SRL is considered as an underlying learning process that enhances students’ learning motivation and reflects on their learning process, thereby contributing to their learning (Michalsky and Schechter, 2013). Through SRL, students can develop a deep understanding of complex issues during the learning process (Labuhn et al., 2008; Panadero and Järvelä, 2015; Tian et al., 2018). Meanwhile, their behaviors and attitudes consistent with SRL also contribute to their self-confidence (Artino and Jones, 2012).

SRL specifically refers to the process whereby learners spontaneously and proactively set goals, employ various strategies, and monitor and evaluate their own behavior and learning outcomes to achieve their learning goals (Zimmerman, 2008). Based on empirical research and a social-cognitive framework, Zimmerman (2002) developed a cyclical framework of academic SRL that consists of various processes that learners purposely use to manage their behaviors, cognition, emotions, and environment to attain their personal goals (Figure 1). This framework revealed that SRL includes three stages: the forethought phase, the performance phase, and the self-reflection phase. In the forethought phase, students should analyze the learning tasks and set specific learning goals and strategies to achieve these goals. The performance phase refers to students learning based on learning strategies, and trying their best to achieve their learning goals (Zimmerman, 2002). During these processes, students could be aware of their performance with regard to certain learning goals, and need to monitor the appropriate learning strategies in order to achieve their goals. The self-reflection phase indicates how students evaluate the correlations between their learning results and learning strategies in order to determine the effectiveness of the learning strategies. This SRL model has been empirically researched and applied to the learning of various disciplines, such as mathematics (Chen and Zimmerman, 2007).

SRL has been a hot topic of research in the field of learning theory, and researchers have conducted a great deal of research on how to promote it. Regarding strategies to develop SRL competence, most of the existing research used motivational strategies (such as attribution training, behavioral control, etc.), metacognitive strategies (such as planning, monitoring, evaluation, etc.), and cognitive strategies (such as organizational information strategies), detailed strategies, and various problem-solving strategies to intervene in students’ SRL process. Depending on the respective underlying model of SRL, the interventions emphasize different aspects of the learning process (Dignath and Büttner, 2008). According to Timmons et al. (2016), early interventions to promote students’ SRL are delivered through cognitive-behavioral modification programs or direct instruction strategies. Innovations in later classroom intervention include changes to traditional classroom arrangements to build learners’ responsibility and independence. This is consistent with Bae and Kwon (2021), who found in recent years that metacognitive interventions have shifted from strategic training methods to creating social environments to support metacognition. Sufficient empirical studies have indicated that SRL can be significantly improved after intervention (Narciss et al., 2007; Chen and Chien-Yuan, 2019). Despite these studies, research in this field is still needed to clarify the effectiveness of various interventions (Schunk, 2005).

Mathematics problem solving refers to the use of mathematics concepts grasped by students to solve problems (Muis et al., 2016). It is considered to be the core of teaching and learning mathematics (Hasibuan et al., 2018) and helps students make associations between the mathematics concepts learned and real-world applications (Verschaffel et al., 2010). Researchers have conducted a number of empirical studies on the classification of math problem-solving difficulties (Mayfield and Chase, 2002), identifying factors that influence the problem-solving processes of elementary school students (Öztürk et al., 2020; Vondrová, 2022; Herbert and Williams, 2023), designing the problem-solving teaching process (Masingila et al., 2018; Copur-Gencturk and Doleck, 2021), and so on. In sum, the ultimate objective of the above studies was to develop mathematics problem-solving skills.

For elementary school students, mathematical problem solving often includes solutions and exercises of mathematical word problems, which require students to extract useful numerical information from descriptive text of the problem context and to perform arithmetic operations on it (Verschaffel et al., 2020). Several previous studies have shown that feedback-based teaching can help students improve their performance in mathematics word problems (Muis et al., 2016; Faber et al., 2017; Söderström, 2023). Researchers have carried out a large number of studies on the effectiveness of the personalized feedback-based approach on mathematics word problem-solving performance for elementary school students.

