Visual representations and the process of visualisation have an important role in geometry learning. The optimal use of visual representations in complex multimedia environments has been an important research topic since the end of the last century. For the purpose of the study presented in this paper, we designed a model of learning geometry with the use of digital learning resources like dynamic geometry programmes and applets, which foster visualisation. Students explore geometric concepts through the manipulation of interactive virtual representations. This study aims to explore whether learning of geometry with digital resources is reflected in higher student achievements in solving geometric problems. This study also aims to explore the role of graphical representations (GRs) in solving geometric problems. The results of the survey show a positive impact of the model of teaching on student achievement. In the post-test, students in the experimental group (EG) performed significantly better than students in the control group (CG) in the overall number of points, in solving tasks without GR, in calculating the area and the perimeter of triangles and quadrilaterals than the CG students, in all cases with small size effect. The authors therefore argue for the use of digital technologies and resources in geometry learning, because interactive manipulatives support the transition between representations at the concrete, pictorial and symbolic (abstract) levels and are therefore important for understanding mathematical concepts, as well as for exploring relationships, making precise graphical representations (GRs), formulating and proving assumptions, and applying different problem-solving strategies.

Researchers and society in general seem to be conflicted regarding the use of digital technology in early childhood education (ECE). Some are focusing on the positive aspects of using digital technology, while others are critical and position it as an enemy of early childhood practice. It has been argued that digital technology is not appropriate for young children’s cognitive, physical, social and emotional development. Nevertheless, supporting and developing young children’s beginning digital competence is implemented in curricula and teacher education globally. The need for teachers’ professional digital competence (PDC) is increasing according to the development and increased use of digital technology in society as a whole, including in the field of education. The field of research has, to a large extent, been focused on primary and secondary education, and there is a lack of research on PDC in ECE. To gain insight into the dynamics of PDC in ECE, we investigated a range of ECE contexts by including different international perspectives in a comparative study of pre-service early childhood (EC) teachers transitioning to being in-service teachers. The survey was conducted in eight different nations (Norway, Slovenia, Portugal, Poland, Turkey, Ukraine, England and Jordan) and resulted in 772 responses from pre-service teachers in the last year of their education. The paper discusses these international perspectives, considering the differences found between nations. It also investigates the dynamics of PDC, understood in this article as comprising attitudes, skills and knowledge. Following this, it also investigates how these dynamics are affecting the pre-service teachers’ expectations related to their future application of digital tools as teachers to be. The results indicate large differences between nations for both single items and multi-item scales. At the same time, the dynamics of digital practices across nations reveal that attitudes, digital skills and knowledge are statistically strong predictors of pre-service teachers’ future use of educational digital technology (EDT). This indicates both similarities and differences across nations and could serve as insight regarding the development of teacher programmes and the importance of including all aspects when developing pre-service teachers’ PDC. This article, due to its limitation, will not elaborate in depth on contextual differences, and further qualitative research is needed to understand the complexity related to educational culture and practice.

Digital technology has become an important part of society and deserves attention and in-depth research, which is still lacking. The study presented in this paper includes international perspectives from six countries and examines which factors influence the use of digital technologies in future pedagogical work in primary schools. Specifically, we investigated how pre-service teachers assess their attitudes, knowledge, and skills towards digital technology, and we determined these factors’ role in the pre-service teachers’ future use of digital technologies in pedagogical work. For the purpose of the research, an online questionnaire was used, which contained open-ended questions, optional questions, and five-point Likert-type scales, and Spearman correlation and Stepwise linear regression statistical methods were used in the data analysis. The sample consisted of 573 full-time and part-time undergraduate pre-service teachers from the Faculties of Education’s higher professional programmes in Norway, Slovenia, Portugal, Turkey, Ukraine, and Jordan. Data were collected between June 2021 and May 2022 and processed using IBM SPSS. The present research showed the significant importance of knowledge and skills about digital technologies and professional attitude towards digital tool factors for pre-service teachers’ future professional use of digital technologies. The demonstrated intention of the future use of digital technologies showed the readiness of pre-service teachers regarding the inclusion of digital technologies in pedagogical work. Opportunities for further research are in the implementation of focus groups after surveying pre-service teachers, as well as regular measurements and the inclusion of other important constructs in the regression model.

In this article, we present the results of empirical research using a combination of quantitative and qualitative methodology, in which we examined the achievements and difficulties of sixth-grade Slovenian primary school students in decimal numbers at the conceptual and procedural knowledge level. The achievements of the students (N = 100) showed that they statistically significantly (z = -7,53, p < .001) better mastered procedural knowledge (M = 0.60, SD = 0.22) than conceptual knowledge (M = 0.37, SD = 0.17) of decimal numbers. Difficulties are related to both procedural and conceptual knowledge, but significantly more students have difficulties at the level of conceptual knowledge. At the level of procedural knowledge, or in the execution of arithmetic operations with decimal numbers, we observed difficulties in transforming text notation into numerical expressions, difficulties in placing the decimal point in multiplication and division, and insufficient automation of mathematical operations with decimal numbers. At the level of conceptual knowledge of decimal numbers, the results indicate difficulties for students in understanding the place values of decimal numbers, in estimating the sum, product and quotient of decimals with reflection and in mathematical justification. In relation to difficulties in justification, we observed an insufficient understanding of the size relationship between decimal numbers and difficulties in expressing them in mathematical language. The results indicate that to overcome such difficulties in the learning and teaching of mathematics, more balance between procedural and conceptual knowledge is needed.

This experimental study examined the impact of learning and teaching ge-ometry in seventh-grade geometry education comparing learning-path and conventional instruction. According to constructivism, a learning path with the use of learning objects should enhance learner autonomy and self-directedness by providing differentiated instruction. We designed a model of path-based geometry learning in a learning management system–based learning environment with the use of dynamic geometry programs and applets, which fosters visualisation and the exploration of geometric concepts through the manipulation of interactive virtual representations. The results show that the experimental group (EG) achieved higher scores on all levels of knowledge and statistically significantly better results in taxonomy level-III tasks (problem-solving knowledge) and overall score than the control group (CG). There was initial equivalence between the EG and CG in prior knowledge. The authors concluded that path-based geometry learning empirically develops knowledge at higher cognitive levels.

Institutions offering teacher education have generally been criticized for giving pre-service teachers an insufficient education regarding the pedagogical use of digital technology. In this study we investigate the dynamics of professional digital competence (PDC) among teacher educators (in primary, secondary and early childhood teacher education programmes) in Norway, Slovenia, and Portugal. A survey was constructed based on the understanding of digital competence consisting of an individual’s knowledge, skills, and attitudes. Three constructed variables from the survey (Attitudes, Knowledge and skills, and Use, regarding digital technology in higher education) were analysed, and we found small differences in mean scores between the three countries. However, a pathway analysis via regressions revealed markedly different dynamics of PDC, and we discuss implications of our findings on teacher educators’ use of digital technology.