The coronavirus disease (COVID-19) has led to more than one hundred million infected humans and millions of deaths worldwide (John Hopkins University, 2022). Confronted with these huge impacts on public health, most governments have implemented social distancing regulations and lockdown measures to reduce the spread of COVID-19. Consequently, more than 90% of the children worldwide were affected by temporary school closures during the pandemic (UNESCO, 2022). Although it is still unclear how the suspension of face-to-face teaching in schools impacted children’s academic skills and achievement in detail, research raises serious concerns about its social, economic, and public health consequences for society (Kuhfeld et al., 2020; Lee, 2020; Engzell et al., 2021; Psacharopoulos et al., 2021; Raw et al., 2021; Waite et al., 2021; Blaskó et al., 2022; Ravens-Sieberer et al., 2022).

In March 2020, school closures in many places were implemented within days and schools had to shift their traditional classroom face-to-face teaching to distance teaching approaches (Fickermann and Edelstein, 2020). For a year and a half, the German school system was predominantly characterized by distance teaching (Ministerium für Schule und Bildung des Landes Nordrhein-Westfalen, 2022). The implementation of distance teaching was under the full responsibility of each individual school. German schools were very different in their readiness to implement distance learning. Likewise, the home learning conditions varied widely across households (e.g., in terms of learning resource, parental learning support, and home learning environment). These together lead to a situation that there were great variations in German children’s learning conditions during the COVID-19 pandemic (Fickermann and Edelstein, 2020; Huber et al., 2020; Huber and Helm, 2020; Porsch and Porsch, 2020; Helm et al., 2021; Steinmayr et al., 2021).

Initial studies indicate great learning gaps compared to typical school years, which could lead to a reduction in global economic growth and a lifetime decrease in individual’ earnings (Engzell et al., 2021; Hammerstein et al., 2021; Psacharopoulos et al., 2021; König and Frey, 2022). Current estimates predict severe socio-economic consequences, especially for low- and middle-income families (Bonal and González, 2020). In particular, students from low-income families seem to have pronounced learning losses and did not experience marked home-based learning opportunities (Engzell et al., 2021; Goudeau et al., 2021). A recent large-scale study showed that the learning losses have been especially marked in mathematics (van der Berg et al., 2022).

To the best of our knowledge, the interrelationships between distance learning and teaching conditions during the pandemic and performance-based outcomes in math have not yet been studied. Until now, the variables were mostly examined in separate research designs and the studies on the relation between distance learning conditions and academic outcomes were measured through observer-ratings by parents, teachers or self-ratings by students (Huber and Helm, 2020; Helm et al., 2021; Steinmayr et al., 2021). Considering this scarcity of research about the impacts of distance education during the COVID-19 pandemic on children’s basic numeracy skills, the necessity for further research to examine this interaction becomes clear.

The suspension of face-to-face learning due to the COVID-19 pandemic has significantly changed children’s mathematics learning in schools. This fact raises questions whether the switch to distance learning has impacted children’s basic number skills. To date, it is unclear whether there are associations between risk factors in the home and digital learning environments during the suspension of face-to-face teaching and primary school children’s basic number skills at the time of returning to face-to-face teaching. Furthermore, it is not known whether distance teaching approaches had an impact on math learning of at-risk children. By examining the interplay between home-based learning environments, distance teaching conditions and basic math skills, the present project will address this gap in educational research.

The suspension of face-to-face teaching during the COVID-19 pandemic changed greatly the learning environment of elementary school children and posed major challenges to teachers and parents (Fickermann and Edelstein, 2020; Jungmann et al., 2021). Because of different approaches to implementing distance teaching in schools and varying home learning conditions across household, children in Germany had very different learning conditions during the pandemic (Helm et al., 2021; Steinmayr et al., 2021). This fact raises the question of whether these conditions have affected the development of children’s basic number skills. Therefore, the aim of this study was to identify risk factors of home-based learning and to examine whether multiple risk factors were related to basic number skills after the suspension of face-to-face teaching.

