Elementary math class in face-to-face,fully online,and flipped mode: A comparative study on students’ achievement and satisfaction

Abstract

Excellent certificates are not enough to make excellent teachers rather, teaching demands constant insight, reflection, and suitable pedagogy. Determining the best pedagogical method of course delivery plagues faculty members and schools across the globe. This paper reports on an investigation and outcomes of a comparative study of three different methods of course delivery offered for the same course in an Indian elementary school before the COVID-19 pandemic. The study followed a Design-Based Research (DBR) approach. Comparisons have been made to the collected quantitative data from each teaching method-face-to-face, blended flipped, and fully online-in respect of students’ learning achievement and satisfaction. Findings revealed that participants in the face-to-face group achieved better than the rest two groups. However, students in the flipped group reported better satisfaction with the course than in the other two modes, and it happened within 8 weeks. These results offer implications for selecting the best method of course delivery for elementary mathematics even in unequipped schools, echoing an insight for practice to add effectiveness to the delivery mode.

Keywords

Face-to-face flipped fully online elementary math achievement satisfaction

Introduction

Albert Einstein, the icon of wisdom and imagination, once said mathematics is, in its way, the poetry of logical ideas (Albert Einstein Quotes, n.d.). Elementary mathematics has a huge role to play in the growth of a child’s mind since mathematics is a fundamental part of human thought and logic, and integral to attempts at understanding the world and ourselves (Bej et al., 2019). The authors pointed out that mathematics provides an effective way of creating the music of reason that encourages logical reasoning and mental rigor. Besides mathematical knowledge base helps in better understanding the contents of other school subjects as well like science, social studies, music, and even art (Yeh et al., 2019). A strong foundation in mathematics is important for students to be prepared for the higher classes, especially for those students having a significant breach in their math performance and achievement (Rockoff and Lockwood, 2010). But the question arises which should be the most effective approach to teach mathematics in elementary classes among in-vogue practices: a face-to-face class using the traditional lecture method (F2F), a fully online class taught asynchronously (FO), and a blended flipped class taught in a hybrid setting (TF). The flipped model has recently been used in various subject disciplines with respectable outcomes like medical education (Lin and Hwang, 2018), mathematics (Lo and Hew, 2017), and language (Lo and Hwang, 2018). But is it equally good for elementary students? Will it be effective for students who used to get a very sparse scope for technology-integrated pedagogy? Which method of course delivery is the most satisfying for these students? This study is an exploration for finding an answer to these questions.

Face-to-face learning paradigm

A face-to-face class follows the lecture method grounded in behaviorism which purports that pupil can learn by observing the teachers’ behaviors and replicating the behaviors they observed (Zhou and Brown, 2015). J. B. Watson (1878–1958) and B. F. Skinner (1904–1990) are the two chief exponents of behaviorist approaches to learning (Psychology Department, 2017) that assume individuals acquire knowledge through observation and repetition of the desired behavior. Rewarded responses are the key element to this learning theory that means the desired response must be rewarded for learning to take place (Parkay and Hass, 2000). The role of the instructor is to model the desired behavior, while the role of the student is to internalize the modeled behavior and regurgitate that behavior when necessary. But the renowned educationist John Dewey (1938) outlined many shortcomings of this paradigm of teaching-learning including making learners passive and learning non-interactive, one-way, and uninteresting. In conclusion, the flaws of the lecture method may depend upon inadequacies in the preparation, presentation, and structure of a particular lecture rather than upon the lecture method per se (Grabe and Christopherson, 2005). Samuel Johnson pointed out in 1766, “people have got a strange opinion that everything should be taught by lectures that were once useful but now when all can read, the books are so numerous, lectures are unnecessary” (Kaur, 2011: 122). Besides this method has been severely criticized for being orthodox, teacher-centered, non-interactive, non-innovative, and subjected to a hard time and space limitations (Wofford et al., 2001). Here from the journey for an alternative and interactive method starts.

