1 Introduction

Mathematics is a mandatory subject at the primary and secondary school levels, a key requirement for educational progression (Federal Republic of Nigeria, 2013). However, many learners still achieve poorly in the subject. The persistently poor student performance in the subject is no longer newsworthy. Mathematics researchers like Azuka (2012) and Badru and Saka (2021) warned the public about the low mathematics proficiency of Nigerian learners from primary, secondary, and university levels of education. The West African Examination Council (WACE) Chief Examiners’ reports highlighted the unfavourable scenario by stating that candidates’ performance has steadily declined (WAEC, 2019–2020). Consequently, mathematics researchers have identified several factors contributing to learners’ poor performance in mathematics over the years. Some of these include inadequate mathematics instruction in primary school, and crowded mathematics classes (Uka & Ezeh, 2022), outdated mathematics resources (Egara et al., 2021; Evans et al., 2019; Mosimege & Egara, 2022), anxiety towards mathematics (Nzeadibe et al., 2023; Sarfo et al., 2020, 2022; Sule, 2017), the strictness of the mathematics teacher, laziness on the part of students and indiscipline towards mathematics (Jameel & Ali, 2016), negative attitude exhibited by students toward mathematics (Wachira, 2016), poor teaching approaches (Egara et al., 2021; Egara & Mogege, 2023a, 2023b, 2023c; Okeke et al., 2023a, 2023b), absence of mathematics teaching and learning materials (Kumah et al., 2016), and lack of retention of mathematics concepts on the part of students (Egara & Mogege, 2023a, 2023d).

Studies have highlighted the challenge of students failing to retain mathematical knowledge over time, posing a significant obstacle to their overall mathematical proficiency (Nzeadibe et al., 2020; Osakwe et al., 2023). Retention, in this context, refers to the ability of students to remember and apply mathematical concepts learned in previous lessons over an extended period (Mosimege & Egara, 2022; Egara & Mogege, 2023b). While addressing poor mathematics performance is crucial, focusing on students’ retention of math concepts as a distinct variable is equally important. The inability to retain essential mathematical knowledge hinders students’ overall mastery of the subject and may lead to difficulties in advanced topics that build upon foundational concepts (Osakwe et al., 2023). Therefore, there is a pressing need to explore instructional approaches that not only enhance mathematics achievement but also promote the lasting retention of crucial mathematical concepts. Mutange (2020) postulated that the Nigerian educational system is deficient in mathematics instruction and called for a better method of mathematics instruction in the classrooms. Due to the value of mathematics in society, this call is necessary. To understand mathematics, teachers must adopt a good teaching and learning approach to foster students’ retention of mathematics concepts, thereby improving their mathematics achievement in internal and external examinations. One method of teaching mathematics, proven innovative and effective, is the blended learning approach, which is the focus of this study.

Blended learning is a brand-new educational approach that combines face-to-face instruction, with all its benefits and drawbacks, with online learning in a virtual environment (Setiawan et al., 2022). Combining the best learning opportunities between these two approaches makes it possible to tailor instruction to the needs of individual students and to the desired outcome to be attained by the end of the semester (Al-abdallat et al., 2020). According to Ceylan and Kesici (2017), blended learning is a student-centred, teacher-facilitated instructional strategy that uses technology and concentrates on the student-teacher relationship to boost independence, engagement, and achievement. In the same vein, Sanwal (2019) views blended learning as a teaching and learning method combining online resources, including PowerPoint presentations, streaming media, online videos, and emails, with conventional classroom instruction. This method, therefore, benefits from both a teacher-dominated classroom setting and an active, student-focused online learning environment. In this study, blended learning, often called hybrid learning, is a method in which conventional face-to-face classroom procedures are coupled with online educational resources and participation opportunities. Students use technology to accomplish learning objectives and learn from and interact with their teachers and peers (Mukhtaramkhon, 2022).

2 Blended learning models

There are four types of blended learning models, according to Staker and Horn (2012). These are “Rotation, Flex, Self-Blend, and Enriched-Virtual models.” Out of these models, this study is interested in the Rotation model. The Rotation Model can also be divided into four sub-models: “Station Rotation Model, Lab Rotation Model, Flipped-Classroom Model, and Individual Rotation Model” (Staker & Horn, 2012).

2.1 Rotation model

When studying online, which is at least one of the learning modalities for online education, students are required to switch between different learning modalities according to a specified timetable or at their discretion. Additional learning methods include tutoring, community projects, small-group instruction, and handwriting exercises. With this kind of setup, many lessons are carried out on a physical campus instead of online. The four sub-models of the rotation model include.

2.1.1 Station rotation model

In this model, students see various learning stations in a classroom. Students might start with teacher preparation, move on to assignments and collaborative activities with other students, and then return to computers or tablets for online education.”

2.1.2 Lab rotation model

Using the lab rotation approach, students can rotate through stations according to a set timetable. This strategy permits flexible scheduling agreements with teachers and paraprofessionals, enabling schools to utilise already-existing computer laboratories (Christensen Institute, 2021).

