1 Introduction and justification

Recent advancements in technology have significantly transformed education, positioning personalized learning as a crucial methodology for enhancing academic outcomes and students’ perceptions of learning (Shemshack et al., 2021). This approach tailors educational experiences to individual competencies and aspirations, optimizing the learning process during critical phases of cognitive development (Kallio & Halverson, 2020).

Integral to this transformation is the integration of Information and Communication Technologies (ICT). ICT has facilitated the development of innovative pedagogical methods that enhance learning outcomes and boost student motivation and engagement (Alamri et al., 2020), as well as knowledge retention and self-efficacy in primary education (Henderson, 2020). Among these technological advancements, Learning Management Systems (LMS) such as Moodle stand out for their ability to enrich the learning process, particularly in mathematics, by providing structured, continuous support (Mínguez‐Pardo et al., 2024).

The teaching of fractions and decimal numbers remains a significant challenge within primary education (Rojo et al., 2023). Early comprehension of these concepts is crucial, as it predicts future academic success in mathematics and beyond (Braithwaite et al., 2022). Personalized methods, enhanced by technology and adaptive learning models, are instrumental in addressing these challenges, thereby solidifying students’ mathematical foundations and positively impacting their academic performance, motivation, and attitudes towards the subject (Higgins et al., 2019).

The implementation of these strategies is essential for addressing diverse educational needs and ensuring effective, meaningful learning experiences. In the context of primary education, this is particularly important as it supports cognitive development and prepares students for future academic challenges. By focusing on the personalized learning of rational numbers in 5th-grade primary education, this research aims to fill a critical gap in existing studies by leveraging digital platforms to evaluate the potential benefits of personalized instruction. Ultimately, this approach, in line with Real Decreto 157/2022 (2022), promotes the use of technology and innovative instructional models that adapt to the needs of students. Furthermore, it considers the stage at which the teaching of fractions and decimals begins, thus fostering a holistic development of mathematical skills, technological proficiency, individual work habits, and self-learning capabilities in 5th-grade students to open a positive prognosis for their development of mathematical competence.

The remainder of this paper is organized as follows. In Sect. 2, we delve into the existing literature, exploring the foundations of personalized learning, the intersection of pedagogy and technology-driven personalization, and the role of LMSs such as Moodle. We also examine the specific challenges students face when learning fractions and decimal numbers and discuss how proficiency in these areas serves as a predictor of overall mathematical success. Section 3 outlines the objectives guiding this study. Section 4 details the methodological approach, including the experimental design, sample characteristics, instruments employed, and sequence of instructional sessions. The results are presented in Sect. 5, followed by a discussion of the conclusions and limitations of the study in Sect. 6.

2 State of the art

2.1 Personalized learning

In recent times, there has been a noticeable surge in the adoption and integration of personalized learning methodologies, propelled by significant advancements in educational technologies (Nandigam et al., 2014). According to Walkington and Bernacki (2020), personalized learning transcends a mere instructional strategy; it embodies a holistic approach aimed at tailoring the entire learning ecosystem to meet the distinct needs of students, drawing upon established learning theories (i.e., behaviourist, cognitivist, or constructivist perspectives) and the collective wisdom of educators and learners.

The concept of personalized learning fundamentally seeks to provide bespoke learning experiences tailored to the unique needs, aspirations, and competencies of each learner, leveraging the transformative power of cutting-edge instructional technology (Shemshack et al., 2021). Despite concerted efforts by scholars and practitioners to elucidate and delineate personalized learning, its precise definition remains somewhat elusive, with various implementation models (Simpson, 2020). This flexibility poses a challenge for researchers attempting to assess its benefits, as the diverse definitions and applications of personalization complicate the evaluation of its effects on learners’ educational experiences and academic outcomes (Walkington & Bernacki, 2020; Halverson, 2019).

Common features of personalized learning environments include the empowerment of learner voice and choice, the adoption of diverse instructional modalities, the strategic use of technology for personalization, competency-based pedagogies, and the flexible allocation of temporal and physical resources (Simpson, 2020; Groff, 2017). Personalized learning is not a new revelation; it is deeply ingrained in educational practice worldwide. Educators routinely customize their pedagogical approaches within traditional classrooms, offering targeted support to struggling learners while challenging high achievers (Holmes et al., 2018).

The extant literature abounds with testimonies attesting to the efficacy of personalized learning interventions. Rigorous empirical investigations by Chien et al. (2016) and Hunsu et al. (2016) have documented the transformative impact of pedagogical strategies tailored to individual learners’ needs. In economically disadvantaged contexts, technology-enabled personalized learning initiatives have yielded statistically significant, moderately positive effects on learning outcomes (Major et al., 2021). These interventions have demonstrated commendable efficacy in both mathematical and literacy domains, irrespective of the degree of teacher involvement in the personalization process.

Furthermore, personalized learning has emerged as a potent tool for enhancing learner motivation, engendering heightened levels of engagement, and fostering deeper comprehension (Falcão et al., 2018). It has the potential to optimize learner satisfaction, learning efficiency, and overall effectiveness (Fabregat Gesa et al., 2014).

2.2 Pedagogy and technology-facilitated personalization

The extensive integration of ICT, particularly the Internet, has precipitated a profound digital transformation. This shift has significantly altered mechanisms of interpersonal interaction, leading to substantial changes across various facets of human existence, notably within the educational sector (Saif et al., 2022). Scholars such as Bruce and Levin (2003) recognized its latent potential as a cognitive scaffold for facilitating effective instruction and collaborative learning within the classroom. Consequently, one of the greatest promises of the technological boom in the field of teaching and learning is the promotion of new perspectives on personalized learning (Yi et al., 2017). The rapid advancement of ICT has enabled the personalization of learning through various methods (Dawson et al., 2010).

Within the educational landscape, technology-facilitated personalized learning has emerged as a veritable pedagogical paradigm (Shemshack et al., 2021). It is against this backdrop that the concept of technology-facilitated personalized learning began to take root, referring to the strategic harnessing of technological tools to support and tailor learning experiences in alignment with the unique attributes and needs of individual learners, as delineated by Major et al. (2021). A robust body of research attests to the manifold benefits of implementing technology-facilitated personalized learning initiatives, ranging from enhanced learning outcomes (Zheng et al., 2022; Simanullang and Rajagukguk, 2020) to heightened levels of learner motivation and engagement (Alamri et al., 2020).