Online learning paradigm

Gone are the days of lecturing, prescribing syllabi, and waiting in one’s faculty office for the assignments to be submitted. This age of specialization demands teachers to understand their students holistically that is the root of phenomenological pedagogy, the heart of teaching (Schoone, 2020). This notion of student-centered flexible education has found a beautiful reification through online learning which refers to network-enabled teaching-learning allowing learners to interact with content, teacher, and other learners (Mukhopadhyaya, 2021). It involves the implementation of advanced technology to direct, design, and deliver the learning content, and to facilitate two-way communication between students and faculty for optimizing human learning, shaping lifelong self-learners by mastering the art of learning in an ever-changing world of knowledge (Thanji and Vasantha, 2016). According to Szparagowski (2014), the teachers and students find online learning as a flexible and effective source of teaching and learning as most of them agreed upon the fact that this helps in distance learning with easy administration and accessibility along with less use resource and time. “Online learning relates to the constructivism (Keis et al., 2017) that posits knowledge acquisition occurs amid four assumptions: learning involves active cognitive processing, learning is adaptive, learning is subjective, not objective, learning involves both social/cultural and individual processes” (Doolittle and Hicks, 2003). Creating a meaningful learning environment is celebrated here where the teacher gives many opportunities to the students to express their understanding and the application of the learning in an immediate meaningful way (Kundu, 2021). Technology-enabled learning could bring a good output if technology integration has been effective (Kim et al., 2014). This integration means a cultural shift-from teacher to learner, from information to exploration, cognitivism to constructivism, and from imposed regulation to self-regulation (Mukhopadhyaya, 2021). Regardless of time and place limits, students can easily access the learning material online which encourages self-paced and self-regulated learning that puts it over face-to-face teaching (Fuller, 2021). The students also become self-directed learners which is an important competency for encouraging lifelong learning (Kim and Jang, 2015). In the traditional approach to teaching, students are often exposed to the material and shown how to solve problems during an in-class lecture hence the amount of classroom time remaining for students to engage in active learning, through practicing problem-solving, is therefore very limited, and students are usually asked to do this for homework after class (Adams et al., 2017) and they’re also students frequently struggle with problem sets assigned for homework (Jensen et al., 2015).

Limitations with the online learning paradigm are also palpable. Infrastructural issues relating to scarcity of attitude, skill, and devices among stakeholders are a vibrant restraint of online learning especially in the context of developing countries (Kundu and Dey, 2018; Kundu et al., 2022). Another typical dilemma with online learning programs is that they are isolated and too separated from the participants’ reality, while online learning materials can help participants cram theoretical concepts into their minds, these learnings often lack context, and without context new information especially among elementary students does not stick (Lo and Hwang, 2018). Here blending could be a viable option imbibing both methods-traditional and online.

Flipped learning paradigm

Flipped learning design is a prominent sub-type of Blended Learning aiming at progressive convergence of traditional face-to-face and computer-mediated instruction (Graham, 2006). It’s been “the thoughtful fusion of face-to-face and online learning experiences” (Garrison and Vaughan, 2008: p. 5) with the objectives to add to the pedagogical richness, access to knowledge, social interaction, personal agency, cost-effectiveness, and ease of revision (Osguthorpe and Graham, 2003). Cleveland-Innes and Wilton (2018) asserted blending has its theoretical base in the Community of Inquiry (CoI) model that assists teachers to adopt constructivist design-based (Dewey, 1938) approaches and reflect on decisions taken to provide an authentic learning experience in their contexts. They further said the “flipped” classroom approach has four main pillars -flexible environment, learning culture, intentional content, and professional educators-that seems an ideal way to free up additional class time for active learning through problem-solving. To quote Flipped Learning Network (2014) it is a “pedagogical approach in which direct instruction moves from the group learning space to the individual learning space, and the resulting group space is transformed into a dynamic, interactive learning environment where the educator guides students as they apply concepts and engage creatively in the subject matter.” As its name denotes in the flipped classroom the learning process is “flipped” and instead of spending entire periods watching a lecture, students watch lectures online outside of class time and use class time to do activities where they get a teacher as an expert facilitator for solving doubts (Kundu and Bej 2022).