2.1.3 Flipped classroom model

The conventional relationship between class time and homework is reversed under the “flipped classroom” model. While instructors use class time for teacher-guided practice or projects, students learn at home via online assignments and lectures. With the help of this model, instructors can give more than just conventional lectures throughout class (Christensen Institute, 2021).

2.1.4 Individual rotation model

Each student is given a specific rotation schedule based on their needs, and at least one is taking classes online. Because not all students rotate through each station or modality, this rotating model often differs little from other modes. A few students, for instance, get one-on-one instruction from the teacher before being directed to an online learning lab. On the other hand, some students are told to practice what they have learned from their teachers before being transferred to the online study lab.

Effective learning is predicated on the instructor’s choice of blended learning models due to the calibre of the students’ content and competencies. The instructor has more freedom to choose any model based on position and pace (Sahoo & Bhattacharya, 2021). Therefore, this research combined the station rotation and the flipped classroom models under the Rotation Model. For this study, the Station Rotation model was adopted during in-class activities. Students engaged in teacher-led sessions, collaborative small group discussions, and utilized online resources. This model promotes a dynamic learning environment where students interact with content through diverse approaches. However, the Flipped Classroom model was integrated into after-class activities. Students accessed video lectures and reading materials at home, allowing class time for reinforcement through quizzes, tasks, and real-world applications. This approach aims to maximize the effectiveness of face-to-face interactions during in-class sessions. The combination of Station Rotation and Flipped Classroom models was chosen strategically to leverage both in-class and after-class learning experiences. This hybrid approach aims to enhance student engagement, encourage collaborative learning, and provide a well-rounded understanding of the mathematical concept.

2.2 Benefits and challenges of blended learning

Students benefit significantly from the utilisation of blended learning. As stated by Tuomainen (2016), the blended learning model can boost students’ motivation for studying, help them manage their time better, and inspire them to be more autonomous and responsible. It was made clear in the previous study by Mozelius and Hettiarachchi (2017) that using a variety of blended learning techniques is preferable to using only one. Therefore, Albhnsawy and Aliweh (2016) acknowledged that blended learning activities present several chances for teachers and students to get feedback and engage in thought-provoking discussions. Likewise, Behjat et al. (2012) concurred that students have more access to educational resources when using a blended learning approach. A blended learning paradigm can make the learning process more alluring and is ideal for education in the twenty-first century, claim Wardani et al. (2018). Compared to traditional face-to-face learning, blended learning, according to Surjono et al. (2017), helps students more in accomplishment and involvement. Most students also see the use of blended learning favourably.

Despite the numerous benefits of blended learning, it also faces some challenges. Blended learning makes extensive use of technical tools and resources; therefore, educators should keep digital tools updated and ensure they’re user-friendly, according to Luo (2021). Access to internet infrastructure is another issue with this limitation. Establishing a good network connection is vital to improving educational quality in some economically backward areas. Secondly, online resources entail additional expenditures, such as yearly database subscriptions or access to reputable academic libraries. Some schools with little funding can be under financial strain due to this teaching method. In a blended learning setting, the students typically require technology outside of the classroom. Mukhtaramkhon (2022) proposed that online learning will be difficult or impossible for some learners due to unequal access to resources. Mukhtaramkhon also stated that students who want to access the course materials may face significant obstacles due to a lack of IT literacy, making the availability of top-notch technical support essential. The diversity of learners, including their age and gender, impacts whether or not a blended teaching-learning technique is accepted (Khechine et al., 2014). Consequently, to ensure that students learn and retain mathematics topics better, mathematics teachers should consider their learners’ interests and preferences while creating blended learning instructions.

2.3 Literature review

In diverse contexts, studies have been undertaken to examine the efficacy of the blended learning strategy and how it impacts learners’ achievement and retention on global and local levels. For instance, Indrapangastuti et al. (2021) conducted a study to assess the effectiveness of implementing a blended learning methodology to enhance trigonometry achievement among secondary school students in Malaysia. The research employed a quasi-experimental design with a sample size of 60 students, and the statistical analysis utilized the t-test. Their findings revealed a significant improvement in the achievement of students in the experimental group compared to their counterparts in the control group. In a parallel investigation, Makkar and Sharma (2021) explored the impact of blended learning on the mathematics achievement of ninth-grade students in Amritsar, India. Employing a quasi-experimental design with a sample size of 65 students, the study utilized the t-test as a statistical tool. The results indicated a noteworthy enhancement in achievement among students in the experimental group compared to those in the control group. Similarly, Tong et al. (2022) conducted a quasi-experimental study to evaluate the efficacy of blended learning in augmenting mathematics achievement among tenth-grade students in Vietnam. The study, which employed a t-test as the statistical tool, included a sample of 96 students across both experimental groups. The outcomes demonstrated the effectiveness of the blended learning approach in improving students’ mathematics achievement.