Ito et al. (2019) investigated the impact of an adaptive learning app on both cognitive and non-cognitive skills among Cambodian elementary students. Their findings indicated positive effects on learning productivity and enhanced students’ adherence to education. Similarly, Escueta et al. (2017) conducted a synthesis of experimental evidence, indicating that personalized computer-assisted learning might be particularly effective in low- and middle-income countries due to significant capacity constraints. They highlighted that its adaptability to learner needs could be crucial in addressing the diverse skill levels that many schools struggle with. However, they also acknowledged the limitations in resources and implementation challenges that may hinder its effectiveness.

Despite its palpable promise and potential, there remains a paucity of comprehensive research interrogating its holistic impact on both learning outcomes and learner perceptions (Zheng et al., 2022). While it is often asserted that technology facilitates personalized learning, a thorough enumeration of the methods by which technology can support individualized student approaches remains uncompiled (Grant & Basye, 2014). Alamri et al. (2020) underscore the imperative of independent empirical investigations aimed at elucidating the effectiveness and repercussions of personalized learning. In line with this, Li and Wong (2020) emphasized the predominance of research in higher education levels regarding technology-facilitated learning, highlighting the need for more studies at the elementary level, as revealed by Kocak (2022). Similarly, Knobbout and Van Der Stappen (2020) state the existence of a conspicuous asymmetry in the adoption and implementation of personalized learning approaches, with its prevalence notably lower in elementary education compared to higher educational tiers.

2.3 Learning management systems (LMS) and Moodle

According to Bradley (2021), LMS provide an invaluable online platform where teachers and students can seamlessly engage in a collaborative and enriched learning journey. Particularly within the context of online classrooms, LMS serve as remarkable enablers, offering scaffolding and support to both educators and learners throughout the learning continuum. Among these platforms, Moodle stands out as the most widely used open-source LMS, known for its flexibility and compatibility with personalized learning systems (Chang et al., 2022). Empirical findings by Simanullang and Rajagukguk (2020) underscore the potential of Moodle-based LMS in bolstering learning outcomes in online learning activities. Handayanto et al. (2018) corroborate these assertions, documenting a noteworthy increase in final exam scores and a surge in student interest in mathematics through their utilization.

Schaffert and Hilzensauer (2008), however, highlight the limitations of LMS, asserting that they confine the role of learners to the possibilities offered by the specific system and the creativity of the instructor, potentially compromising meaningful student engagement. Despite these limitations, stakeholders within the educational community leveraging LMS platforms must marshal empirical evidence substantiating their efficacy in enhancing students’ learning outcomes across diverse academic domains (Høgheim & Reber, 2015; Kehrwald & Parker, 2019).

Future research should focus on evaluating the efficacy of LMS platforms within school contexts, with a particular emphasis on gauging learner performance and satisfaction (Jung & Huh, 2019; Kumi-Yeboah, 2015).

2.4 Mathematics and difficulties: Decimals and fractions

Mathematics is inherently crucial not only for its direct applicability in daily life and problem-solving prowess across a spectrum of challenges (Cázares et al., 2020), but also for its profound interdisciplinary ties that span different domains of the curriculum (Gilat & Amit, 2013). The ability to generalize mathematical concepts into routine contexts is fundamental to its role as a cornerstone skill in educational frameworks (Alonso et al., 2015). Specifically, mathematics proficiency underpins core competencies in science and technology, laying a robust foundation for understanding complex scientific phenomena and technological innovations. This interconnectedness underscores its pivotal role in fostering critical thinking, logical reasoning, and quantitative literacy essential for navigating contemporary societal challenges and advancements in various fields.

Despite its pressing relevance, the comprehension of mathematical concepts often presents a significant challenge for students in their early stages of learning, particularly in the domains of decimal and fractional numbers. Understanding fractions and decimals involves recognizing their magnitudes, facilitating comparisons, ordering, and placing them on number lines (Siegler et al., 2011). However, this comprehension continues to pose challenges for many children, both in terms of fractions (Braithwaite et al., 2018) and decimals (DeWolf et al., 2015; Resnick et al., 2019). Furthermore, many children also exhibit insufficient proficiency in arithmetic involving rational numbers, evident in both fractions (Hansen et al., 2015; Siegler et al., 2011) and decimals (Hurst & Cordes, 2018).

For fractions, studies have shown that students often perform calculations without a deep understanding of the underlying mathematical concepts (Kerslake, 1986; Gabriel et al., 2013). Teaching tends to prioritize procedural knowledge over conceptual understanding of fractions. Consequently, children frequently learn through rote procedures, which can lead to misconceptions about fractional numbers. Unlike whole number magnitudes, understanding fraction magnitudes involves deriving them from the ratio of two values, a process that typically diminishes accuracy, speed, and automatic access to magnitude representations (English & Halford, 2012). Moreover, accessing fraction magnitudes necessitates comprehension of whole number division, widely regarded as the most challenging among the four arithmetic operations (Foley & Cawley, 2003). Bassarear (2012) posits that the intuitive understanding linked with fractions cannot be imparted directly through instruction; instead, it evolves from recognizing the interconnections and nuanced relationships among different concepts and procedures. Therefore, educators must present diverse contexts that depict a broad array of scenarios involving fractions for students (Kazemi & Rafiepour, 2018).

Regarding decimal numbers, challenges frequently arise due to persistent difficulties in transitioning from viewing numbers solely as natural numbers to encompassing natural, rational, and real numbers. Throughout this conceptual shift, students frequently develop multiple misconceptions related to decimal magnitudes (Desmet et al., 2010). Roell et al. (2017) highlight the prevalence of treating decimal places as whole numbers, leading to numerous erroneous operational strategies and misconceptions. Similarly, Steinle (2004) lists misconceptions regarding decimal number understanding and interpretation, such as whole number thinking, reciprocal thinking, denominator-focused thinking, column overflow thinking, reverse thinking, and money thinking.