Flipped learning design was first proposed by two school teachers Jonathan Bergmann and Aaron Sams (2012) in their book: Flip your classroom: Reach every student in every class every day (2012) that speaks the language of today’s students, helping struggling students, allowing students to pause and rewind their teacher, increasing student-teacher interaction, allowing teachers to know their students better, bringing better classroom management, better students achievement, and it is a great technique for absent teachers. Lo and Hew (2018) stated flipped design is based on two main theoretical propositions-first, Merrill’s (2002) First Principles of Instruction Design and second, the Self-determination Theory of Motivation of Ryan and Deci (2000). The first principles of instruction (Merrill, 2002) asked for five principles to promote learning-problem-centered, activation, demonstration, application, and integration (Figure 1). Self-determination theory (Ryan and Deci, 2000) reported autonomy, competence, and relatedness are the three inherent psychological requirements of human beings that need to be satisfied to motivate and engage pupils (Fredricks et al., 2004).

Figure 1.

First principles of instruction (in Merrill, 2002).

In the flipped approach, basic factual information can be provided before class time (e.g. through online lectures), and then classroom time can be used as an active-learning environment like involving group work on problem sets, case studies, and discussion (Fuller, 2021; Jdaitawi, 2021; Jensen et al., 2015; Kastner, 2020; Kazakoff et al., 2017; Love et al., 2014; Shahabadi and Uplane, 2015; Tune et al., 2013; Yen, 2020). This approach replaces homework assignments with alternative forms of direct instruction such as Video Lectures, PowerPoint Presentations, or Reading Assignments to expose the students to new concepts outside of the classroom (Adams et al., 2016; Bergmann and Sams 2012; Kuiper et al., 2015; Szparagowski, 2014; Gariou-Papalexiou et al., 2017; Tay and Wang, 2016). It follows Revised Bloom’s Taxonomy (Anderson and Krathwohl, 2001) where the lower level of cognitive works take place before class as presented in the pyramid in Figure 2. When students come to class, they can engage in higher cognitive levels of learning with the presence of peers and facilitators.

Figure 2.

How flipped modes helps in revised Bloom’s Taxonomy (Source: Authors).

The flipped classroom has become increasingly popular in the past few years (Adams et al., 2016). It has begun to revolutionize the way students receive information from their teachers ushering in a new era of active and creative thinkers (Roach, 2014), opportunities for self-paced learning (Jacot et al., 2014), complement traditional collegiate classroom (Chen and Line, 2012; Freeman et al., 2014), improved student’s learning experience and achievement (Kim et al., 2014; Vidic and Clark, 2016), and assisting struggling students (Love et al., 2014; Tune et al., 2013). Several other articles relating flipped model suggest that the students taking the flipped course performed significantly better than students enrolled in courses using the traditional method of instruction (Castedo, 2019; Lo and Hew, 2018; Nielsen, 2018; Phillips and Phillips, 2016; Winquist and Carlson, 2014). Few other studies assert that it can improve student learning by allotting more class time for faculty to address misconceptions while the student is working through an activity, and not days later when assignments are graded and returned (Castedo, 2019; Chen and Line, 2012; Lo and Hew, 2017; Nielsen, 2018; Phillips and Phillips, 2016; Wilson, 2013; Winquist and Carlson, 2014). However, some educators resist flipping the classroom because of students’ perceptions that they are teaching themselves (Kuiper et al., 2015). A mathematics class in flipped mode is found more effective than traditional F2F delivery mode (Chen et al., 2017; Fazal and Bryant, 2019; Greer at al., 2014). However, hesitations are also available for example Jensen et al. (2015) pointed out literature supporting the effectiveness of the flipped approach, which mostly consists of surveys, case studies, and reports, and very few quantitative studies have been described that directly compare the flipped and non-flipped approaches when all other components (instructor, materials, assessments, etc.) are kept constant. Lo and Hew (2018) said to extend our understanding of flipped learning more comparative studies are required in different contextual perspectives. This demands more investigation into its potential strengths especially at the elementary classes in underdeveloped classrooms wallowed in teacher-dominated pedagogy and the current study moved to cater to this demand.