Lin et al. (2017) conducted a quasi-experimental study to examine the impact of blended learning on mathematics achievement among Junior secondary students in Taiwan. Employing the ANCOVA statistical tool, suitable for a quasi-experimental design, the study included a sample of 54 students. The results indicated the effectiveness of the blended learning method in improving mathematics achievement within the experimental group compared to the control group. Furthermore, the study reported a greater gain for male students compared to their female counterparts in utilizing the blended learning approach. In a related context, Awosdeyi et al. (2014) investigated the influence of blended learning on university students’ achievement in pre-algebra in Nigeria. Their study, employing a pretest-posttest randomized experimental design with the ANCOVA statistical tool (suitable for quasi-experimental designs), demonstrated that blended learning significantly enhanced students’ achievement in the pre-algebra course compared to alternative methods. Notably, the results revealed that gender did not exert a significant influence on the effectiveness of the blended learning approach.

In their 2019 study, Minaz and Melanie adopted a non-experimental design, specifically a quantitative comparative research design, to investigate the impact of blended learning, specifically the station rotation model, on sixth-grade students’ math achievement in the USA. Involving 413 students, the research revealed that the blended learning approach led to higher scores for students in the experimental group compared to those using traditional face-to-face settings. This suggests that blended learning is more effective in promoting academic growth in math, particularly for students requiring additional support within a school year. Concurrently, Joseph-Charles (2019) examined the effects of a blended learning instructional model on mathematics performance in a small northeastern urban school district in the USA. Employing a quasi-experimental design, the study compared the 2018 Spring PARCC mathematics scale score means for sixth and seventh-grade students in the treatment group (blended learning instruction) with those in the control group (traditional instruction). The findings indicated that grade 6 students in the blended learning model achieved statistically higher scores than their counterparts in traditional settings. However, for grade 7 students, although scores were higher numerically, the difference lacked statistical significance.

Sivakumar and Selvakumar (2019) investigated the efficacy of the blended learning approach in enhancing physics achievement and retention among higher secondary learners in India. Utilizing a quasi-experimental design with a sample size of 40 students and employing the t-test statistical tool, their findings demonstrated significant improvement in physics performance and retention among the experimental group compared to the control. Importantly, the study revealed that both male and female students achieved and retained physics concepts equally through the blended learning approach. In a related context, Suleiman et al. (2017) examined the effectiveness of computer-based blended learning on chemistry retention among secondary school students in Niger State, Nigeria. Employing the ANCOVA statistical tool suitable for a quasi-experimental design and a sample size of 120 students, their research indicated the effectiveness of blended learning in enhancing students’ chemistry retention. Furthermore, Olatunde-Aiyedun and Adams (2022) conducted a study on the effectiveness of blended learning models on university students’ achievement and retention in science education courses in Abuja, Nigeria. Using a quasi-experimental design with a sample size of 120 students and the t-test statistical tool, their findings demonstrated that students in the experimental group exhibited improved science achievement and retention compared to their counterparts in the control group.

Despite these encouraging findings, the persistent challenges in mathematics education, especially in secondary schools, necessitate a closer examination. In the context of Uzo-Uwani LGA in Enugu State, Nigeria, students continue to grapple with poor performance in mathematics (Okeke et al., 2023a, 2023b; Osakwe et al. 2023). The relevance of this issue is further underscored by the broader concerns raised by researchers like Azuka (2012) and Badru and Saka (2021) about the overall low mathematics proficiency of Nigerian learners. This study seeks to address the identified problem by investigating the impact of blended learning on secondary school learners’ mathematics achievement and retention. Notably, no prior research, to the best of the researchers’ knowledge, has explored the effects of the blended learning strategy on learners’ mathematics achievement and retention in Nigeria, including its impact on gender. To bridge this gap, it is crucial to determine the effect of the blended learning strategy on secondary school students’ mathematics achievement and retention in the Uzo-Uwani LGA of Enugu State, Nigeria, particularly among male and female students. However, while the reviewed studies utilised the quasi-experimental design, most of the studies (Indrapangastuti et al., 2021; Makkar & Sharma, 2021; Olatunde-Aiyedun & Adams, 2022; Sivakumar & Selvakumar, 2019) did not apply the ANCOVA that is the appropriate statistical tool for quasi-experimental design; instead, t-test was used. The current study applied the quasi-experimental design and used the appropriate statistical tool (ANCOVA). By adopting a quasi-experimental design and utilizing the ANCOVA statistical tool, our research aims to not only contribute to the growing body of knowledge on blended learning but also to address the gaps identified in the existing literature. The comparison of our results with previous findings will illuminate the effectiveness of blended learning in a distinct educational setting, ultimately providing valuable insights for educators, policymakers, and researchers. Therefore, this research’s primary purpose was to determine the effect of the blended learning approach on learners’ achievement and retention in mathematics. However, this study comprised of two groups, learners in the experimental group learnt the math concept using the blended learning approach, while learners in the control group received instruction through the conventional method. Additionally, our study included a pretest in the first week, followed by a four-week intervention or treatment period. The posttest was conducted in the sixth week, and a post-post-test (retention test) was administered four weeks after the posttest measure.