2.5 Understanding of fractions and decimal numbers as performance predictors

The understanding of mathematical concepts, particularly decimals and fractions, often poses a formidable challenge for students at early stages. However, these concepts also serve as strong indicators of cognitive competence development within and beyond mathematics. Ten Braak et al. (2022) state that the correlation between young children’s initial mathematical proficiency and their future academic success is well-established, influencing not only mathematics but also reading skills. Siegler et al. (2012) found that elementary school students’ understanding of fractions and whole-number division significantly predicts their high school mathematics achievement. This predictive capacity surpasses that of proficiency in whole-number addition, subtraction, and multiplication, as well as verbal and nonverbal proficiency, working memory, family educational background, and family income.

In line with these findings, DeWolf et al. (2015) demonstrated that comprehension of decimal magnitudes, assessed through a number line task, and the relational understanding of fractions are significant predictors of algebra performance. Consistently, Resnick et al. (2019) discovered that the ability to reason about fractions, decimals, and whole numbers at the beginning of fourth grade uniquely predicted mathematics achievement by the end of that year. These results remained significant even after accounting for various behavioral and cognitive factors, indicating that an early grasp of numerical magnitudes in various forms is critical for later mathematical success.

Liu (2018) further assessed the impact of fraction understanding by evaluating students in a cross-sectional study before and after fraction instruction in fourth grade using proper-fraction estimation on a number line. The study proved that fraction magnitude understanding predicted mathematics achievement after primary fraction instruction but not before. These studies collectively highlight the critical role of early mathematical understanding in predicting future academic performance, underscoring the importance of fostering robust mathematical foundations in young learners.

2.6 Technology and personalization in mathematics: Fractions and decimal numbers

In light of the aforementioned challenges, new teaching models involving technology and personalized instruction based on the inherent difficulties of mathematics and the needs of students have been considered and implemented. Early observations by Vrasidas and Glass (2005) underscored the sporadic utilization of technology for teaching mathematics, despite its immense promise for augmenting pedagogy (Connel, 1998). The blended learning instructional model aligns with the urge to adapt instructional approaches to support personalized learning and provide feedback to students (Karam et al., 2017; Phillips et al., 2020). This model requires teachers to adapt to new tutoring and coaching roles, utilizing new tools in a restructured setting (Staker & Horn, 2012).

The new paradigm of technology-monitored learning and personalization has given rise to numerous resources and branches of didactic and experimental thought. Example of this are the Intelligent Tutoring Systems (ITSs), defined as computer-based learning environments designed to help students master knowledge and skills through intelligent algorithms that adapt to individual students and implement complex learning principles (Graesser et al., 2016). ITSs incorporate features such as active student learning, interactivity through systematic responses to student actions, adaptivity by providing personalized information, and performance-based feedback (Huang et al., 2016).

The significant contribution of ITSs to education is well-documented through numerous literature reviews and meta-analyses. VanLehn (2011) compared the effectiveness of human tutoring, computer tutoring, and no tutoring, concluding that while ITSs should not replace the entire classroom experience, they can match the effectiveness of individualized human tutoring, particularly in STEM disciplines. Similarly, Kulik and Fletcher (2016) observed greater effectiveness of ITSs, especially in elementary and high school settings, in their meta-analysis examining the impact of ITSs on K-12 mathematics performance. Further supporting this, Shih et al. (2023) developed an ITS for learning multiplication and division of fractions and conducted a quasi-experimental study involving 6th graders. This ITS identified students’ errors and misconceptions in real-time, and the results showed that the group using the math ITS significantly outperformed the control group, with a notable effect on lower-performing students.

In the domain of game-based learning and difficulty detection, Chu et al. (2021) employed a concept-effect relationship and an interactive game-based learning system to organize learning materials and create a diagnostic system for identifying students’ learning challenges. Their experiment in an elementary school math course showed improved learning outcomes, enhanced attitudes toward learning, self-efficacy, and reduced cognitive load. These findings contrast with those of Bhatia et al. (2023), who compared the effects of an educational fractions game with traditional fractions instruction in 5th-grade students and found that the traditional teaching control group outperformed the experimental group in overall fraction performance, though the educational game positively impacted decimal learning.

The use of online platforms and learning applications extends to higher levels of education, demonstrating their value across age groups. Wang (2024) examined the impact of an adaptive learning platform (EdReady) on underprepared students’ success in corequisite math courses in college, finding that the platform significantly improved passing rates. Bush (2021) introduced an adaptive software tutor for fractions and decimal numbers, incorporating virtual manipulatives, realistic contexts, and procedural feedback for 4th and 5th graders in a randomized crossover trial. The integrated approach significantly enhanced student achievement in fractions and decimal number domains. Focusing on decimals, Mínguez‐Pardo et al., (2024) implemented an experimental design comparing the effects of homework tasks with correct and incorrect examples on 5th and 6th-grade students, evaluating their impact on understanding decimal numbers on the number line using the LMS Moodle platform. Findings endorsed the efficacy of online homework in enhancing students’ proficiency with decimal numbers, revealing that incorrect examples were advantageous for students with higher prior knowledge, whereas correct examples were preferable for those with lower prior levels.

Despite significant advances in the application of technology in education, there remains a notable lack of research on the use of LMS for personalized learning of fractions and decimal numbers in primary education. Current studies have predominantly focused on higher education levels and other disciplines, creating a gap in understanding the potential of LMS in early mathematics education. This study addresses this gap by exploring how they can be effectively utilized to enhance the comprehension of fundamental mathematical concepts among primary school students, thereby justifying the relevance of the subsequent intervention objectives and implementation.

3 Objectives

The present study aims to investigate the effectiveness of personalized learning sequences, delivered through an interactive online platform, in enhancing mathematical understanding in 5th grade elementary school students. Consequently, the following research questions have been formulated:

  • RQ1: How does the implementation of personalized and non-personalized learning sequences, facilitated by an LMS, affect the learning outcomes of 5th-grade students in the areas of fractions and decimal numbers?

