The flipped classroom (FC; synonyms: inverted classroom, flipped learning, inverted learning) is a teaching method that has become increasingly popular in recent years with a growing focus on research that has all been conducted within the last 15 years (Cevikbas and Kaiser, 2020; Hwang et al., 2019; Kapur et al., 2022). Zhang et al. (2024) for example provide an overview of current research trends on FC across all age groups and professions. Although there is no single definition of FC, almost all characterizations include the reversed order of traditional teaching as a “minimum requirement.” In contrast to traditional teaching—i.e., the knowledge acquisition happens in school and most of the practice has to be done as homework—the concept of FC means that new knowledge is acquired independently by students before the actual lesson to allow more time for reflection, elaboration, and practice in class (Bishop and Verleger, 2013; Lage et al., 2000). In terms of acquiring knowledge at home, students are often required to watch instructional videos and are sometimes given short additional quizzes to test their understanding of the content (e.g., Hew et al., 2021; Wagner et al., 2020). Some authors specify options for the subsequent plenary phase, for example group work, class surveys, cooperative learning, and student presentations or discussions (Bergmann and Sams, 2012; Bishop and Verleger, 2013; Lo et al., 2017). Meanwhile, there are a lot of individual studies investigating the effect of FC in K-12 teaching (see Supplementary Table 1). Taken together, these studies provide important insights into ideas, conditions, and consequences on teaching with the FC method.

Like any method, FC has potential opportunities as well as potential pitfalls (Cevikbas and Kaiser, 2023). We summarize seven meta-analyses investigating the effect of FC regarding K-12 teaching that all were conducted within the last 7 years (in Table 1). We selected analyses that examined the effects in the K-12 sector separately and explicitly listed the included studies. All seven meta-analyses generally conclude that FC is more effective than traditional teaching in K-12 with effect sizes ranging from g = 0.21 to d = 1.89. The effect of these meta-analyses is in line with a recent review of meta-analyses from Li et al. (2024) with an overall positive effect of g = 0.53 in favor of FC in K-12 teaching. There are even two more reviews on meta-analyses (Hew et al., 2021; Kapur et al., 2022), yet, they deal predominantly with the tertiary level (for the restriction to K-12 teaching in the present article see 1.3).

A common finding of the meta-analyses is that most of the included studies compare FC based on instructional videos that have to be watched at home by students with traditional teaching without videos (e.g., see Zhu, 2021). Furthermore, the positive effects of FC are often attributed to short quizzes (e.g., see van Alten et al., 2019), at least when students receive feedback (Wagner et al., 2020).

However, the evidence is mixed in terms of the subjects considered. While Wagner et al. (2020) reported a larger effect in STEM subjects than in the humanities, Strelan et al. (2020) found the opposite.

In Supplementary Table 1, we provide an extensive overview of the about 50 individual studies comparing learning gains from FC to traditional teaching that were included in at least one of the seven meta-analyses in Table 1. The first letters of the names (bold) in Table 1 are used in the left column in Supplementary Table 1 to indicate which study was included in which meta-analysis. Since most meta-analyses critically remark the generally small sizes of the FC studies conducted so far (e.g., Cheng et al., 2019; Wagner et al., 2020), we sorted the studies in Supplementary Table 1, first, according to the average number of classes per experimental condition and, second, by the total number of participating students. As statistical multilevel modeling, which diminishes potential class effects, is only possible if more classes per condition are implemented, we chose the number of classes per condition as the core principle to judge the “largeness” of an FC study. Notably, in Supplementary Table 1 the bivariate Pearson correlation coefficient between the number of classes per condition and the effect sizes reported in Supplementary Table 1 yields r = − 0.3 i.e. the larger a study, the smaller the observed effect in favor of FC.

More specifically, from Supplementary Table 1, which contains 51 individual FC studies, it becomes clear that 40 studies implemented only one class per experimental condition. So far, there seems to be only one ‘large’ FC study concerning K-12 teaching (Wagner and Urhahne, 2021) with an average of 10 classes per condition, which was too new to be included in the meta-analyses of Table 1. In this study, however, the most effective method was not FC, but watching the instructional video in class followed by student-centered instruction. Since the learning materials were basically identical in all conditions, the study by Wagner and Urhahne (2021) has a high internal validity, but at the same time, there is a trade-off regarding external validity because instructional videos are typically not shown in class. Thus, there currently seems to be a major contradiction between the results of seven meta-analyses and an actual, large and internally valid FC study.