2.4 Theoretical framework

The theoretical foundation of this study is rooted in John Dewey’s (1933) Constructivism learning theory, complemented by insights from Jean Piaget and Lev Vygotsky. Dewey’s Constructivism profoundly influences technology advancements in both macro and micro educational contexts, drawing from Vygotsky’s structural theory (1978) and Piaget’s cognitive development principles (1952). Dewey’s constructivist theory places a significant emphasis on inquiry and the seamless integration of in-class and extracurricular (after-class) activities (Dewey, 1933). In line with Piaget’s view that learners actively build knowledge through exploration and interaction with their environment (Piaget, 1952), and Vygotsky’s emphasis on the role of social interactions in cognitive development (Vygotsky, 1978), Dewey contends that learners must engage with their background knowledge, experiences, and interests to forge meaningful connections while constructing knowledge collaboratively.

The application of blended learning in this study aligns with Piaget’s (1952) and Vygotsky’s (1978) perspectives. Blended learning, combining traditional teaching methods with the interactive and flexible features of online education, encapsulates inquiry, real-world mathematics activities, and instructional practices that synergistically enhance students’ enthusiasm, reflective thinking, self-reliance, and independence—attributes consistent with Dewey’s constructivist framework. By integrating these theoretical perspectives, the study seeks to explore how the practical implementation of blended learning strategies aligns with constructivist principles, fostering enhanced mathematics achievement and retention among secondary school learners. The study thus serves as an empirical exploration and application of these theories in the context of mathematics education.

2.5 Research questions

The study’s research questions (RQ) included the following;

  1. 1)

    What are the achievement scores of learners who received math instruction using the blended learning approach versus those in the control group?

  2. 2)

    What are the achievement scores of male and female learners who received math instruction using the blended learning approach versus those in the control group?

  3. 3)

    What are the retention scores of learners who received math instruction using the blended learning approach versus those in the control group?

  4. 4)

    What are the retention scores of male and female learners who received math instruction using the blended learning approach versus those in the control group?

2.6 Hypotheses

The following hypotheses (HO) guided the study at a 0.05 significance level.

  1. 1)

    No statistical difference exists between the achievement scores of learners who received math instruction using blended learning versus those in the control group.

  2. 2)

    No statistical difference exists between the achievement scores of male and female learners who received math instruction using the blended learning approach.”

  3. 3)

    No statistical difference exists between the retention scores of learners who received math instruction using blended learning versus those in the control group.

  4. 4)

    No statistical difference exists between the retention scores of male and female learners who received math instruction using the blended learning approach.”

3 Methods

In this study, we employed a quasi-experimental design, specifically pretest-posttest non-equivalent control group, to investigate the impact of blended learning on mathematics achievement and retention among secondary school students. The dependent variable, ‘Mathematics Achievement and Retention,’ was observed among students. The independent variable, ‘Blended Learning Approach,’ involving a mix of traditional/conventional and online teaching, served as the intervention. Validity was enhanced through a control variable: the control group (CG) received ‘Conventional Teaching Method’ to establish a baseline for comparison with the experimental group (Exp). The quasi-experimental design was employed because intact classes were used other than randomising students into groups, which is impossible in quasi-experimental studies (Fraenkel et al., 2023). The total population of learners in Senior Secondary 1 (SS1) in the Uzo-Uwani Local Government Area (LGA) of Enugu State, where the study was conducted, is 375 students. However, for the purposes of this research, a sample of 94 students (comprising 49 males and 45 females) was purposively selected from two secondary schools with information and communication technology facilities, and their age range from 14 to 16 years (Post Primary Schools Management Board, 2022). The reason for purposively selecting two schools was because only the two schools have information and communication technology facilities. Out of the two schools chosen one was allotted to the experimental group (48 students) and the other to the control group (46 students) through simple random sampling by balloting.

The instrument used for data collection in this study was the Mathematics Achievement Test (MAT). Furthermore, separate lesson plans/notes were crafted for both the experimental and control groups. Data collection involved administering the MAT to both the experimental and control groups. The MAT consisted of 20 multiple-choice items designed based on a test blueprint/ table of specification, ensuring comprehensive coverage of the mathematical concepts. The blueprint aimed to maintain a consistent distribution of items across various cognitive domains, ensuring a fair and balanced representation of the material. Each item on the MAT was carefully crafted to gauge the depth of students’ knowledge and their ability to apply mathematical concepts learned during the intervention. The multiple-choice format was chosen to allow for efficient and standardized scoring, enabling a systematic and objective evaluation of each participant’s performance. While the MAT may not have been a standardized test in the traditional sense, its development followed best practices in educational assessment (Nworgu, 2003). The careful crafting of items, alignment with the test blueprint, and consideration of various cognitive levels aimed to enhance the validity and reliability of the test for the specific context and objectives of the study. Sample Items of the MAT include:

Sample Item 1: What is the measure of an angle at the centre of a circle if the corresponding arc measures 90 degrees? (A) 45 degrees (B) 90 degrees (C) 180 degrees (D) 360 degrees.

Sample Item 2: In a cyclic quadrilateral, the opposite angles are: Supplementary B) Complementary C) Equal D) None of the above.

Sample Item 3: If a tangent and a chord intersect at a point on a circle, the measure of the angle formed is: 45 degrees B) 90 degrees C) 180 degrees D) Variable based on specific conditions.

Sample of Item Difficulty Analysis: The item difficulty analysis for the MAT was conducted to assess the proportion of participants who answered each sample item correctly. This involved calculating the percentage of participants who selected the correct response for each sample item. For example:

Sample Item 1: Correct Response: B) 90 degrees; Item Difficulty: 85%.