  • RQ2: What differences, if any, are observed between the outcomes of students who engaged in personalized learning sequences and those who participated in non-personalized sequences for learning fractions and decimal numbers?

4 Method

4.1 Design

To address the research inquiries outlined, a quantitative-experimental study employing pure randomization was conducted. This design was selected due to its suitability for investigating personalized learning interventions facilitated through technology, specifically within the Moodle platform. This approach empowered students to autonomously engage in their learning activities. By adopting this design, potential influences of extraneous variables unrelated to the research objectives were minimized, thereby establishing a robust framework for replicating results under similar conditions (Hedges, 2018).

The significance of this design choice in the context of personalized learning sequences cannot be overstated. Pure randomization mitigated biases associated with factors such as students’ initial levels of mathematical proficiency, particularly in decimal and fractional concepts, as well as variations in instructional methodologies among teachers. This method ensured the integrity and reliability of the findings. Moreover, it encompassed diverse student cohorts, enhancing the study’s generalizability. This rationale is supported by scholarly consensus, which recognizes pure randomization as the most rigorous method for establishing causal relationships among investigated variables (Leppink, 2019).

As for the theoretical framing, although personalized learning may incorporate behaviourist principles —especially depending on the type of feedback used as reinforcement—, in our study, personalized feedback was designed to encourage deeper cognitive processing and concept consolidation, helping students to engage more actively with mathematical concepts. Reinforcement activities, while adaptive, were intended to encourage reflection and understanding rather than simply rewarding correct answers. This blend of approaches aligns more closely with cognitivist frameworks.

4.2 Sample

Before initiating contact with schools to invite their participation in the study, necessary approvals were obtained from the Ethics Committee on Social Research of the University of Castilla-La Mancha and the Provincial Delegation of Education, Culture, and Sports of Albacete. Subsequently, schools interested in joining the study were approached to clarify the study’s objectives, procedural details, and expected timeline. Following these communications, two schools from Albacete confirmed their willingness to participate.

The initial sample consisted of 88 5th-grade primary education students. The choice of this grade level was primarily due to the students’ demonstrated autonomy, typically aged between 10 and 11 years, and their proficiency in using laptops with minimal assistance. This proficiency streamlines session logistics by reducing the need for extensive explanations, thereby maximizing engagement time in activities. Additionally, this age range aligns with the curriculum stage where fractions and decimal numbers are typically introduced, following the guidelines of Real Decreto 157/2022 (2022) currently in effect.

For the analysis of the previously defined research questions, only participants who completed both the Pre-test and Post-test, provided explicit consent, and disclosed their gender were included in the final analysis. This resulted in a total sample size of 73 students, comprising 44 boys and 29 girls. In addition to the tests, students received a physical consent form detailing the study’s nature and objectives to be reviewed with their families. Parental or legal guardian consent was mandatory for students to participate and have their data included in the study. The return of signed consent forms facilitated the inclusion of students in the research.

Demographic details of the groups are summarized in Table 1.

Table 1 Demographic data of the groups under study
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According to the experimental framework, these 73 students were randomly assigned to one of two experimental conditions. The first condition involved participating in an adaptive learning sequence tailored to individual performance on decimal and fractional number tasks (hereafter referred to as the experimental group, EG). This sequence included foundational learning modules with additional tasks provided as needed based on each student’s mastery of specific mathematical concepts. A total of 37 students were assigned to this group. Conversely, the second experimental condition (hereafter referred to as the control group, CG) followed the same foundational learning sequence but without the provision of additional tasks personalized to individual performance. This group comprised 36 students.

4.3 Instruments

In order to comprehensively address the research questions, both Pre- and Post-intervention assessments were conducted using validated instruments to measure proficiency in the utilization and understanding of fractions and decimal numbers.

To evaluate students’ proficiency in decimal number concepts, a carefully selected subset of 50 items from the validated assessment developed by Durkin (2012) was utilized. Similarly, for the assessment of students’ comprehension of fractions, the instrument developed by Pantziara et al. (2012) was employed, comprising a total of 23 items after the subdivision of two items for efficiency. Concerning the latter, its items were translated, and some visual models were redesigned to enhance comprehension. All decimal and fraction items all items associated with their corresponding dimensions and tasks are reflected in Table 2.

Table 2 Items by dimension and task
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4.4 Resources

The LMS Moodle platform served as the cornerstone for developing instructional and learning phases throughout various sessions of the study, specifically leveraging its Lesson Activity feature. This feature enabled the integration of diverse mathematical activities presented in different formats tailored to the specific types of responses and reasoning required by each mathematical question and the individual needs of students. These activities were sequenced and coded to incorporate explanatory theoretical elements to enrich the learning experience. Moreover, Moodle provided functionalities to include feedback elements based on user responses, ensuring that sessions not only focused on problem-solving but also engaged students in holistic, self-paced, and sequenced mathematical activities and content. This approach anticipated different dimensions of classroom teaching in a digital, fully personalized, and automated format.

The primary rationale for selecting Moodle was its capability to create sequences of activities and personalized reinforcement mechanisms, thereby allowing the development of unique educational sequences tailored to different student groups. Consequently, two distinct sequences were designed for this study: a control sequence presenting activities and educational elements continuously and linearly, and an experimental personalized sequence that dynamically introduced alternative reinforcement activities based on students’ errors. To assign students to each group, they were randomly and individually provided with a user code and password corresponding to one of the two sequences. Moodle’s privacy features ensured that students could only access and complete their assigned sequence at the designated time, preserving the integrity of the experimental design.

Four sessions were structured, each comprising sequences of activities, educational content, and feedback aligned with the qualitative dimensions of fractions and decimal numbers assessed in the Pre-test and Post-test. These sessions incorporated two distinct pathways for the EG and CG, systematically covering all aspects of mathematical thinking aforementioned in the instrument section through varied question formats and digital reinforcements.

As highlighted by Usiskin (2018), digital teaching platforms like Moodle offer diverse modalities such as text, images, and interactive activities to present content, thereby influencing students’ perceptions of mathematics. Figure 1 illustrates examples of different activity formats included in the sequences: multiple-choice questions, true or false questions, matching questions, and numeric input questions, each designed to cater to specific learning objectives and engagement levels.