Orosco et al. (2013) designed a dynamic formative assessment strategy for mathematics in which teachers provided the feedback associated with students’ reading and language comprehension levels, and assessed its effectiveness on word problem solving for Latino English learners. Results showed that this feedback-based approach could significantly improve students’ mathematics word problem-solving performance. With the development of artificial intelligence technology, the subject of implementing feedback teaching has gradually changed from teachers to computers, and digital formative assessment tools have become the main implementation vehicles (Xu et al., 2021). Faber et al. (2017) designed a digital formative assessment tool that provides student feedback, teacher feedback, and personalized homework functions, and verified its effects on elementary school students’ mathematics word problem-solving performance and mathematics learning motivation. The results showed that the tool had a positive impact on students’ mathematics word problem-solving performance and learning motivation. To sum up, the current vehicles for personalized feedback-based approach are driven mainly by digital formative assessment tools, and the effectiveness of formative assessment tools largely depends on their feedback content. Thus, it is very important to design feedback tools to support the formative assessment process.

This study used the interactive e-book editing platform to implement a TLF approach. All teaching activities were implemented on the interactive e-book editing platform. Compared to the SRLF approach, the TLF approach provided feedback about the rate of correctness. The specific approach is shown in Figure 2.

First, the teacher introduced the teaching process before learning so that students could understand it. Second, students solved mathematical problems and submitted their answers via the interactive e-book editing platform. After that, the platform automatically corrected the answers and presented feedback on the correctness of their answers to the students. Finally, students self-reflected and corrected their responses based on the feedback results.

Similar to the TLF approach, this study also used an interactive e-book platform to implement a SRLF approach which provided specific guidance on the cause of the errors, so that students could reflect and correct the answers according to the feedback.

The teacher introduced the teaching process before learning so that students could understand the process. After that, students set learning goals and solved mathematical problems on the platform. The platform automatically diagnosed students’ performance and provided feedback for them to identify the causes of their errors. Students identified the causes of their errors based on the feedback from the interactive e-book editing platform. The platform provided different feedback based on the cause of the errors. Students self-reflected and corrected their answers based on the feedback results. The specific approach is shown in Figure 3.

Various feedback teaching tools have been widely used in teaching to support self-regulated learning (Sung et al., 2016). However, most researchers have focused on a single tool (Yang et al., 2018), while there has been a lack of attention to the impact of data-driven feedback-based teaching systems on SRL. Therefore, in order to validate the effectiveness of the personalized feedback-based approach, in this study we constructed a data-driven feedback-based teaching system (DDFTS) to support students’ SRL in the process of mathematics learning.

The design principle of the DDFTS system is based on the three-phase model of SRL (Zimmerman, 2002), in which learning consists of the forethought, performance, and self-reflection phases. The structure of this system is shown in Figure 4.

The student side consists of the input interface and the feedback interface. On the input interface, students can set learning goals, which is the forethought phase. The students’ editing page on the interactive e-book platform is shown in Supplementary Figure 1. The interface for setting learning goals is shown in Supplementary Figure 2. Students used this platform to flip pages, add sticky notes, set learning objectives based on options, and so on. After that, students tried to understand mathematical problems, chose the answer and submitted it, which was the performance phase. On the feedback interface, students could receive three different types of feedback: accuracy, cause and direction feedback. The interface for cause feedback is shown in Supplementary Figure 3. When the feedback was returned, students determined the cause of the error and reflected based on the feedback in order to better understand how to solve the mathematical problems, which was part of the self-reflection phase.

The server side consists of automatic correction and feedback processing. The teacher interface consists of a test module, an expert summary module, and a feedback module. In the test module, teachers can plan online learning activities, including setting learning goals, organizing the mathematical problem test and setting up the mathematical problem’s correct answer. In the expert summary module, teachers can summarize the cause of error for the mathematical problem test. In the feedback module, teachers can give specific guidance based on the cause of error. Then, teachers upload these course materials to the platform. The teacher’s edit interface is shown in Supplementary Figure 4. Teachers can preview the courseware, insert test modules and pictures, and so on.

