Villarreal’s (2005) concept of “humans-with-media” which emphasizes that knowledge is not produced by humans alone but results from a collaborative effort between individuals and various forms of media. This framework emphasizes the technological dimension of thinking and intelligence, acknowledging that the nature of problem-solving and conceptual understanding can change significantly depending on the tools or media used. Barrera-Mora and Reyes-Rodríguez (2013) illustrate how the use of digital technologies has influenced mathematical problem-solving, indicating a change in the methods of instruction and acquisition of knowledge. They emphasized the role of digital technologies in facilitating problem-solving activities. The digital transition is regarded as fostering students’ mathematical skills.

Integrating digital technology, including conveyance tools and mathematical action technologies, into mathematical learning environments helps promote and expand discussion among learners and teachers (Santos-Trigo, Reyes-Martínez, & Aguilar-Magallón, 2015). The authors argue that digital technologies are crucial in problem-solving, enabling students to explore novel ways of representing and solving problems. This encourages creative solutions and enhances problem-solving strategies such as examining special cases. New heuristic strategies, such as dragging and finding foci, emerge during task construction, enhancing dynamic models’ effectiveness. Çekmez and Bülbül (2018) argued that mathematical performance requires problem-solving, and well-designed problem-solving-based learning environments can help students understand mathematical concepts and techniques. Math educators consider dynamic mathematics software a viable tool for building such settings. da Silva, Barbosa, Borba, and Ferreira (2021) reported that integrating GeoGebra and Excel software to explore mathematical problems could be effectively incorporated into mathematical investigations. Abramovich (2022) stated that one of the most notable changes is the growing reliance on digital tools that provide real-time feedback and support for interactive problem-solving. These tools have transformed how students approach mathematical challenges.

Teachers’ digital literacy involves the ability to use and manage technology effectively in educational settings and the skills to assess and understand its broader implications (Hasse, 2017). This includes an awareness of how technology impacts teaching and learning processes, alters relationships and identities in the classroom, and influences complex power dynamics. Teachers must have these competencies to navigate and integrate technology responsibly and effectively into their educational practices. Building on these principles, our research divides teacher digital literacy into two fundamental components: the practical use of tools and pedagogically grounded utilization. This distinction emphasizes the technical ability to handle digital tools and the importance of integrating technology underpinned by sound pedagogical principles (Loveless, 2011).

Mathematics teachers’ attitude toward technology integration in mathematics teaching refers to their perceptions, beliefs, and inclinations regarding using technological tools to support and enhance the teaching and learning of mathematics in education. This encompasses their attitudes toward the potential benefits, challenges, and perceived barriers to incorporating technology into their instructional practices (Pierce & Ball, 2009).

Considering the literature background, we refined our research question by asking, “which factors distinguish mathematics teachers who use action software frequently from those who use general ICT technologies frequently but action tools less frequently and those who use ICT technologies hardly.” The answers were based on a sample of Hungarian mathematics teachers. However, we believe that our research question is sufficiently general and fills a gap in the literature.

While this study focuses on broader applications of digital tools in mathematics education, advancements such as automated reasoning tools exemplify how technology can push the boundaries of engagement and exploration, underscoring the importance of rethinking digital integration in curricula (Recio & Dana-Picard, 2024).

3 An Illustrative Example of Technology-Aided Problem Solving

To illustrate how digital tools can support problem-solving, we provide the following example with emphasis on Polya’s problem-solving phases. What follows is an example of using technology in problem-solving, designed for eighth-grade students (on average, 14 years old) included in the Hungarian National Public Education Portal’s online platform. The Hungarian Government supports this portal, and it is compatible with the National Curriculum.

In 1867, Russia accepted the American offer to purchase its territory in Alaska, deemed of little value. They received 7.2 million US dollars for approximately 1.7 million square kilometers of land, amounting to about $4.2 per square kilometer. Considering inflation alone, if the average annual rate of monetary depreciation had been 2%, what would be the equivalent cost 150 years later? In other words, how many dollars would match the value of 7.2 million USD 150 years later?

The result is 7.2·1.02¹⁵⁰ million US dollars. The inflation calculation is a prime example of exponential growth and helps students see how to handle real-life financial problems. However, the exponential expression in the result is not always enough for everyday context. Placing the result into Polya’s four-phase model, the “devise the plan” phase is present: the result shows how to set up the calculation, i.e., formulating a strategy for solving the problem. Although this expression reflects the conceptual understanding of the problem, we naturally ask for the practical value of the result. Polya’s “execute the plan” phase is missing from the above form; moreover, there is no concluding reflection. For practical value, a calculator or spreadsheet application can be used (Figure 1). Repeated multiplication can be used without a reference to power if we use a spreadsheet application, as shown in the figure.

Figure 1

Calculation of the practical value of the exponential expression. Note. Lines 3-148 are hidden in the spreadsheet application screenshot (right).

The fourth Polya step (look back and reflect) may include discussing whether the inflation rate is reasonable. Calling for WolframAlpha, we learn that based on authentic data, the average rate of inflation is 1.91% per year (Figure 2). The deviation between the results (140.4 million versus 123.1 million) is a good possibility that this can be explained by the ratio of (average) inflation rates and has nothing to do with the initial amount of 7.2 million dollars.

Figure 2

The “Look back” phase supported by WolframAlpha, based on the Consumer Price Index.