Fig. 1
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Multiple choice question: activity 3.15 A (left) and matching question: activity 2.8 B (right)

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4.5 Procedure

During the intervention phase, which spanned six weeks, six sessions lasting between 30 and 45 min each were scheduled in collaboration with the students’ tutors during their regular teaching hours. The Pre- and Post-tests on fractions and decimal numbers, previously described, were administered at the beginning and end of this period, specifically during the first and sixth sessions, respectively. These tests were conducted in physical format, requiring students to use pencil or pen and submit their completed tests at the end of each session. The distribution of sessions allowed for the assessment of students’ baseline mathematical knowledge before the educational intervention commenced. To maintain standardized testing conditions and prevent information exchange between students, exam-like conditions were simulated in the classroom during both the Pre-test and Post-test.

Regarding the intervention sessions themselves, they were structured sequentially, occurring once per week between the Pre-test and Post-test, as depicted in Fig. 2. Each session followed a consistent format where students engaged with specially designed activities tailored for this study, using their laptops provided by the school. While activities were intended to be completed within 30 min, the full duration of the regular class period was utilized when necessary, occasionally extending sessions to 45 min or longer to accommodate varying completion rates among students.

Fig. 2
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Design of the sessions

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The instructional sequences, personalized and non-personalized, were implemented using the LMS Moodle platform. Within this online environment, an interactive course was specifically curated for the study, as previously outlined. All participating students were enrolled in this course and provided with unique usernames and passwords to access activities corresponding to their experimental condition. Additional user accounts were prepared in case any student required assistance with their access credentials.

To ensure the integrity of the study, the availability and visibility of sessions were regulated such that students assigned to the non-personalized sequence did not have access to those assigned to the personalized sequence, and vice versa. This measure aimed to maintain uniformity in perceived activity across all participants, safeguarding the study’s experimental design. Furthermore, access to activity sequences was managed according to each school’s schedule, ensuring sessions were conducted on different days for students from different institutions to prevent premature exposure.

The content was structured across sessions in an alternating fashion, addressing tasks related to fractions in the first and third sessions and focusing on decimal numbers in the second session. The fourth and final intervention session integrated both fractions and decimals to provide a comprehensive overview. Additionally, activities utilizing the GeoGebra app were introduced during this session to supplement the main instructional sequence, emphasizing interactive tasks involving number lines.

Students were instructed on how to access the platform using their unique user codes and passwords. They were required to maintain an exam-like environment during sessions to promote individual work and uphold the experimental conditions of the study. Any queries regarding procedural understanding or technical issues with the platform were addressed promptly at their respective workstations.

4.5.1 Session 1; Pre-test

During the initial 45-minute session, students were introduced to the study, which focused on mathematics, and were informed about the total number of sessions it would involve. However, specific details regarding the control and experimental sequence groups were withheld to prevent bias in the study’s procedure and results. Subsequently, students were given the Pre-test to complete, and any procedural questions unrelated to the content were addressed. Additional time beyond the regular class duration was allocated to accommodate students with varying work paces.

4.5.2 Dynamics of the sequenced instruction in Moodle

This section will serve as an illustrative model to elucidate the functionality of the instruction sequence on the Moodle platform, preceding a detailed description of the unique characteristics of each session. It aims to provide readers with a comprehensive understanding through practical examples, offering an immersive view into the sequential and dynamic structure of the intervention sessions. The flowchart of the experimental sequence in session 4 or the 3rd intervention session; as seen in Fig. 3, will be utilized as a clear example due to its straightforward sequential layout in order to highlight its various elements. Each session also included an alternative non-personalized sequence for the CG. However, only the former will be discussed hereafter.

Fig. 3
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Flowchart of the activities and theory slides of session 4 (3rd interventional session)

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All sessions adhere to a structured sequence of activities designed to cover various dimensions of mathematical thinking related to decimal and fractional numbers, as assessed in the Pre- and Post-tests. The primary sequence of activities in each session is denoted in dark blue on the flowchart, while personalized reinforcement activities or the personalization line are depicted in light blue directly below the main activities. These personalized reinforcement activities are exclusive to the personalized sequences, as exemplified in the present case. Each main activity in the personalized sequence is paired with at least one personalized reinforcement activity addressing the same mathematical content, also shown in light blue. The number of personalized reinforcement activities may vary, with up to three complementing the same main activity. The personalized sequences share all main line activities with their corresponding non-personalized sequences, except that the latter integrate a limited number of reinforcement activities from their corresponding personalized sequence into their single line of activities in a random order, not consistent with the customization process. This approach avoided the need for additional activities to complete and extend the control sequence, maintaining the same activities without personalization features. This increased the comparability of both sequences based on the personalization feature.

As an example, Activity 3.4 A (which stands for activity 4 from the main sequence A in the 3rd interventional session) will be used to illustrate the functioning of the sequence based on the flowchart of the personalized sequence for the third intervention session (session 4), as depicted in Fig. 4.

Following the input of a response, as reflected in the key of Fig. 3, there are different possible routes:

  • Correct input: The user is directed to the next question in the main sequence, as indicated by the green arrow.

  • Incorrect input from a main sequence activity: The user is directed to a personalized reinforcement question, represented by the red arrow. If there are multiple personalized reinforcement questions, an incorrect input may lead from one reinforcement question to another. A correct input during any of the reinforcement activities will redirect the user back to the next main sequence activity. Upon reaching the last reinforcement activity derived from any main sequence activity, any input, whether correct or incorrect, will result in the initiation of the next main sequence activity.

Fig. 4
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Illustration of activity 3.4 A from the perspective of the personalized activity diagram

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In the event of a negative input, all activities include a transition element before redirecting to the next activity. This element is the feedback aid, which appears as a pop-up window before the next activity, allowing the user to proceed after reading and understanding the provided information. The feedback aids in building and consolidating understanding of the failed tasks through textual explanations, visual models, and manipulative representations that present the key concepts of each activity in an accessible manner.

As shown in Fig. 5, after an incorrect input in Activity 3.4 A, the user is redirected to a feedback window before the personalized reinforcement question.