Sample Item 2: Correct Response: A) Supplementary; Item Difficulty: 72%.

Sample Item 3: Correct Response: B) 90 degrees; Item Difficulty: 63%.

These percentages represent the proportion of participants who answered each item correctly, indicating the level of difficulty for each item. The results reflect a range of item difficulty, ensuring a mix of challenging and moderately challenging items. This analysis contributes to the overall validity and reliability of the MAT used in the study.

The researchers created lesson plans/notes for the treatment groups’ lessons. Experts in Mathematics Education and Measurement and Evaluation validated the MAT alongside the lesson plans/notes. The MAT was trial tested on 40 SS 1 students in a school outside the local government area of study. The reliability of the MAT was determined using the Kuder-Richardson formula 20, and an internal consistency of 0.86 was obtained employing a statistical package for social sciences (SPSS) software version 28.

3.1 Experimental procedure

The Post Primary Management Board, Nsukka Zonal office, Enugu State, approved the research before it began on November 30, 2022, with reference number REC/PPSMB/22/04133. Additionally, the heads of the chosen schools granted their permission for the study. Informed consent was acquired from both students and their guardians, clearly articulating the study’s nature and objectives. Participation was voluntary, and students had the option to withdraw at any stage without facing consequences. Four research assistants were employed for this study. The assistants were the regular mathematics teachers at the schools selected. They received one week of training on using the blended learning approach to implement and deliver the mathematics concepts. The mathematics teachers in the experimental and control groups were given lesson plans/notes as a guide. The experimental group’s lesson plan/note was prepared following the blended learning approach, whereas the control group’s lesson plan/note was prepared in line with the conventional method. The mathematics concept that was taught to the SS 1 students was Geometry (Circle theorem). The Table 1 below shows the comparison of instructional activities between experimental and control groups.

Table 1 Comparison of instructional activities between experimental and control groups
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The SS 1 students received a pretest conducted before the treatment. The actual treatment lasted for four weeks (45 min per period, 5 periods per week). The posttest was conducted in the sixth week. The pretest items, before being used in the posttest, were, however, rearranged to give the items a fresh appearance and to prevent the students from recognising the items. The results from the post-test were observed and utilized to present data on students’ geometry performance, categorized by both gender and treatment group. The post-test items were also reorganized in anticipation of the post-post-test (retention test). Subsequently, data regarding students’ retention, classified by gender and treatment group, was compiled using the post-post-test (retention test) outcomes. Figure 1 below shows summary of the experimental procedure represented in a flowchart.

Fig. 1
figure 1

Summary of experimental procedure

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3.2 Data analysis

SPSS was used to evaluate the data gathered from the pre-, posttest, and retention test. The study questions were reported using the mean (M) and standard deviation (SD), and the hypotheses were tested using analysis of covariance (ANCOVA) at a significance level of 0.05. In our quasi-experimental study, ANCOVA was chosen due to its ability to control for pre-existing differences between groups using covariates, ensuring a more accurate assessment of the treatment effect while increasing statistical power. Decision: If the probability value (p) is less than or equal to 0.05 (p < .05), reject the hypothesis. If p > .05, do not reject the hypothesis.

4 Results

In Table 2, the mean achievement scores of learners in the experimental and control groups are presented. Students in the experimental group demonstrated a mean achievement score difference of 23.73, as calculated from pretest mean scores of M = 60.85 (SD = 7.47) and posttest mean scores of M = 84.58 (SD = 11.33). In comparison, the control group exhibited pretest scores of M = 61.33 (SD = 7.61) and posttest mean scores of M = 64.15 (SD = 8.77), resulting in a mean gain difference of 2.82. The analysis indicates that students in the experimental group attained higher mean achievement scores than those in the control group.

The findings are presented in line with the research questions and hypotheses.

RQ 1

What are the achievement scores of learners who received math instruction using the blended learning approach versus those in the control group?

Table 2 Achievement mean scores of learners in the EXP and CG in both the pretest and posttest
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HO1

No statistical difference exists between the achievement scores of learners who received math instruction using blended learning versus those in the control group.

Table 3 presents the ANCOVA results, illustrating the disparity between the achievement scores of students in the experimental group exposed to blended learning and their counterparts in the control group exposed to traditional instruction. The analysis revealed a significant main effect for treatment groups (F(1, 89) = 107.737, p = .000). Given that the p-value (0.000) is below the predetermined significance level of p < .05, the null hypothesis positing no significant difference is rejected. Consequently, we conclude that students in the experimental group demonstrated significantly better achievement scores than students in the control group, who received conventional math instruction. Moreover, the analysis indicated a substantial effect size, as reflected by a partial eta squared value of 0.548. This signifies that the blended learning strategy accounted for a noteworthy 54.8% difference in learners’ achievement scores.

Table 3 Analysis of Covariance (ANCOVA) of the difference in the achievement scores of learners
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RQ 2

What are the achievement scores of male and female learners who received math instruction using the blended learning approach versus those in the control group?