In this study, the teacher introduced the teaching process before teaching, and two groups of students completed a pretest with mathematics word problems, and submitted their answers via the interactive e-book editing platform, which automatically corrected the test questions and gave feedback to the students, including on the accuracy of their responses. The feedback interface of automatic correction on the interactive e-book editing platform is shown in Supplementary Figure 5. This interface shows the automatic correction feedback. Supplementary Figure 6 shows the direction of the feedback interface on the interactive e-book editing platform, giving an example of a mathematics question. Finally, students reflected and corrected their answers according to the feedback.

In the formal teaching stage, the control group continued to use the TLF approach. The students in the experimental group used the SRLF. According to the results of the pretest and the interviews with the students, this study attributed the reasons for students’ errors in solving mathematics word problems to “failure to understand the meaning of the problem,” “unclear known data and problem,” and “wrong calculation.” The above reasons were presented as options on the interactive e-book platform, and students could choose multiple items according to their situation and click on them to jump to the corresponding feedback scaffolding for self-reflection and correction. The self-reflection activities-based feedback on the interactive e-book platform is shown in Supplementary Figure 7. On this interface, students could self-reflect and correct their answers on sticky notes based on the feedback they received.

The 69 participants (32 female and 37 male students) were from two fifth-grade classes of a public elementary school (the best primary school in W city), with ages ranging from 11 to 13 years old. Their parents’ social status was at an upper-middle level. The average age of the participants was 11.73 years (min: 11, max: 13). They participated in a 4-week mathematics course that focused on mathematical problem solving.

The experimental group, including 35 students, learned using the SRLF approach. On the other hand, the control group with 34 students learned with the TLF approach. Before teaching, they were informed of the learning instructions and test, and signed a consent form to participate in a series of teaching activities along with their parents’ approval. After comparing the means of the two groups, we found that there was no significant difference. Therefore, one of the classes was designated as the experimental group and the other students were assigned to be the control group.

This research was reviewed and approved by the Institution Review Board of the affiliated institution (Code number: WZU-2023-099). The experiment was conducted in this study to investigate the effects of the personalized feedback approach on students’ mathematics word problem-solving performance and SRL. Both classes of students took the course guided by the same teacher. The entire experimental process followed a double-blind rule, whereby neither teachers nor participants were informed of the purpose of the experiment in advance. All students had previously completed the information technology courses and had mastered basic software and hardware knowledge. In other words, all the students had similar information technology backgrounds and experience.

Figure 5 shows the experimental procedure. The whole experiment lasted for 4 weeks with one 35-min lesson per week. In the first week, the students from both groups took the pretest of mathematics word problem solving and the SRL survey. Following that, the teacher introduced the teaching process to the students in both groups. From the second to fourth week, students in the control group learned to solve mathematical word problems with the TLF teaching model, while students in the experimental group learned with the SRLF teaching model to support their mathematics word problem solving. In the fourth week, all of the students took the posttest of mathematics word problem solving and completed the self-report of self-regulated learning.

The instruments used in this study involved the pretest and posttest of mathematics word problems, as introduced in 4.3.1, the self-reported SRL questionnaire, as introduced in 4.3.2, and the interactive e-book software, as introduced in 4.3.3.

This study used the students’ pretest scores of mathematics word problem solving and self-regulated learning, respectively, as covariates. Before ANCOVA, the homogeneity of covariate regression coefficients was examined to justify the assumption of regression homogeneity for ANCOVA. If satisfied, ANCOVA was conducted to analyze the differences between the experimental group and the control group in mathematics word problem solving and SRL (Supplementary Figure 11).

ANCOVA was conducted where students’ pretest scores were treated as a covariate. First, the assumption of homogeneity of regression was accepted (F = 2.711, p = 0.104 > 0.005), which indicated that ANCOVA could be used to interpret the effect of the personalized feedback approach on their mathematics word problem-solving performance under the control of the pretest.

In addition, according to the Shapiro–Wilk data normal distribution test, the p-values of the pretest of SRL and the five dimensions were 0.120, 0.071, 0.069, 0.134, 0.176, and 0.095, respectively, which satisfy normal distribution. Therefore, in this study, the independent samples t test was conducted to analyze the pretests of SRL competence and the five dimensions, with SRL competence and the pretest score of each dimension as the dependent variable and the feedback approach as the grouping variable. The ANCOVA and one-way repeated ANOVA were conducted to analyze the posttest of SRL and the five dimensions.