Fig. 5
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Illustration of the feedback pop-up window of activity 3.4 A from the perspective of the personalized activity diagram

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After reading the feedback and confirming the continuation, the first personalized reinforcement activity, 3.4B, is introduced, as shown in Fig. 6. Since this is a single activity, any type of input, whether correct or incorrect, will redirect the student to the next main sequence question, 3.5 A. However, in the case of an incorrect input for personalized reinforcement activity 3.4B, specific feedback will be provided before transitioning to the next activity. This ensures that the dynamics described in this section are consistently applied throughout the various sequences of activities.

Fig. 6
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Illustration of the reinforcement activity 3.4 B from the perspective of the personalized activity diagram

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Finally, it is pertinent to highlight the diverse theory slides located throughout the different sequences. These slides introduce various theoretical contents with textual explanations and visual models, interspersed among the activities in both the EG and CG. They provide integrated and holistic support to consolidate and complement the interactive contents of the activities. These theory slides are represented by green circles on the session flowchart, as shown in Fig. 3. For illustrative purposes, three consecutive theory slides from the reference model, 3.1, 3.2, and 3.3, are schematically represented in an immersive manner in Fig. 7.

Fig. 7
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Illustration of the theory slides 3.1, 3.2, and 3.3 from the perspective of the personalized activity diagram

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Next, the general characteristics of the intervention sessions will be briefly described, highlighting noteworthy elements of each.

4.5.3 Session 2; 1st learning sequence

The second session of the study, which was the first intervention session, began with providing the students their user codes and passwords for subsequent intervention sessions. The access steps to the platform were explained prior to the execution of the tasks.

Both the experimental and control sequences of this session included three non-personalized activities to serve as an introduction and a reminder of the contents. Additionally, the personalized sequence incorporated personalization chains, consisting of up to three reinforcement activities for each main sequence activity.

The primary focus of this session was on fractions, specifically targeting the comprehension of the part-whole subconstruct and equivalent fractions dimensions.

4.5.4 Session 3; 2nd learning sequence

The second intervention session introduced a more intricate personalization element in the experimental sequence, featuring the repetition of main sequence questions and different personalization routes for the same activity based on multiple-choice input.

This session also included activities designed to address common misconceptions about decimal numbers identified by Steinle (2004). These misconceptions include whole number thinking, reciprocal thinking, denominator-focused thinking, column overflow thinking, and reverse thinking. Addressing these misconceptions aimed to enhance and refine students’ understanding and use of decimal language. Additionally, this session explored the comparison, density, and number line dimensions of decimal numbers.

4.5.5 Session 4; 3rd learning sequence

The experimental and control sequences of the third intervention session explored the part-whole subconstruct, measure subconstruct, equivalence of fractions, comparison of fractions, and sum of fractions dimensions. The experimental sequence maintained a simple personalization structure, as described in the section on the dynamics of sequenced activities in Moodle, with each main sequence question corresponding to a single personalized reinforcement question.

4.5.6 Session 5; 4th learning sequence

The experimental and control sequences of the fourth session explored the dimensions and properties of decimal numbers and fractions from the previous sessions with one personalized reinforcement activity per main sequence activity in the experimental sequence. Unlike the rest of the sequences, this one included interactive activities originally designed in the GeoGebra application by Mínguez‐Pardo et al., (2024) and integrated into the Moodle sequences to develop decimal numbers and fractions in their number line and measure dimensions, respectively. These activities allowed the user to move a marker along a number line to represent the numbers required by the questions and included feedback as represented in Fig. 8. The variety of questions included decimal and fractional numbers to be represented on the number line with and without segmentation to represent their subdivisions, with and without an additional reference number on the number line to facilitate locating the number to be represented, and proper and improper fractions.

Fig. 8
figure 8

Illustration of the GeoGebra Applet reinforcement activity 4 from the perspective of the personalized activity diagram of session 5: 4th interventional session

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4.5.7 Session 6; Post-test

The sixth and final session focused on administering the Post-test to the students following the intervention sessions. Additional time was allocated beyond the regular class duration to ensure all students had ample opportunity to complete the test.

5 Results

Considering the two research questions of the present study, this section first presents the results of the didactic intervention in the two groups involved; EG and CG, in their two main mathematical dimensions; decimal numbers and fractional numbers. Subsequently, data concerning the influence of personalization on the results in the dimensions of decimal and fractional numbers are presented. For this purpose, the various individual items found in the Pre- and Post-tests corresponding to activities in both dimensions were initially coded between 0 and 1, with 0 representing an incorrect response and 1 representing a correct response. Subsequently, the resulting data were standardized from 0 to 10 to facilitate their interpretation in the educational context.

5.1 Analysis of the effect of instruction for each group and dimension

In this section, the results related to the first research question, concerning the effect of the didactic intervention for each group and dimension, are presented. Table 3 shows both the mean of the results (M) and the standard deviation (SD) in the Pre- and Post-tests by group and mathematical dimension.

Table 3 Results by dimension and group
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Initially, at a descriptive level, a clear higher starting level is observed in the dimension of decimal numbers, approximately 4 points above the dimension of fractional numbers in both groups: 3.9 in the CG and 4.01 in the EG. A substantial improvement is also evident in both groups for both dimensions. In the case of decimals, this improvement is notably homogeneous, being 1.12 points for the CG and 1.21 points for the EG. In contrast to these data, in the dimension of fractional numbers, which has a much lower starting level than decimal numbers, a significant and heterogeneous gain between the groups is observed. In the case of the CG, this gain is 1.18 points, similar to those found in the dimension of decimal numbers, while in the EG, this gain increases to 2.01, which is 0.83 points higher than the CG. To evidence the level of significance of the results and evaluate the effectiveness of the activity sequences, a paired-samples t-test was conducted in the different groups to compare the Pre- and Post-test results. In the dimension of fractions, the CG showed significant differences between Pre-testCG (M = 2.17, SD = 1.58) and Post-testCG (M = 3.35, SD = 1.96); t(35) = 5.87, p < .001, d = 0.98). Similarly, in the EG, for the dimension of fractions, significant differences were reported between Pre-testEG (M = 1.87, SD = 1.38) and Post-testEG (M = 3.88, SD = 2.06, t(36) = 7.88, p < .001, d = 1.29. Regarding the dimension of decimal numbers, the CG again evidenced statistically significant differences between Pre-testCG (M = 6.07, SD = 2.49) and Post-testCG (M = 7.19, SD = 2.53, t(35) = 5.11, p < .001, d = 0.85). Lastly, the EG also showed significant differences in the dimension of decimal numbers when comparing Pre-testEG (M = 5.88, SD = 2.44) and Post-testEG (M = 7.09, SD = 2.65, t(36) = 6.1, p < .001, d = 1.0). In light of these results, it is concluded that statistically significant differences have occurred between the Pre- and Post-test results in both groups: EG and CG; and in their two dimensions: decimal numbers and fractional numbers.