In Table 4, the analysis of achievement scores among male and female learners who received math instruction through the blended learning approach, as compared to a control group, notable gender-specific differences emerged. In the experimental group, male learners demonstrated a pretest mean score of M = 61.63 (SD = 6.85) and posttest mean scores of M = 82.81 (SD = 12.54), resulting in a substantial mean gain difference of 21.18. Conversely, female learners exhibited a pretest mean score of M = 59.86 (SD = 8.27) and posttest mean scores of M = 86.86 (SD = 9.37), yielding a noteworthy mean gain difference of 27.00. These findings indicate that, on average, female learners in the experimental group achieved a higher mean score in the posttest compared to their male counterparts. In the control group, male learners displayed a pretest mean score of M = 64.59 (SD = 8.65) and posttest mean scores of M = 69.05 (SD = 8.39), resulting in a mean gain difference of 4.46. Female learners in the control group had a pretest mean score of M = 58.33 (SD = 5.05) and posttest mean scores of M = 59.67 (SD = 6.51), yielding a mean gain difference of 1.34. Comparatively, both male and female learners in the control group exhibited smaller mean gain differences compared to their counterparts in the experimental group. A between-group comparison reveals that male learners in the experimental group demonstrated a significantly higher mean gain difference (21.18) than those in the control group (4.46). Similarly, female learners in the experimental group exhibited a substantially higher mean gain difference (27.00) compared to their counterparts in the control group (1.34). These results suggest that the blended learning approach had a more positive impact on both male and female learners’ achievement scores than traditional instruction in the control group.

Table 4 Achievement scores of male and female learners in experimental and control groups
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HO2

No statistical difference exists between the achievement scores of male and female learners who received math instruction using the blended learning approach versus those in the control group.

Hypothesis 2

was evaluated within the context of the ANCOVA results displayed in Table 3. The analysis of disparity between the achievement scores of male and female students in the experimental and control groups revealed a non-significant effect for gender (F(1, 89) = 0.910, p = .343), thereby failing to reject the null hypothesis. However, a significant interaction effect between Gender and Group was observed (F(1, 89) = 9.908, p = .002), suggesting that the relationship between gender and math achievement scores is not uniform across different instructional groups. While there may not be an overall difference between male and female students in terms of achievement scores, the significant interaction effect highlights the importance of considering instructional group differences in understanding the nuanced relationship between gender and math achievement outcomes. Further analysis revealed that within the blended learning group, female students exhibited significantly higher mean gain differences compared to male students (see Table 4), contributing to the observed interaction effect. Therefore, we draw the conclusion that the achievement scores of male and female students who received maths teaching utilising the blended learning strategy significantly differ from one another.

RQ 3

What are the retention scores of learners who received math instruction using the blended learning approach versus those in the control group?

In Table 5, the mean retention scores of learners in both the experimental and control groups are presented. The mean gain difference for learners in the experimental group was calculated as 2.62, derived from pretest scores of M = 84.58 (SD = 11.33) and posttest scores of M = 81.96 (SD = 11.95). In contrast, learners in the control group exhibited a pretest score of M = 64.15 (SD = 8.77) and a posttest score of M = 56.43 (SD = 6.54), resulting in a mean difference of 7.72. The findings suggest that learners in the experimental group retained information more effectively, as evidenced by higher mean retention scores compared to their counterparts in the control group.

Table 5 Retention mean scores of learners in the EXP and CG groups in both the pretest and posttest
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HO3

No statistical difference exists between the retention scores of learners who received math instruction using blended learning versus those in the control group.

Table 6 presents the results of an ANCOVA examining the differential retention scores between learners in the experimental group, instructed through blended learning, and their counterparts in the control group that received conventional instruction. A significant main effect for treatment groups was observed (F(1, 89) = 51.207, p = .000). Given that the p-value (0.000) is below the predetermined significance level of p < .05, the null hypothesis positing no significant difference is rejected. Consequently, it is concluded that a substantial difference exists in the retention scores of learners who underwent math instruction using blended learning compared to those who experienced the conventional approach in the control group. This distinction favours learners in the experimental group. Further analysis revealed a significant effect size, as indicated by a partial eta squared value of 0.365. This result suggests that the blended learning approach had a notable and singular influence, accounting for 36.5% of the variance in learners’ retention scores. This significant effect size underscores the practical significance of the difference observed in retention scores, further supporting the conclusion that learners in the experimental group, who underwent math instruction through blended learning, exhibited higher retention scores compared to their counterparts in the control group.

Table 6 Analysis of Covariance (ANCOVA) of the difference in the retention scores of learners
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RQ 4

What are the retention scores of male and female learners who received math instruction using the blended learning approach versus those in the control group?