In experimental psychology, it is not uncommon for effects found in small studies to fail to be replicated in large and controlled experiments. Beyond the well-known problems demonstrated in the replication crisis (e.g., Maxwell et al., 2015; Shrout and Rodgers, 2018), Bartoš et al. (2023), Kvarven et al. (2020), and Sotola (2022) examined meta-analyses in particular. The latter one investigated meta-analyses that were published in Psychology Bulletin and demonstrated that the risk of a meta-analysis confirming a positive effect when, in fact, there is a null effect is particularly high when the number of participants in the included studies is very small. He claimed in such cases that for every included study, there must be another study that was not published, meaning that these estimated unpublished 50 percent of all conducted studies might show no or a negative effect. While Kvarven et al. (2020) assume that effect sizes in meta-analyses are overestimated almost by a factor of three, Bartoš et al. (2023) stress that such effect sizes might be overestimated even more. The general conclusion of all three reviews is that meta-analyses, of course, are not unreliable per se, but should probably be interpreted with caution, and all agree that the reported effect sizes might be overestimated.

In the absence of contrary arguments or specialties that discriminate the meta-analyses of Table 1 from those reviewed by Bartoš et al. (2023), Kvarven et al. (2020) and Sotola (2022), one might speculate that the theoretical analyses of the three papers may also—at least partly—underlie the seemingly overwhelming evidence in favor of FC instruction. This hypothesis is consistent with Kapur et al.’s (2022) review of meta-analyses exclusively on FC, which also suggests that effect sizes might be overestimated due to small sample sizes of the included studies and publication bias (see also Hew et al., 2021). Yet, neither Kapur et al. (2022) nor Hew et al. (2021) focus on K-12 students (instead 90% of the studies considered by Kapur et al. were from the tertiary level). Of course, all authors of the meta-analyses in Table 1 are aware that their analyses depend on the individual studies included (e.g., Strelan et al., 2020; Låg and Sæle, 2019), and discuss a possible publication bias (Zhu, 2021), small study bias (Doğan et al., 2021), or the novelty effect, meaning that there is an initial boost in performance or enthusiasm that occurs when a new tool or method is introduced (Wagner et al., 2020).

To provide the desired benefit of extended learning time for FC, students must prepare effectively for the lesson at home, since, otherwise, the success of the FC method is threatened (Cheng et al., 2019; Gillette et al., 2018; van Alten et al., 2019). The issue of self-regulated learning (“SRL”) and the need to support self-regulation, especially for young students, is the reason why we focus on K-12 teaching in this paper. While studying at university requires strong self-regulation skills, students at school usually receive more help and explicit support (Vosniadou, 2020). In the K-12 classroom, teachers implementing the FC method cannot automatically assume that learning at home, especially for very young students, will be competent and successful (or be done at all). Indeed, the review of meta-analyses by Kapur et al. (2022) indirectly supports the claim that the relevance of SRL support decreases as students get older: At the tertiary level, the average effect size for FC (without specific SRL support and compared to traditional teaching) is the highest (g = 0.93), while the younger the students, the lower the effect size (high schools: g = 0.63, elementary schools: g = 0.40).

However, in experimental FC studies, elaborated support regarding the appropriate use of instructional videos is found only rarely. Table 2 summarizes three studies that focus specifically on SRL in K-12 teaching by experimentally comparing two FC conditions with and without explicit SRL support (all three without implementing an additional control group regarding traditional teaching).

The SRL support in the studies in Table 2 consists, for example, of short prompts that are implemented in the videos. However, general research on SRL over the last few decades has shown that it is not easy to guide students to actually use SRL strategies by simply transferring knowledge, but rather practical exercises are needed in addition (Dignath and Büttner, 2008; Zeidner and Stoeger, 2019). In principle, it would be possible to address SRL even more dedicatedly—based on general research on SRL (e.g., see Pintrich, 1999)—and to develop strategies explicitly designed for watching instructional videos, for instance, by following the ICAP framework (Chi and Wylie, 2014), which especially deals with digital media.

In sum, despite many existing studies on the FC method in K-12 (Supplementary Table 1), it is still not certain whether this method is generally more effective than traditional teaching. Wagner et al. (2020, p. 14) state that “in particular, more randomized controlled trials with larger sample sizes and objective quantitative measures are needed.” With respect to experimental control, for instance, Låg and Sæle (2019) and Cheng et al. (2019) mention that most of the existing FC studies do not apply precise outcome measures and are therefore “noisy” (Strelan et al., 2020). For example, often researchers themselves were the teachers in the studies, which violates the double-blind principle (Låg and Sæle, 2019), or there was no pretest to control for differences (Cheng et al., 2019).