Rationale of the study

The purpose of this study is to compare the performance of elementary students enrolled in the same course using three different instructional methods namely traditional face-to-face (F2F), fully online (FO), and blended flipped (BF). In each section, the faculty used the same instructional content, forms of assessment, the scale for grading, and student evaluation survey. Data was collected from each of these sections and evaluated using statistical methods. This data has become particularly valuable due to the COVID-19 pandemic has started affecting schools across the world bringing online learning into the limelight (Kundu and Bej, 2021). Most schools have shut down their operations and steered away from face-to-face teaching to online, an altogether new experience for many of them. Now necessary measures need to be taken on the demarcated areas for improving digital education in marginal socioeconomic households who were significantly disadvantaged during the COVID-driven virtual education scheme. Freeman et al. (2014) compared active learning with the traditional lecture format and suggest research needs to be focused on determining how best to teach with active learning? What could be the relationship between the amount of time spent in active learning and student success? Adams et al. (2016) asserted the use of active learning in the classroom was equally effective whether the entire class period or just a fraction of it was devoted to active learning and conclude “there was no main effect of gender, major, or ethnicity, on success in the whole cohort or either section (p. 21)”. In this context, an investigation into the possible effects on the three very popular modes of course delivery and outcomes having empirical bases will be helpful for all concerned especially in the context of developing countries like India.

To focus on the insights for practices the researchers followed a designed-based research (DBR) approach here since the normal school environment was not suitable for the operation of online or blended learning and to showcase the practice. Researchers worked hand-in-hand with the teachers to conduct this study. This paper will discuss the teaching methods used and the findings from the data collected, in addition to that, the authors aimed to ascertain the level of students’ satisfaction among the three groups witnessing three different modes of educational delivery. The following two research questions (RQ) guided the study:

RQ.1: Which teaching method yields the highest student achievement?

RQ.2: Which teaching method best fosters students’ satisfaction?

Methodology

The study followed the Designed Based Research (DBR) method. Blending in learning is exceedingly complex (Fazal et al., 2019) and it becomes more challenging when there has been an acute shortage of teachers’ technological knowledge, pedagogical readiness, digital contents, and techno-equipment (Kundu et al., 2020). The school, cite for this study was a poor performer in all these aspects, it appeared very challenging for the researchers to introduce the research set up (Kundu et al., 2022; Kundu and Bej, 2022). Still, they made this possible with the affable help from the teachers and parents of those little participants without whom this study would not have realized, in other words, researchers and teachers worked together to make this study possible that was the main point to be called it a DBR. Armstrong et al. (2020) pointed out in an educational setting, DBR is a research approach that engages in iterative aspects to develop knowledge that improves educational practices that originated because some researchers believed that traditional research methods failed to improve classroom practices. It welcomes researchers as agents (Kundu et al., 2021a) of change and research subjects as collaborators, produced both new designs and theories, and consisted of an iterative process of design and evaluation to develop knowledge (Kundu et al., 2021b). Simply, DBR helps researchers address design problems (Siko and Barbour, 2016). DBR occurs in real settings with the cooperation between teachers and researchers, employs mixed methods, operates in periods of designing, implementing, and adjustment; and relies on team reflection and decision-making (Anderson and Shattuck, 2012).

Sites and participants

This study took place at one of the elementary schools in the state of West Bengal in the Eastern part of India, representing the country in numerous aspects, having high population density, low educational penetration in rural areas, low women education rate, poor quality of education, schools having a very poor pool of educational infrastructures, bopping rote learning, and overcrowded classrooms with teacher dominated age-old pedagogies. The selected school hosted 1148 students total in Grades 5–10; a bigger part of them (75%) belong to BPL (below poverty line) families under the control of 15 teachers (10 males and five females). All available 200 children (150 boys and 60 girls) in the fifth-grade class (10–11 years of age) were chosen as samples and they were randomly allotted into three groups. There was a total of 50 students in the face-to-face class (F2F), 100 in the fully online (FO) class, and 50 in the blended flipped (BF) class. Out of 15 teachers, three specialized mathematics teachers participated in this study to deliver the specific course contents among students of three separate groups developed by the researchers. All three teachers delivered for all three groups following a specific routine so that each teacher had an equal number of classes with each group of students to reduce the effects of teaching quality variable as minimal as possible.