ANCOVA results of mathematics word problem-solving performance are shown in Table 2. As for their mathematics word problem-solving performance, the adjusted mean score of the experimental group (42.73) was much higher than that of the control group (37.66), and a statistically significant difference was observed (F = 7.91, p = 0.006 < 0.005, η² = 0.107).

Based on the ANCOVA results, the personalized feedback approach promoted the students’ mathematics word problem-solving performance. In particular, the SRLF approach significantly improved students’ mathematics word problem-solving performance, since it scaffolded students’ SRL, helping them identify difficulties in problem solving, and providing appropriate personalized feedback to improve their mathematics word problem-solving performance.

The independent samples t test results of the analysis are shown in Supplementary Table 2. No significant difference was found between the two groups on the SRL pretest. In order to measure the differences between the experimental group and the control group on SRL and the five dimensions, we analyzed the pretest and posttest of SRL and the five dimensions of the two groups by using one-way repeated measures variance analysis. The results of the analysis are shown in Supplementary Table 3. With regard to SRL, a statistically significant difference was observed in the time variable. However, there was no significant difference in the time variable for other dimensions. Meanwhile, there was no significant difference in the SRL of the two groups. In other words, both personalized feedback approaches promoted the students’ SRL. Therefore, we analyzed the pretest and posttest changes of the two groups separately using paired-samples t tests. The results of the analysis are shown in Supplementary Table 4. According to Supplementary Table 4, there was no significant difference in SRL or in other dimensions for the experimental group. However, for the control group, SRL, cognitive strategies, and metacognitive strategies all significantly improved.

In addition, according to Supplementary Table 3, we found that the interaction between the time and group was more significant for cognitive strategies and SRL. Figure 5 shows the interaction effect between time and group on SRL, and found that there was a significant change in the SRL of the control group compared to the experimental group. Supplementary Figure 8 shows the interaction effect between time and group on cognitive strategies, and found that there was a significant change in the cognitive strategies of the control group compared to the experimental group. In other words, the TLF approach had a greater impact on cognitive strategies and SRL.

In order to further explore the differences between the two feedback approaches in terms of SRL, an analysis of covariance (ANCOVA) was employed using the students’ self-regulated learning pretest scores as a covariate. The assumption of homogeneity of regression was satisfied for ANCOVA (F = 1.505, p = 0.224 > 0.005). Hence, ANCOVA was used to verify the effect of the personalized feedback approach on students’ SRL under the control of the pretest.

As illustrated in Table 3, there was no statistically significant difference between the two groups (F = 2.36, p = 0.129 > 0.005), while the adjusted mean score of the experimental group (99.88) was slightly higher than that of the control group (95.31). Meanwhile, from Table 3, there were no significant differences in academic goal setting (F = 1.33, p = 0.253 > 0.005), cognitive strategies (F = 1.35, p = 0.250 > 0.005), metacognitive strategies (F = 0.93, p = 0.337 > 0.005), intrinsic motivation (F = 0.63, p = 0.430 > 0.005) or self-efficacy (F = 1.29, p = 0.260 > 0.005). However, the experimental group, respectively, showed slightly higher adjusted mean scores in these five aspects than the control group. Combining the pretest and paired-sample t-test analysis results of SRL, the TLF approach was slightly superior to the SRLF approach during the short-term experimentation.

The experimental results showed that both feedback approaches promoted students’ math problem-solving scores. This finding is consistent with previous studies which argued that data-driven feedback teaching tools positively affect students’ mathematics performance (Koedinger et al., 2010; Bokhove and Drijvers, 2012; Bulunuz et al., 2014; De Witte et al., 2015). Meanwhile, this result also validated the point of Greene et al. (2018) who conducted a stratified randomized controlled trial to evaluate mathematics addition and subtraction fluency instruction embedded within a feedback teaching framework. Students in the experimental group received multiple interventions, including validating and corrective feedback. The results showed that the experimental group’s academic performance in mathematics significantly improved.