In the present paper, we report a controlled FC study regarding mathematics teaching in grades 6 and 7. With the implementation of n = 12 classes per condition (a total of N = 950 students were examined), this is the largest study in this area so far. Specifically, (a) a control group of “traditional teaching” was investigated and, therefore, we contribute to Supplementary Table 1. In addition, we (b) implemented two FC-conditions, one with and one without explicit SRL-support for watching the instructional videos at home. In doing so, we contribute to Table 2. Furthermore, we tried to manage all the requirements mentioned in Låg and Sæle (2019) such as clearly reporting the study design with a detailed description of the intervention, double-blind assessments, and psychometrically sound outcome measures.

The intervention study with a pre‒post design was conducted in 6th and 7th grade mathematics classes in Bavarian schools (Figure 1). The participating classes were randomly distributed into three groups. The students were taught by their respective math teachers who received standardized training and materials prior to the intervention (see 3.3.4). Within each group, the teachers were following the identical manual (see 3.2). This uniform design of the lessons is intended to eliminate differences due to varying materials and to create comparability within, but also between experimental conditions. Basically, only the order of the used materials changed between the groups; therefore, all students received the same tasks and explanations except for the instructional videos (see 3.3.1) that were only obligatory in the FC conditions (Figure 1). Students’ performance was measured before and after the intervention using a pretest and a posttest (see 3.3.5). The lessons are described in more detail in 3.2.

To answer RQ1, we compare classes in the traditional teaching (TT) condition with classes in the (typical) FC setting, in which students are provided with instructional videos but receive no explicit SRL support for watching them at home (FCn). A second FC condition (FCS) was implemented to answer RQ2: this group received an additional lesson on strategies (not mathematics-specific) about how to use instructional videos (see column “SRL” in Figure 1). It is important to note that no mathematical content was conveyed during this lesson to guarantee that no group had an advantage in this regard (3.2.2).

All teachers received a standardized teacher training in which the content and the standardized implementation of the lessons were explained by the test administrator (the first author). They received background information on the administration of the study and teaching material (e.g., manuals for each lesson, worksheets, quizzes, solutions, etc.). The instructional videos and the quizzes were provided online.

Data were gathered from N = 950 students of grade 6 and 7 of all school types across various locations in the state of Bavaria (Germany) in the school year 2022/23. In Germany basically there are an academic track (“Gymnasium”), a medium track (“Realschule”) and a vocational track (“Mittelschule”). The classes were chosen so that all students had the same prior knowledge: All classes knew fractions (common and decimal) and percentages, but none of them had explicit experience with the other three formats before. The students were taught in n = 37 classes; these classes were distributed among n = 20 schools. Three teachers taught two different classes (two of the TT group and one of the FCn group); thus the students were taught by n = 34 teachers. Table 5 shows the distribution of students, classes, and teachers separated by condition. An overview of class size and gender distribution is provided in Supplementary Table 2, Table B.4.

Of all teachers who volunteered to participate in the study, 16 were female and 18 were male, with an average work experience of 14.2 years. In all three groups, the average work experience, gender distribution of teachers and school type were comparable. Prior to data collection, the Bavarian Ministry of Education, school principals, teachers, parents, and the students themselves consented to the committed participation in the study.

Table 7 provides an overview of the descriptive results from the pre- and posttest. Both scales yielded satisfactory internal consistency aggregated across all groups as indicated by Cronbach’s α (α_pretest = 0.79; α_posttest = 0.84). Across all three groups the average score in the pretest was 8.51 (SD = 2.96) and in the posttest 11.38 (SD = 3.30) with a Cohen’s d of 0.95 (The male participants achieved an average score of 8.67 (SD = 3.06) in the pretest and 11.75 (SD = 3.25) in the posttest, corresponding to a Cohen’s d of 0.98. For the female participants, the score was 8.34 (SD = 2.83) in the pretest and 10.94 (SD = 3.22) in the posttest, with a Cohen’s d of 0.86.).

Figure 3 displays the resulting line diagram regarding students’ pre- and post-performances separated by the three experimental conditions.