Beyond the statistical significance in all groups and dimensions, assuming the effect size threshold values suggested by Cohen (1988), where d = 0.2 represents a small effect, d = 0.5 represents a moderate effect, and d = 0.8 represents a large effect, it is concluded that the effect of the intervention has been large in both groups and dimensions. Values even equal to or greater than one pooled standard deviation are found in the EG in the dimension of decimal numbers (d = 1) and in the dimension of fractional numbers (d = 1.29).

5.2 Comparative analysis between personalized and non-personalized instruction

Due to the fact that the previous analysis only offers comparative information between Pre- and Post-tests without providing specific information to compare the effectiveness of the two types of intervention (personalized and non-personalized) on the results in both dimensions, an analysis of covariance (ANCOVA) was conducted to address the second research question of the present study. This analysis uses the Post-test as the dependent variable and the Pre-test as the covariate for both groups within the same mathematical dimension, considering possible differences in students’ initial knowledge. In the case of the dimension of fractional numbers, the ANCOVA to evaluate the effect of the type of instruction on the Post-test revealed a significant effect of personalized instruction, F(1, 70) = 6.39, p = .014, with a η2 partial eta squared effect of 0.08, as shown in Fig. 9, where the CG is represented as “0” and the EG as “1”. Moreover, according to the following categories of partial eta squared effect size: small ≥ 0.01, moderate ≥ 0.06, large ≥ 0.14 (Cohen, 1988; Richardson, 2011), a moderate effect size was observed in favor of the personalized intervention type on the Post-test results.

Fig. 9
figure 9

ANCOVA of the fraction dimension

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Similarly, an ANCOVA was conducted for the dimension of decimal numbers. This analysis revealed a non-significant effect of personalized instruction compared to non-personalized instruction, F(1, 70) = 0.06, p = .812, with a partial eta squared effect size of 0.00081. These results reflect a lack of effect of personalized instruction on the post-test results compared to non-personalized instruction. The descriptive graph of the analysis of covariance for the dimension of decimal numbers is depicted in Fig. 10.

Fig. 10
figure 10

ANCOVA of the decimal dimension

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6 Discussion and conclusion

Given the limited empirical research on the actual use of digital technology in schools that have implemented personalized learning on a school-wide basis (Schmid et al., 2023); particularly in the STEM fields, where personalized learning has a mutually beneficial relationship (McClure et al., 2017), and in line with the ongoing search for tools to promote active and personalized learning by researchers and educators (Gross & DeArmond, 2018), this study was undertaken. The primary objectives were to evaluate the impact of personalized and non-personalized lesson sequences with activities in the Moodle LMS on the performance of 5th-grade students in mathematical dimensions related to fractions and decimal numbers, and to compare the differences between these instructional methods in the aforementioned dimensions. It is noteworthy that these sequences were designed to be instructive and holistic, incorporating theoretical explanations, feedback, and interactive tools specifically created to complement the activities. However, to the best of available knowledge, there is a lack of research that combines the use of personalized sequences and pathways in LMS with respect to rational numbers at the primary education level, integrating the aforementioned holistic approach to meet various dimensions of traditional instruction in a digital and automated manner. Consequently, the results and conclusions will be compared with research experiences that share these elements to the greatest extent possible.

The data collected, at a descriptive level and aside from the main objectives of this study, indicate a low initial level in the fractions dimension, with average pre-test scores of 2.17 in the CG and 1.87 in the EG. These findings align with the existing notion of poor competence in the domain of fractions, both in understanding and arithmetic application (Gabriel et al., 2013; Hansen et al., 2015; Hecht & Vagi, 2012; Braithwaite et al., 2018). In contrast, the initial average results in the domain of decimal numbers show higher average scores, with 6.07 in the CG and 5.88 in the EG, averaging around 4 points higher than the fractions scores. This reveals a stronger baseline in decimal numbers, contrasting with the findings of DeWolf et al. (2015), Resnick et al. (2019), Hurst and Cordes (2018), and Rittle-Johnson and Koedinger (2009).

The statistical results pertaining to the first research question, which aimed to evaluate the effectiveness of personalized and non-personalized lesson sequences with activities, explanations, and feedback in fractions and decimals, demonstrated significant improvement in both groups across both mathematical dimensions (EGFRACTIONS, CGFRACTIONS, EGDECIMALS, CGDECIMALS). Comparative data consistently showed highly significant differences between Pre-test and Post-test scores, with a large effect size (Cohen, 1988). The magnitude of these results corroborates the positive premise for personalization and tutoring highlighted in the literature review of VanLehn (2011). In line with this statement, the present study therefore provides evidence of the positive impact of lessons based on sequences of activities with explanatory, comparative, and integrative elements, coupled with student feedback, aligning with experimental studies in the same domain.

This holistic and personalized approach to digital education and its positive effects on mathematical understanding and rational number comprehension is also a common element in the works of Rau et al. (2012) and Chu et al. (2021). Their work, in alignment with the present study, revealed enhanced learning following comparative experimental interventions in the area of mathematics and fractional numbers, characterized by an integrative approach focusing on worked examples and game-based learning, respectively, with an emphasis on meaningful feedback. This highlights the importance of integrating various forms of connection-making support to foster deep understanding in students when working with mathematical dimensions.