The data provide first empirical evidence that certain conditions during distance learning were associated with weaker basic math skills after the interruption of face-to-face teaching. The absence of a laptop or internet at home can be considered as risk factors for children’s basic number skills. Logically, these children were less likely to participate in digital learning opportunities offered by their teachers or to take up digital learning opportunities on their own initiative. Another risk factor was identified in the learning environment at home. Children who were learning in a room with other children and without adult guidance showed clear deficits in their basic number skills. Since most elementary school children are not yet able to manage self-regulated learning processes in a group setting without adult guidance (Stoeger and Ziegler, 2011; Godwin et al., 2016), it is very likely that these children more often engage in non-task behavior compared to peers who have been supported by an adult. Interestingly, children who learned alone did not show poorer math skills. One explanation for this could be that this group consists of rather high-achieving children who are trusted by their parents to learn on their own. Analyses of the influence of multiple risk factors (at-risk levels) showed a negative association with basic number skills. Children affected by multiple risk factors during distance learning – which applied to 12% of children – were more likely to have deficits in their basic number skills. The more risk factors were present, the worse basic skills were observed after the interruption of face-to-face teaching. However, the question arose as to whether these differences were due solely to socioeconomic resources and thus may have existed prior to the pandemic.

Consistently with previous research (Helm et al., 2021), the data revealed that some of these risk factors were related to the sociocultural background. Children from families with more resources were more likely to have the digital prerequisites to participate in digital learning opportunities and were less likely to learn in non-conducive learning environments at home (without adult guidance, but with siblings or friends). In light of the predictive value of socioeconomic status on the development of children’s math skills (Sirin, 2005; Lee et al., 2016) and the particularly large differences in math performance according to social background in Germany (compared to OECD average: OECD, 2019b), the question arises whether the observed risk factors and their influences on basic skills were not confounded by sociocultural background. Mediation analysis provided evidence that the link between risk levels and basic math skills was only partially mediated by sociocultural capital. Accordingly, although the influence of risk factors on basic math skills could be partially explained by differences in sociocultural capital, there was also a direct impact of risk factors on mathematical skills after the interruption of face-to-face teaching. It therefore appears that the differences are not due to socioeconomic factors alone, but that specific conditions of distance education are responsible for individual differences in basic mathematical skills.

Based on the findings on the negative impact of risk factors on basic numeracy skills, the question was whether specific teaching or tutoring services during the pandemic were able to reduce these negative repercussions. At the beginning of the pandemic, elementary schools in Germany were asked to take children from families whose parents worked in critical infrastructure into emergency care classes. These classes were taught by teachers or other educational professionals (e.g., social worker) and the children often did not attend these classes consistently (Fickermann and Edelstein, 2020; Blum and Dobrotić, 2021; Ministerium für Schule und Bildung des Landes Nordrhein-Westfalen, 2022). The data provided no evidence that children who participated in these classes showed different math skills after the interruption of face-to-face teaching. Similar results were observed for private tutoring. These services do not appear to have been able to reduce the negative effects of risk factors in home-based learning. One could hypothesize that due to the varying frequency of participation as wells as the different didactic concepts and qualities, the assumed benefits of face-to-face settings did not materialize.

Although information and communications technology (ICT) has been considered important for improving the quality of math teaching for several years, the implementation of digital technologies in German schools was not well advanced at the beginning of the pandemic (De Witte and Rogge, 2014; Huber and Helm, 2020; Eickelmann and Drossel, 2020a). There was a lack of digital infrastructure and sufficient training for teachers in the use of digital media (Eickelmann et al., 2019; Schuknecht and Schleicher, 2020; Eickelmann and Drossel, 2020b). This limited experience led to significant difficulties in providing digital learning opportunities (e.g., video conferencing, LMS, video tutorials), especially shortly after the suspension of face-to-face teaching (Helm et al., 2021). To date, there are no empirical studies focusing math skills and digital learning environments during the pandemic in Germany. Only one study (Steinmayr et al., 2021) measured children’s academic outcomes (learning progress) and activities of teachers by means of parent ratings. Using this indirect assessment method, an association was found between teaching via videoconferencing and learning progress. The data from the present study provide no evidence of a positive effect of videoconferencing or digital communication between students and teachers. These findings could be explained by the likely low teaching quality of videoconferencing, possibly due the lack of teacher training (Eickelmann et al., 2019). It could be assumed that a more frontal class teaching approach via videoconferencing – a logical adaption of traditional teaching methods given the low digital literacy of teachers – might be difficult for primary school children. However, for these conclusions, differentiated methods are needed that can capture the teaching design of videoconferencing.

Online learning methods are likely to increase in use, even where school learning is not currently disrupted, and may be useful both in conjunction with face-to-face instruction, and where necessary as a substitute for it. Spitzer and Musslick (2021) found quite positive results for German pupils from a curriculum-based online learning software for mathematics. This had been in place before the school closures of 2020 but was used more during these closures. Pupils showed better performance on this mathematical software during the school closures than the previous year; and there appeared to be some narrowing of the gap in performance between low- and high-achieving students. However, it must be noted that children, who experience the risk factors discussed here, and especially those who lack access to the internet, are not able to benefit fully from such software.