According to the research questions, in the LMM, the FCn condition was chosen as reference group (Table 8). There was no significant difference in the pretest scores between the TT group and the reference group FCn ( β TT = − 1.61 , p = 0.10). Similarly, the pretest scores of the FCS group did not significantly differ from those of FCn group ( β S = − 1.39 , p = 0.07). Consequently, the remaining difference cannot be significant (obviously, the pretest scores of TT and FCS are closest to each other, Figure 3). The general comparability of the three groups with respect to the pretest contributes to the internal validity of conclusions from the model, since possible interaction effects are less likely biased by varying a priori competencies of the students.

Note that the intercept of 9.33 (i.e., the pretest score of the reference group FCn) in Table 8 slightly varies from Figure 3 (9.12), which indicates the correction due to the implemented multi-level modeling. The significance only indicates its difference from 0. Moving on to the posttest results, there was a significant improvement of the reference group (FCn) due to the teaching sequence ( β time = 2.48 , p < 0.001). In terms of inferential statistics, RQ1 and RQ2 can be answered by comparing the slopes in Figure 3. The difference in the slopes is analyzed by the interactions. Regarding RQ1, the interaction effect between time and TT did not yield significant differences in the improvement ( β TT × time = 0.45, p = 0.07). Regarding RQ2, the interaction effect between time and FCS was significant ( β FCS × time = 0.76 , p = 0.003), indicating different learning gains between the participants of the FCn condition and the FCS condition. Therefore, supporting students by explicitly providing them with strategies for watching instructional videos indeed seems to have a crucial effect. Since the model displayed in Table 8 uses FCn as reference group, it allows no inferential statement on the difference between TT and FCS. However, when, e.g., alternatively selecting TT as the reference group, no significant difference between the TT and the FCS condition occurs ( β FCS × time = 0.30, p = 0.22).

The Intraclass Correlation Coefficient (69%) was computed to assess the reliability of the model and the proportion of variance explained by the random effects. Furthermore, the marginal R² indicated that the fixed factors accounted for approximately 19% of the variance, while the conditional R² suggested that fixed and random factors together explained approximately 64% variance.

Including all control variables (see 3.3.6 and Supplementary Table 2, respectively) individually as possible predictors in the LMM, only the interaction of time with the student scale strategies for using instructional videos (after intervention) was significant (aggregated across all groups), providing further evidence from another (self-reported) perspective for the importance of teaching such strategies.

Regarding RQ1, the learning gains between FCn and TT did not differ significantly (without implementation of control variables), yet with a p-value close to significance (p = 0.07). Here, six student variables turned this interaction into being significant when individually implemented in the LMM (but no teacher variable). However, one must note that the p-value varied only moderately even in these cases, meaning that individually implementing student variables leads to corresponding p-values ranging from 0.02 to 0.13. Thus, the (nearly or indeed) significant difference between both groups was also relatively stable with respect to the control variables implemented (see Supplementary Table 2).

Concerning RQ2, only one of the teacher variables, namely the teachers’ self-perceived instructional quality during the intervention, changes the significance of the differential improvements between FCS and FCn into non-significance (RQ2). Furthermore, none of these variables affected the non-significance of the differential improvements of the TT and the FCS group in the alternative model (see above). Taken together, this indicates a robust difference between the two FC conditions, on the one hand, and, on the other hand, a stable comparability between a professionally prepared TT and an FC teaching in which students are not left alone with instructional videos. Note that the superiority of FCS (significant with respect to FCn and only at a descriptive level compared to TT) is remarkable especially, when considering group differences in the control variables. Concerning the four variables in which an ANOVA revealed a significant difference (2 x instructional quality, previous use of digital media/videos; see Supplementary Table 2), the prerequisites in the FCS conditions were even worse.

Figure 4 provides a comprehensive visual summary of class-level interactions, illustrating the overall diversity observed in the study by highlighting the substantial variations between classes.

Note that a large range of both pretest and posttest scores was observed across the sample in general but also within each group (Figure 4). One intriguing class-related result is, for example, that class no. 36 in the FS n group that achieved the highest posttest score of 14.9 also reached the second highest pretest score of 10.6. Interestingly, this class also exhibited the second-largest improvement. Class no. 7, which was part of the FCS condition, had an average pretest score of 4.5 and demonstrated the greatest improvement with a gain of 4.8 points. Notably, in all conditions, there were single classes with small and with large improvements. In sum, Figure 4 illustrates that a) neither floor nor ceiling effects were present in the study, and b) no single class reduced their competence level, which indicates the effectiveness of the sequence in general. However, it also becomes clear that c) when randomly choosing just one or two classes per condition, based on our data, almost any interaction effect had been possible.