4 Method

5 Results and Discussion

5.5 Variables Examined in the Different User Groups

Figure 3 represents the scores of the four variables under study (ICT literacy, pedagogical competence, attitude, and belief).

Figure 3

Descriptive plots of mean scores of the four components in the three groups. Group 1: Frequent users of math action tools; Group 2: General aim tool enthusiasts; and Group 3: Infrequent Users. The error bars are based on standard error.

5.5.1 Perceived ICT Literacy Across Groups

The results indicated a statistically significant difference between groups (H(2) = 24.199, p < 0.001). Dunn’s post hoc tests were conducted to examine pairwise differences. The results revealed highly significant differences between groups 1 and 3 (z = 4.894, p _bonf < 0.001). Significant differences were also observed between groups 2 and 3 (z = 2.486, p _bonf = 0.026). The difference between groups 1 and 2 was not so pronounced (z = 2.370, p _bonf = 0.053).

5.5.2 Perceived Pedagogical Competence in the Use of ICT Across Groups

The Kruskal–Wallis test confirmed significant differences among the groups, H(2) = 36.731, p < 0.001. During Dunn’s post hoc comparisons, highly significant differences were found between groups 1 and 3 (z = 5.740, p _bonf < 0.001) and groups 2 and 3 (z = 4.150, p _bonf < 0.001). There was no significant difference between groups 1 and 2 (z = 1.665, p _bonf = 0.288).

5.5.3 Attitude Toward ICT Use Across Groups

The Kruskal–Wallis test confirmed significant differences in attitudes among the groups, H(2) = 57.007, p < 0.001. Dunn’s post hoc comparisons showed significant differences during all pairwise comparisons. The result between groups 1 and 2 is z = 2.754, p _bonf = 0.018; for groups 1 and 3, z = 7.349, p _bonf < 0.001; and groups 2 and 3, z = 4.625, p _bonf < 0.001.

5.5.4 Beliefs About the Role of Digital Tools in Problem-Solving Across Groups

We also got a significant difference for this variable, H(2) = 15.264, p < 0.001. Dunn’s post hoc comparison reveals a significant difference between groups 1 and 3 (z = 3.777, p _bonf < 0.001) and groups 2 and 3 (z = 2.478, p _bonf = 0.040). There was no significant difference between groups 1 and 2 (z = 1.324, p _bonf = 0.557).

The results show that the attitude variable is the only significant separation factor for group 1 (frequent users of math action tools) from the other two groups. Moreover, the Kruskal–Wallis statistic is the highest for this variable. Even though action technology users rate their digital competence highest, the level of digital competence significantly separates infrequent users from the other groups, and the separation of Group 1 from Group 2 is not so pronounced. Similarly, those who use ICT technology in mathematics classrooms rate their digital pedagogical competence as better than infrequent users, regardless of the technology they use.

The analysis of the belief variable gave a surprising result because using digital tools in problem-solving was expected to be an essential separating factor for the group that frequently used action technologies. Nevertheless, we found no significant difference between the first and second groups. A possible explanation for this phenomenon can be found by looking at the answers to the questions about the different phases of the Polya. The analysis of problem-solving phases reveals a significant divergence in evaluating the fourth phase (look back) compared to the other phases. The mean score for the fourth phase stands notably higher at M = 3.662 (SD = 0.557), whereas the mean scores for the preceding phases are lower: first phase (M = 3.223, SD = 0.831), second phase (M = 3.269, SD = 0.740), and third phase (M = 3.241, SD = 0.784). The Wilcoxon signed-rang test statistically supports this disparity. In examining the differences between various phases, there was a significant difference between the first phase and the fourth phase, W = 1265.00, z = −8.309; between the second phase and the fourth phase, W = 1374.00, z = −8.286, p < 0.001; and between the third phase and the fourth phase, W = 1006.00, z = −8.404, p < 0.001. No other significant differences were found. These findings emphasize the distinctive role of the “look back” phase in technology-aided problem-solving in the researched population. Furthermore, although the “look back” phase is much richer than checking results (see our example for technology-aided problem-solving), it will likely be predominant in school practice. Narrowed down to checking, phase 4 does not necessarily require dynamic approaches because a simple calculator is usually enough.

6 Summary

Based on the literature, interactive action technologies, such as dynamic geometry tools and computer algebra software, are crucial in teaching mathematics, especially mathematical problem-solving. Considering this fact, we formulated our research question by asking which factors distinguish mathematics teachers who use action software frequently from those who use general ICT technologies frequently but action tools less frequently and those who use ICT technologies hardly.

To answer this research question, our study examined the following factors in Hungarian mathematics teachers: attitudes toward ICT, their perceived ICT literacy and pedagogical competence in using ICT, and beliefs about the role of digital tools in mathematical problem-solving. We grouped mathematics teachers based on their usage frequency of ICT tools, categorizing them into frequent users of action tools, general aim tool enthusiasts, and infrequent users. The result shows that infrequent technology users had the worst scores in all categories. Moreover, the only stable discriminating factor for frequent math action tool users is the attitude toward technology usage.

Since attitude toward technology usage seems to be the critical factor among mathematics teachers in integrating action tools in teaching, teacher education and professional development programs should encourage favorable ICT attitudes. Inspiration, examples of effective use, and showing how ICT tools affect mathematical problem-solving might influence teachers’ enthusiasm to use these resources. Thus, training programs should prioritize building confidence and positive perceptions around the use of technology in mathematics education.