The analysis of Table 7 reveals the retention scores comparing the effectiveness of a blended learning approach versus conventional instruction outcomes for male and female learners in both the experimental and control groups. In the experimental group, male learners displayed a posttest mean score of M = 82.81 (SD = 12.54) and a retention mean score of M = 77.48 (SD = 13.05), resulting in a mean difference of 5.33. Conversely, female learners in the experimental group exhibited a posttest mean score of M = 86.86 (SD = 9.37) and a retention mean score of M = 87.71 (SD = 7.25), yielding a mean difference of 0.85. These findings indicate that, on average, female students in the experimental group achieved slightly higher mean retention scores compared to their male counterparts. In the control group, male learners demonstrated a posttest mean score of M = 69.05 (SD = 8.39) and a retention mean score of M = 57.18 (SD = 6.75), resulting in a mean difference of 11.87. Female learners in the control group exhibited a posttest mean score of M = 59.67 (SD = 6.51) and a retention mean score of M = 55.75 (SD = 6.42), yielding a mean difference of 3.92. Comparing the experimental and control groups, male learners in the control group experienced a significantly higher mean difference in retention scores (11.87) compared to those in the experimental group (5.33). Similarly, female learners in the control group showed a higher mean difference in retention scores (3.92) compared to their counterparts in the experimental group (0.85). These findings suggest that, on average, both male and female learners in the experimental group retained more knowledge than their counterparts in the control group. In addition, female students in the experimental group attained higher mean retention scores compared to their male counterparts.

Table 7 Retention mean scores of male and female learners in experimental and control groups
Full size table

HO4

No statistical difference exists between the retention scores of male and female learners who received math instruction using the blended learning approach versus those in the control group.”

The ANCOVA results presented in Table 6 were examined to assess the difference in retention scores between male and female students in the experimental group who received math instruction through blended learning, as opposed to those in the control group that underwent the conventional instruction. The results indicated a statistically significant effect for Gender (F(1, 89) = 9.828, p = .002). Given that the p-value (0.002) is below the predetermined significance level of p < .05, the null hypothesis positing no significant difference is rejected. Consequently, we conclude that male and female students in the experimental group demonstrated significantly higher retention scores than their pairs in the control group. In conclusion however, the analysis reveals that, contrary to the null hypothesis, a notable disparity exists between male and female students who received math instruction using the blended learning approach, with female students exhibiting higher retention scores.

5 Discussion

This study aimed to determine the effect of the blended learning approach on secondary school learners’ achievement and retention in mathematics. The findings showed that the blended learning approach is effective in enhancing learners’ achievement in mathematics compared to the conventional approach to teaching. However, when hypothesis one was put to the test, it was discovered that there was a significant difference in the achievement scores of students who received math instruction through blended learning compared to their peers who received math instruction via the conventional means, favouring the students who used the blended learning approach. This implies that the blended learning approach effectively enhanced learners’ achievement in mathematics. The reason for improving learners’ achievement could be in their active participation in small group discussions and collaborative activities. The observed improvement in secondary school students’ mathematics achievement through blended learning aligns with similar findings in studies by Indrapangastuti et al. (2021), Makkar and Sharma (2021), Lin et al. (2017), and Tong et al. (2022). These studies, conducted in diverse contexts such as Malaysia, India, Taiwan, and Vietnam, consistently reported enhanced mathematics achievement with the blended learning approach compared to conventional methods. The convergence of findings across different regions and educational settings highlights the robustness and transferability of the blended learning approach. Overall, our study contributes to the growing body of evidence supporting the effectiveness of blended learning in improving mathematics achievement among secondary school students, holding implications for educators and policymakers seeking to optimize instructional strategies in mathematics education.

The study’s findings showed a no significant difference between the achievement scores of male and female learners who received maths instruction using blended learning approach and those that received math instruction using the conventional method. However, a significant interaction effect between gender and instructional methods was observed. Further analysis revealed that within the blended learning group, female students exhibited significantly higher mean gain differences compared to male students, contributing to the observed interaction effect. The presence of this significantly higher mean gain differences of the female learners over their male counterparts in utilizing the blended learning strategy during the mathematics learning process could be related to the comparable involvement and participation of the female learners over the male learners. Another reason for boosting the female learners’ mathematics achievement in the concepts taught could be that the blended learning approach is student-centred, enabling the female learners to construct more knowledge and facts than the males. Our study’s findings regarding gender influence in blended learning are not consistent with Awosdeyi et al. (2014), affirming equal benefits for both genders. Contrary to Awosdeyi et al., our results align with Lin et al.‘s (2017) research, which suggests a gender difference in the effectiveness of blended learning. However, a notable contradiction arises with Lin et al.‘s study, where they reported greater gains for males. This difference may be attributed to varying levels of persistence and commitment. While our study underscores the inclusivity of blended learning, the observed discrepancy highlights the complexity of factors influencing educational outcomes based on gender. Furthermore, the identified discrepancy serves as a catalyst for future research, prompting a deeper exploration of gender dynamics in blended learning. This, in turn, can inform the development of targeted and inclusive instructional strategies that recognize the diverse factors influencing educational outcomes. Overall, our study contributes valuable knowledge that can guide educators, policymakers, and researchers in optimizing blended learning practices for the benefit of a broad spectrum of students.