Design

The study was conducted in between 10^th January to 10 March 2020, just before the sudden outbreak of COVID-19. Three homogenous groups of students (in respect of learning achievement and satisfaction) were taught the same content from the first unit of fifth-grade mathematics in three different modes- F2F, FO, and BF. For each course section, the faculty designed very consistent syllabi. The course content covered five sections- LCM and HCF, Fractions, Percentages and Decimals, Geometry (Square and Rectangle), and Decimal Multiplication. The classes were held on every official working day during school hours and beyond school hours by the three teachers on their own under the strict supervision of the three researchers. To minimize the teaching variances all three teachers were allowed to take classes in three modes following a particular routine each teachers had equal number of classes.

The first group received instruction in the traditional lecture method (F2F). Conventionally, mathematics instructors present concepts and procedures to their students using the lecture method. This group of participants received direct instruction most of the time followed by a set of homework problems the students had to complete to gain mastery of the concepts presented in the lesson (Bergmann and Sams, 2012; Eggen and Kauchak, 2006). The homework assignments for each of the chapters were available after each of the face-to-face meetings. The faculty required the completion of the homework for each of the sections before students could jump to the next section. This being the prevalent mode teachers didn’t face much difficulties here.

The second group received instruction in the fully online class (FO) in the asynchronous mode that refers to interactions taking place at different times, not in real-time (Graham, 2006). The researchers arranged a Learning Management System (LMS) to give the students access to instructional materials. Instead of face-to-face lectures, the instructor posted PowerPoint presentations and Online Videos created for students to access at their convenience. The faculty did not require the students to travel to campus to attend the class sessions, however, students had the option to visit the classes if they wished. The online students received the same assignments and assessments administered to the students enrolled in the face-to-face course, however, the online students completed the assignments and assessments online without proctoring. Since this was not a normal practice of the school, three teachers were training beforehand and researchers helped in the content development and online delivery.

The third group received instruction in the blended flipped (TF) model built on Merrill’s (2002) first principles of instruction. For pre-class learning activities included-activation, demonstration, application. To activate students towards learning their prior knowledge was recalled with revision videos. They were demonstrated with the content roughly through instructional videos. Online follow-up exercises and quizzes were provided to them to apply their knowledge. To structure their whole learning experience in-class learning activities contained all five principles of Merrill’s (2002) first principles of instruction (stated earlier in the literature). To make learning problem-based students were engaged in solving real-world problems. Short reviews and quizzes were there to make students active in in-class activities. Students’ queries were resolved with mini-lectures and demonstrations. New problems were given to apply their knowledge. During prob-solving collaboration and student-student interactions, the group works, integrations were focused. Throughout the process, sustained feedbacks were provided to indicate their progress over time. For the flipped group, the faculty held one class session in person each week. The faculty posted PowerPoints and videos online and asked students to learn the material, complete the homework and attempt to complete the quizzes online before that week’s class session. If a student performed well on the quiz, they were not required to attend the class that week. If a student did not perform well on the quiz, they were expected to come to class to ask questions and receive additional instruction, before retaking the quiz in the class to improve their grade. The weeks containing exams and the final had mandatory attendance in the class to complete the proctored assessments.

Procedures

The classes were conducted by the three teachers under the supervision of the researchers for 2 months. Three teachers were specially trained and equipped for the type of class he was assigned to teach. These 2 months’ time-frame was stipulated by the School Governing Body for this study as they did not want longer alien interference in their normal school operations. The quantitative data were collected through achievement tests and satisfaction tests conducted at the end of the study by the eighth week. The tests were conducted twice at the beginning and the end of the study. The researchers prepared a computerized educational program, designed LMS, PowerPoints, Online Videos for the selected content units, and also provided necessary equipment supports to the participants that is the specialty of a DBR.