In this study, teachers indicated whether they used LMS to organize learning material for their students. The results showed a positive relationship between the use of LMS and basic math skills after the suspension of face-to-face teaching. Children appeared to benefit from a structured digital presentation of their learning material, which is consistent with studies that report a positive effect on student academic performance when digital learning programs are used to supplement classroom instruction (Skryabin et al., 2015; Comi et al., 2017; Hu et al., 2018; Laakso et al., 2018). Nevertheless, latest findings highlight that it is not so much the mere use of LMS that can be conducive for learning, but rather the specific design of digital learning opportunities by teachers (De Witte and Rogge, 2014; Mergoni et al., 2022). Consequently, further research is needed here that takes other teacher variables into account.

A key and, to our knowledge, unexplored question is whether a personalized teaching approach during distance teaching was able to counteract the negative repercussions for children with home-based risk factors during distance teaching. Personalized teaching is not clearly defined and functions as an umbrella term for didactic approaches that focus individualized student support (Stebler et al., 2018). Several meta-analyses highlighted the positive effect of feedback on student performance (Hattie and Timperley, 2007; Wisniewski et al., 2020) and a long research tradition focuses adaptive teaching concepts, in which teachers adjust their teaching approach to individual students learning (Hattie, 2009; Brühwiler and Blatchford, 2011; Hardy et al., 2011). In recent years, this personalized learning has been linked to digital media in educational research, and it has been found that it can have positive impacts on learning outcomes (Major et al., 2021; Zheng et al., 2022) when the technological applications are used effectively by the teaching staff (Cheung and Slavin, 2013; Delgado et al., 2015; Tondeur et al., 2017). The data from the present study did not show an overall positive effect of personalized teaching. However, an interaction effect was observed suggesting that students with home-based risk factors for distance learning benefit more from personalized teaching. Adaptive teaching that provided frequent feedback to children and parents may have counteract negative effects for children at-risk. This is an interesting and important finding, as further implications for school practice can be derived from it. In addition to differentiated education and training opportunities on personalized instruction for teachers, it would seem appropriate in schools with a higher number of at-risk students to have more staff resources to adequately implement individualized support (e.g., feedback to children and parents). These findings are consistent with research that demonstrates the positive impact of teacher-student interaction on learning in online education (Lin et al., 2017), as well as recent studies during the COVID-19 pandemic that highlighted the importance of teacher-student interaction for learning satisfaction and success in distance education (Schneider et al., 2021; Sun et al., 2022).

Technology-enhanced personalized learning is gaining more and more attention in research, governmental agencies, and popular media (FitzGerald et al., 2018). However, personalized learning technologies are still in their infancy (Shemshack and Spector, 2020), even though, already today, rather complex models of personalized feedback can be implemented into digital learning systems (Vasilyeva et al., 2007). However, this algorithm-driven learning management, which expanded during the pandemic, is not without problems (Williamson, 2021). Effective use of educational technologies should be one of the key topics of research in the post-pandemic schools.

Future studies should investigate the relationships between the factors studied here and other factors that may influence home learning and mathematical performance. One would expect that the effects both of school closures in general and of particular distance learning techniques would vary not only with home resources but with a variety of aspects of parental and child characteristics, and with home-school relationships. For example, Darragh and Franke (2021) found that a sample of New Zealand parents had very varied perspectives on home-learning of mathematics during lockdown. 35.5% were positive; 29.9% were negative, 29.5% gave mixed responses and 5.24% were neutral. Parents of younger children were more positive than parents of older children. Negative reactions were associated with parental levels of stress and anxiety, though it was not possible to determine direction of causation. School provision of materials and guidance was perceived by parents as an important influence on the experience of home-learning. Harper et al. (2021) looked at American parents’ responses to surveys about home mathematics education during the pandemic; and at their ‘tweets’ on the subject. It is likely that these parents, especially those in the Twitter study, were particularly interested in mathematics education and had particularly fast internet access. Nevertheless, their views seemed similar to those found in other studies: they worked a lot with their children on mathematical activities, focusing mainly on elementary-level content, and they expressed a need for more opportunities to interact directly with their children’s teachers.