Moreover, the SRLF approach can more significantly stimulate students’ mathematics word problem-solving scores than the TLF approach. Hattie and Timperley (2007) argued that TLF allows learners to focus on the task, such as providing information about the correct answer (e.g., “You explained the limitations, but you could also explain why they are unreliable”). In this case, feedback is powerful if it is more information-focused (e.g., correct or incorrect), leads people to obtain more information or different information, and builds more surface knowledge. It also appears to be more effective when the learner is a novice. The SRLF approach involves the ability to self-evaluate, increase task effort, or seek further feedback (e.g., “What will happen if you increase the temperature in your study?”). At this level of feedback, there will be more information directed at the learner’s self, and more information to guide the learner when and where to use both process-level strategies. In general, it is not that more specific feedback information is more conducive to students’ higher academic performance and SRL ability. In fact, simple feedback may be more effective for novices. The results of this study illustrate exactly this point.

In general, TLF is the basis of SRLF (Hattie and Timperley, 2007). In this study, the experimental group adopted a SRLF approach, which included reflection on the causes of errors and learning scaffolding for the particular erroneous cause. In contrast, the control group adopted a TLF approach, which only involved the accuracy of their answers. Therefore, the experimental group used a feedback instrument that was much more detailed than that used by the control group. There was a significant positive correlation between the frequency of students’ tool use and their learning effectiveness (Faber et al., 2017). In addition, it has been proven that “knowledge of results” feedback (i.e., feedback that provides correct answers) has a less positive effect, whereas detailed feedback has a more positive effect on learning effectiveness (Lipnevich and Smith, 2009; Candel et al., 2021). Specific feedback informs students of which mistakes they made, as well as providing an explanation of the correct answer. Specific feedback can be more effective than simple feedback (knowledge of the results) when students solve complex problems (Candel et al., 2021). Studies on the effectiveness of digital formative assessment algorithms and mathematics tools also verified this opinion (Bokhove and Drijvers, 2012).

The experimental results indicated that both feedback approaches significantly improved students’ SRL. At different levels, the effects of feedback are different. However, the two types of feedback, task-level and self-regulation-level, often give students the most appropriate suggestions for choosing the next step, fostering more self-regulation of the learning process, deepening their own understanding, and obtaining more information (Hattie and Timperley, 2007). This is consistent with Afzaal et al.’s finding that providing intelligent feedback and suggestions in a data-driven manner can improve students’ SRL (Afzaal et al., 2023). It is also consistent with Kim and Hannafi’s finding that feedback teaching strategies in a computer environment are an important method to promote students’ SRL (Kim and Hannafin, 2011).

In addition, this study also found that there was no significant difference between the effects of the two feedback approaches on SRL, but the control group slightly outperformed the experimental group. In other words, the TLF approach had a greater impact on SRL, particularly in terms of SRL and cognitive strategies. Moreover, the feedback type and learning time had significant interaction effects on total scores of SRL and cognitive strategies. This means that in terms of SRL and cognitive strategies, changes throughout the experiment were more significant for the control group, but for the experimental group, the change was unremarkable. The results of this experiment exactly verify Heidi and Timperley’s view, namely that simple feedback may be more effective than complex feedback, especially in terms of SRL ability. Meanwhile, this result is consistent with the studies of Boesen et al. (2014) and Candel et al. (2021). Boesen et al. (2014) pointed out that if problem solving is facilitated by providing TLF, that is, not providing feedback on how to solve the task or the steps, students will be able to think harder and more positively about solutions to mathematics problems when faced with learning tasks, boosting their regulated learning ability. Furthermore, Candel et al. (2021) concluded that digital learning environments may become more effective if the feedback includes a personal diagnostic element, that is, the capacity to provide feedback on whether it is correct or not. In this study, the TLF approach provided feedback on the correctness of mathematical word problem solving, while the SRLF approach provided appropriate personalized feedback based on the students’ causes of error. Students who learned with the TLF were able to think more positively about how to solve the mathematical word problems, which stimulated their SRL competence. Therefore, it explains the larger effect on SRL in the control group that learned with the TLF approach than in the experimental group that learned with the SRLF approach.