Tools

Achievement Test. The researchers prepared an achievement test to measure the level of students’ achievement at three different groups and the effectiveness of digital interference in improving students’ achievement in mathematics. The test in its final form consisted of 30 multiple-choice questions (6 from each section). Each item of the questions was given one mark for the correct answer and zero for the wrong answer; the maximum mark of the test was 30 and the testing time was 50 min. This tool was confirmed by the virtual validity method for the test by presenting it in its initial form with a list of behavioral objectives, to 10 members of the teaching staff of universities, all of whom were doctorates in curricula development and methods of teaching science and mathematics. The content was adjusted according to their recommendations. The researchers verified the reliability of the achievement test by using the test-retest method. The test was applied to a sample not included in the sample of the study, and 2 months after the test was reapplied to the same sample of fifth-grade students. After that, Pearson’s correlation coefficient between the two applications was calculated. The total reliability coefficient of 0.91 was considered satisfactory and appropriate to serve the purposes of this study.

Students’ satisfaction scale. To address the second research question and determine the students’ level of satisfaction with the course, a Likert-type scale survey was administered to the participants before the final exam to minimize the likelihood that students’ performance will influence their answers, but late enough in the semester so students had experienced much of the course to be able to form an opinion. Five items were designed to assess students’ satisfaction with the course with five possible answers (1) strongly agree, (2) agree, (3) neutral, (4) disagree, (5) strongly disagree. The first item was: “I am satisfied with this mode of teaching-learning”. The second item stated: “The course assignments/classwork are arranged in a clear logical and orderly manner”. The third item purported: “The course increased my interest in the subject”. The fourth item stated: “I would recommend that the current teaching approach in this course continue to be used”. The fifth item was: “I am satisfied with the cordiality of my teachers in this particular learning mode.” The lowest possible score was five and the highest was 25. The higher score indicated a higher level of satisfaction. This scale was also standardized following the same method as the earlier scale. The reliability coefficient for this scale was 0.85 which was acceptable as per the rule of thumb.

Data collection and analysis

Researchers collected data carefully from each participant of the three different sections concerning two variables-achievement and satisfaction. The allied data were collected at two stages for both variables-at the beginning, termed as a pre-test stage, before the experiment formally started to note the state of homogeneity among participants, and at the end, named as a post-test stage, to jot down the changes after experimentation. The study could have named a quasi-experimental design bit the researchers preferred to name it DBR since researchers acted as the agents of change and were actively involved in the whole process to accost the changes, a prominent characteristic of the design study. To address the first research question and determine whether a significant difference in students’ learning achievement exists among the three groups, the researchers performed a one-way analysis of variance (ANOVA) at two stages using Statistical Package for the Social Sciences (SPSS). The final grade for the course was calculated based on the requirements stipulated in the syllabi. To ascertain which of the three cohorts performed better in the course, the final ANOVA was followed by post-hoc analysis which is customary (Kundu et al., 2022). Regarding the second research question, to assess the satisfaction level of the students participating in three modes of course delivery corresponding ANOVAs and post-hoc analysis was also conducted.

Results relating to RQ1

Before the experimentation starts the homogeneity of the students’ groups was determined through a pre-test when two surveys were distributed and outcomes were analyzed. Pre-test results in Table 1 shows at the beginning students’ achievement in all three groups had slight difference.

Table 1.

Descriptive statistics of the achievement test results.

Groups	N	Pre-test		Post-test
Groups	N	Mean	Std. Deviation	Mean	Std. Deviation
F2F	50	15.20	5.132	23.80	3.375
FO	100	14.91	4.221	19.98	4.339
BF	50	14.86	4.941	20.86	3.251

The ANOVA results in Table 2 shows this difference was not statistically significance (p = 0.130 < 0.05). The assumed null hypothesis was accepted that there was no difference of learning achievement levels among three groups of students.