Moreover, the effects of the pandemic go beyond school closures and include things like isolation from friends and relatives; physical restriction, especially for those living in small houses and flats without gardens; financial insecurity and increases in poverty; health anxiety; and in some cases, bereavement (Ravens-Sieberer et al., 2021; Feinberg et al., 2022). While children in the age-group studied here usually do not experience serious illness from Covid themselves, it does happen occasionally (Kompaniyets et al., 2021), and far more are and (especially pre-vaccines) were affected by the serious illness of parents, grandparents and other family members.

Implications of the findings are that children’s home learning is likely to be affected both by general social and economic disadvantages, and by specific practical risk factors, such as limited or absent access to the internet; lack of a device such as a tablet or laptop; not having a quiet room where to study and lack of adult support for schoolwork at home. Awareness of such problems may make it possible to identify and provide assistance to children at risk, both as regards routine home learning activities such as homework, and for children experiencing long-term disruption to face-to-face learning at school, due to individual problems such as family illness or large-scale problems such as future pandemics.

It would be interesting to investigate whether the effects of the risk factors were similar for other subjects besides mathematics. In at least some countries, including the United Kingdom, persistent numeracy difficulties are significantly commoner than persistent literacy difficulties (Parsons and Bynner, 2005; BIS, 2012); and it therefore seems at least possible that numeracy would be even less resilient than other subjects to a significant disruption such as that caused by the pandemic. Kuhfeld et al. (2020) reported results suggesting that performance in mathematics was particularly seriously affected by the pandemic. There needs to be future research on the nature, extent and long-term persistence of effects of the pandemic and school closures on children’s attainment in different subjects. This knowledge is needed, as even though large-scale school closures like during this pandemic are rare, local disruptions of school-going occur regularly in many countries for a variety of reasons: e.g. extreme weather conditions.

Some limitations of the applied research approach should be noted. First, the cross-sectional design did not allow to draw conclusions about the development of math skills over time, as no data were assessed before the pandemic. Therefore, the study can only provide hypotheses about the cause-effect relationships. Secondly, the study did not look at possible differential effect on different aspects of mathematics, or on other subjects in the curriculum. Third, the study excluded children with special educational needs, so it cannot provide any information about them. Fourth, the research design used student self-reports to assess the conditions of distance learning at home and used teacher self-reports to assess the conditions of distance teaching. It cannot be guaranteed that their ratings are influenced by memory biases. To ensure the validity of the information, the assessments were conducted immediately after the suspension of face-to-face teaching. In addition, teacher responses were compared to other evidence as to resources available at the school, in order to check whether their responses might be influenced by social desirability effects. Not all teachers responded similarly, suggesting that there were likely differences in how much they used personalized approaches. Fifth, the study was carried out in a single area of Germany, and it is possible that the findings might not be fully applicable to other places, especially internationally. Moreover, this study focused only on children at grade levels 3 to 4. Having a larger sample with children from younger and older age-groups would be important to better understand the connections in studying and learning mathematics under distance learning conditions.

The present study provides first empirical evidence on the relationship between distance learning conditions during the COVID-19 pandemic and basic number skills after the interruption of face-to-face teaching. By applying a performance test of basic numeracy skills, the study extends the previous descriptive research on the realization of distance teaching in Germany and provides risk factors of home-based learning. Based on the findings, concepts can be derived to ensure effective implementation of distance learning for future pandemics or emergencies causing suspension of face-to-face teaching. In view of the serious economic (Psacharopoulos et al., 2021), health (Ravens-Sieberer et al., 2022) and educational consequences (König and Frey, 2022) of the suspension of face-to-face teaching, every effort should be made in the future, even in exceptional circumstances, to provide all children with equal educational opportunities in terms of human rights (UN General Assembly, 1948). For this purpose, schools and educational ministries should provide a stable digital infrastructure and support families with fewer resources. A mere consideration of socioeconomic background does not seem entirely sufficient here, even though this index reveals many educational disadvantages. In the context of teacher education and in-service training, ICT, personalized teaching approaches and the exchange with the parental home should play a greater role to counteract the negative repercussions for children at-risk. Nevertheless, the question arises to what extent elementary schools in Germany have adequate staffing (Bieber et al., 2020) for an intensive and professional exchange with parents and children outside the classroom.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by Institutional Review Board of Instituto De Psicologia Da Universidade Federal Do Rio Grande Do Sul. Written informed consent to participate in this study was provided by the participants’ legal guardian/next of kin.

LO, AF, VH, AD, and PR conception and design of the study. LO performed the statistical analysis and wrote the first draft of the manuscript. All authors contributed to manuscript revision, read, and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.