The findings revealed that the blended learning approach boosted learners’ retention in mathematics compared to the conventional approach. However, hypothesis three was tested and revealed a significant difference between the retention scores of learners who received math instruction utilising blended learning and their contemporaries who obtained math instruction through the conventional approach, favouring learners in the experimental group. This implies that the blended learning approach effectively enhanced learners’ retention in mathematics. The reason for enhancing learners’ retention could be that the learners’ abilities were sustained through the activities embedded in the blended learning approach. The observed positive impact of blended learning on students’ retention in science-related subjects aligns cohesively with findings from Sivakumar and Selvakumar (2019), Olatunde-Aiyedun and Adams (2022), and Suleiman et al. (2017). Each of these studies independently supports the notion that the blended learning approach contributes significantly to enhancing students’ retention in the realm of science education. The collective alignment of our study’s findings with these research endeavours reinforces the robustness of the conclusion that blended learning significantly contributes to improved retention in science-related subjects. This consistency across diverse geographical and educational contexts underscores the broad applicability and effectiveness of blended learning strategies in promoting long-term understanding and retention of scientific concepts, particularly geometry.

Furthermore, the finding revealed that male and female learners in the experimental group had higher retention in mathematics than their counterparts in the control group. Nonetheless, further analysis in testing hypothesis four showed a significant difference in retention scores between male and female students who received maths instruction utilising both methods, favouring the male and female students that utilised the blended learning approach. However, in the realm of the blended learning approach, the finding showed that female learners attained higher mean retention scores more than their male counterparts. The difference might be that the female students showed a greater passion for the activities embedded in the blended learning approach during the mathematics instruction process than the male learners. Nonetheless, the finding of this study contradicts the result of Sivakumar and Selvakumar (2019), who revealed that male and female students retained the physics concept equally when the blended learning approach was utilised. The observed contradiction between our study and Sivakumar and Selvakumar’s (2019) findings on gender-based retention through blended learning highlights the intricate nature of gender dynamics in science education. While their study reported equal retention for both genders, ours indicates a difference, with females showing higher mean retention scores. Possible factors contributing to this disparity include variations in instructional design, content delivery, and cultural context. This emphasizes the nuanced understanding needed when interpreting results in the context of blended learning and science education.

6 Conclusion

Using the blended learning strategy greatly improved students’ mathematical achievement and retention. This was observed in the mean achievement and retention scores of learners in the experimental group, which were higher than their pairs in the control group. Furthermore, a significant difference exists between the achievement scores of male and female students who received math teachings utilising the blended learning approach and those that utilised the conventional approach. This suggests that both male and female students did not benefit equally from the blended learning approach in enhancing their achievement in mathematics. These results suggest that the effectiveness of the blended learning, may be influenced by gender, necessitating a more tailored approach to address the specific needs of male and female students within these contexts. Accordingly, a significant difference exists between the retention scores of male and female learners who received math teaching utilising both methods, favouring male and female learners that utilised the blended learning approach. This research makes an important contribution to mathematics education because it is the first to investigate how implementing the blended learning approach in the Uzo-Uwani LGA impacts learners’ retention and achievement in mathematics. This investigation is also the first to report gender differences in learners’ retention of mathematics concepts using blended learning, favouring female learners. The research also demonstrates to experts in mathematics education exactly how the blended learning strategy might aid students in improving their achievement and retention in mathematics, especially regarding geometry.

6.1 Limitation

This study has limitations. While the study’s positive findings suggest the effectiveness of the blended learning approach, it is important to recognize the potential influence of a novelty effect due to the newness of the instructional method. Future research should explore the sustainability of these positive effects over time. Additionally, concerns about the sampling technique, involving purposive selection from schools with specific facilities, may introduce biases. Acknowledging this limitation, future studies using more diverse sampling methods could enhance the generalizability of findings across different student populations. This study did not consider potential differences in the skills of mathematics teachers, including teaching style and experience, which may have influenced retention scores. Teacher-related factors were not explicitly measured or controlled for, and addressing these variables in future research could enhance the understanding of the impact of instructional strategies on student outcomes. Lastly, while no significant gender differences were found on average, the presence of a significant interaction effect underscores the intricate interplay between gender and instructional methods, emphasizing the need for a nuanced understanding of these dynamics. Future research could explore the specific instructional strategies within blended learning that contribute to gender differences, allowing for a more targeted and nuanced understanding of how instructional methods interact with gender in influencing academic outcomes.

6.2 Recommendations

Based on the findings and conclusions of this study, the following recommendations were proposed:

  1. 1.

    Educational institutions are encouraged to embrace the blended learning approach, making it an integral part of mathematics education. This method, proven to enhance both students’ achievement and retention, holds great potential for creating a dynamic and impactful learning environment within secondary schools.

  2. 2.

    To facilitate the seamless integration of blended learning, a key priority should be providing mathematics educators with comprehensive professional development. This involves empowering teachers through training sessions that cover essential skills, including crafting engaging online content and orchestrating collaborative activities.

  3. 3.

    There is a critical need to champion inclusive practices within the blended learning framework at the secondary school level. Recognizing diverse learning needs, it is imperative to underscore that both male and female learners can equally benefit from this approach, contributing to an overall improvement in mathematics achievement and retention.

  4. 4.

    As part of a comprehensive strategy tailored for secondary education, secondary schools are encouraged to gradually incorporate successful elements derived from blended learning into the standard mathematics curriculum. This deliberate integration ensures sustained benefits, fostering continual improvement in student outcomes over an extended period within the specific context of secondary education.