The results concerning the second research question of the study, which aimed to examine the disparities in outcomes between personalized and non-personalized instructional sequences with activities, explanations, and feedback in the domains of fractions and decimal numbers, revealed significant differences in personalized instruction with a moderate effect size in the analysis of covariance (Cohen, 1988; Richardson, 2011). These findings indicate promising prospects for digital personalization in the domain of fractions. However, personalized instruction in the domain of decimals did not show significant differences in impact compared to that of fractions, despite its consistent efficacy relative to the first research question of the present study.

The favorable results in the domain of fractions underscore the importance of a holistic and relational approach for their proper conceptual understanding. The integration of such an approach across various learning modalities is necessary and enhanced by feedback and personalization. This perspective is shared by Bassarear (2012) and Lamon (2020), who advocate for an intuitive understanding of fractions. They argue that this understanding should not result from direct instruction but rather from the metacognitive evolution that arises from recognizing the interconnections and nuances of other related concepts and procedures.

Under this premise, the present study serves as a precursor to transformative thinking in educational perspectives, advocating for the use of various contexts that facilitate the introduction of diverse learning scenarios with integrative and intuitive opportunities for students’ understanding of fractions (Kazemi & Rafiepour, 2018). In alignment with the educational paradigm described, the present study finds agreement with the works of Bush (2021), Rau et al. (2012), and Shih et al. (2023), which reveal improved learning outcomes and enhanced connection-making in the realm of fractions following the implementation of systems monitored through effective feedback and adaptive learning sequences.

In the specific context of this study, additional factors may explain the significant differences observed in personalized instruction for fractions, beyond the aforementioned elements. Given that the EG presented slightly lower average prior knowledge due to random distribution, the implementation might have benefited them more significantly (Park et al., 2024). Moreover, the comparative use of rational numbers and the number line (Liu, 2018), combined with the integration of different representations of these numbers with digital models and manipulatives (Rich, 2023), could explain part of these differences. This is especially pertinent considering the enhancing effect of understanding decimal numbers on the comprehension of fractions (Braithwaite et al., 2022) observed in the EG.

Overall, the findings of this study elucidate the value and potential of implementing personalized instructional sequences with a holistic perspective, featuring reinforcement activities to provide meaningful learning in case of errors, feedback, and theoretical elements to establish conceptual interconnections. Despite the lack of evidence from studies that meet these characteristics within the emerging field of digital personalized learning in an increasingly digitalized paradigm (Groff, 2017; Shemshack & Spector, 2020), this work paves the way for digital personalization in the classroom. It represents a useful example for teachers facing the challenge of providing tailored attention to the specific needs of students (Dixon et al., 2014; Goddard et al., 2015). Additionally, it suggests new possible directions and paradigms, such as its implementation to support teachers handling large and heterogeneous groups of students (Major & Francis, 2020; Van Schoors et al., 2021; Bernacki et al., 2021). The implications of these dynamics are conducive to flipped classroom models, which, as noted by Güler et al. (2023), could aid in the instruction of specific mathematical concepts within the scope of personalization. Another emerging issue is the role of the teacher, which, despite its importance in personalized education, is a nearly absent element in contemporary literature on the subject (Van Schoors et al., 2021).

As seen, the perspectives of this study lay the foundation for and call for the investigation of new models and questions within the paradigm of teaching and learning through personalization and technology. The scope and potential of developing these methodologies appear especially promising with the introduction of artificial intelligence. Studies such as that by Orhani (2024) show significant improvements in students’ performance in solving mathematical tasks, demonstrating a great ability of personalized technology to adapt to the needs of each student, and forecasting the possibility of creating a learning environment fully tailored to the academic needs and circumstances of each student. Finally, the exploration of the dimensions and contexts surrounding personalized mathematical learning can be further expanded in future research lines inspired by the literature surrounding this work. An example of this is the study by Hwang et al. (2023), which, in order to evaluate the effectiveness of intelligent mechanisms for personalization, contextualization, and socialization in geometry learning, used a mobile application to provide augmented reality experiences in a real-world environment. This study demonstrated improvements in geometry measurement and problem-solving for the experimental group compared to the control group.

6.1 Limitations and future research

Ultimately, and exclusively concerning the present study and its implementation, certain observations, limitations, and points for improvement should be highlighted. The first is the duration of the sessions, which proved insufficient in some instances. The estimated time for completing the sequences of activities was 30 min, which required extension up to 45 min, occupying the entire allotted session time and even exceeding this limit. Future implementations of similar models should, therefore, consider time margins adapted to the needs and varied work paces of the students, as well as the temporal structure of their activities in primary school. Conversely, its pertinent mentioning that the sample size was also limited, which suggests that the results may represent the characteristics of the studied population less accurately.

Regarding elaboration time, the preparation of this study is notably demanding since all activities, theoretical elements, feedback, and sequential designs were self-made. Thus, although its intervention replication is straightforward once established, its initial preparation is costly and time-consuming.

Another limitation during the intervention phase was related to the provision of feedback after each activity. Observations and in-person monitoring of the sessions revealed a tendency among some students to skip this feedback in order to immediately proceed to the next activity or sequence element, thus depriving the session of its full didactic and integrative potential and eliminating part of the implicit self-learning element. Future strategies to ensure the benefits of feedback could include emphasizing its importance prior to the session or setting a timer to increase the minimum required time before advancing to the next task, despite the implications this would have on the total session duration. Other alternatives might include using brief key questions during the feedback provision to verify its reading and assimilation or even providing feedback before the task is completed to make meaningful use of it during the activity (Espasa et al., 2018).

Finally, one of the implications and potential limitations of this study is its high technological demand. For its implementation, schools must have sufficient information technology infrastructure to provide all students with the opportunity for digital and individual access and completion of the tasks. This requirement could exclude schools with limited resources that do not meet these criteria. However, studies such as that by Mínguez‐Pardo et al., (2024) exemplify alternative solutions to this problem, offering an out-of-classroom approach for the implementation of personalized digital models in the field of mathematics. Their results revealed promising improvements following the use of correct and incorrect examples in decimal activities for home study among 5th and 6th-grade students, demonstrating that personalization can manifest in various ways and be facilitated outside the school environment.