Table 2.

One-Way ANOVA comparing students’ achievement in pre-test stage.

Variables	Sum of squares	df	Mean square	F	Sig
Between groups	521.535	2	221.432	19.921	0.130
Within groups	1987.142	197	11.761
Total	3564.221	199

Note: Significance determined at (p ≤ 0.05).

To investigate “which teaching method yields the highest student achievement?” the post-test achievement results were analyzed as presented in Table 1. It is evident from this table that students’ achievement is the highest in F2F mode followed by BF and FO. This outcome is expressed more clearly with the help of a mean plot analysis in Figure 3.

Figure 3.

Mean plots of students’ achievement (post-test stage).

To investigate the statistical significance of these differences a one-way ANOVA was conducted and the results are presented in Table 3 that shows this difference is statistically significant (p = 0.000 << 0.05) indicating there having reasons behind these differences than being a mere chance occurrence though these reasons were not investigated in this study.

Table 3.

One-Way ANOVA comparing students’ achievement in post-test stage.

Variables	Sum of squares	df	Mean square	F	Sig
Between groups	492.215	2	246.108	16.491	0.000^a
Within groups	2939.980	197	14.924
Total	3432.195	199

^aStatistically significant at (p ≤ 0.05).

Since the above ANOVA found statistically significant, it needs to conduct a post-hoc analysis to ascertain which of the three groups had the best overall performance. The Levene’s Statistic to test the homogeneity of variance in Table 4 was found significant (p = 0.005 < 0.05) that ensures equal variance assumed.

Table 4.

Test of homogeneity of variances for achievement data (post-test).

Levene statistic	df1	df2	Sig
5.509	2	197	0.005^a

^aStatistically significant at (p ≤ 0.05).

Hence, Turkey HSD post-hoc analysis was conducted and the results are presented in Table 5 that reveals the face-to-face (F2F) group performed significantly better than the fully online group (FO) at the 0.05 significance level (p = 0.000). Besides this group also performed significantly better than the blended flipped (BF) group at the 0.05 significance level (p = 0.001). The data also revealed no statistically significant difference between the FO group and BF group (p = 0.39> 0.05).

Table 5.

Post-hoc analysis of students’ achievement test data (post-test).

(I) Delivery mode	(J) Delivery mode	Mean Difference (I-J)	Std. Error	Sig	95% Confidence interval
(I) Delivery mode	(J) Delivery mode	Mean Difference (I-J)	Std. Error	Sig	Lower bound	Upper bound
F2F	FO	3.820^a	0.669	0.000	2.24	5.40
F2F	BF	2.940^a	0.773	0.001	1.12	4.76
FO	F2F	−3.820^a	0.669	0.000	−5.40	−2.24
FO	BF	-0.880	0.669	0.388	−2.46	0.70
BF	F2F	−2.940^a	0.773	0.001	−4.76	−1.12
BF	FO	0.880	0.669	0.388	-0.70	2.46

^aThe mean difference is significant at the 0.05 level.

Results relating to RQ2

Regarding the second research question- “which teaching method best fosters students’ satisfaction?”- the allied survey was conducted two times as earlier case and the findings are reported in Table 6. In the pre-test stage all three groups exhibited poor satisfaction level in their stipulated mathematics course having difference almost none.

Table 6.

Descriptive statistics of the satisfaction test results.

Groups	N	Pre-test		Post-test
Groups	N	Mean	Std. Deviation	Mean	Std. Deviation
F2F	50	11.33	3.732	15.70	2.261
FO	100	10.51	2.866	12.80	3.315
BF	50	10.36	4.051	18.76	2.520

That slight difference discovered was found statistically not significant as per the ANOVA results in Table 7 (p = 0.062>0.05) and it may be ignored as a chance occurrence. Thus, the equivalence of satisfaction level among three groups was ascertained.

Table 7.

One-Way ANOVA comparing students’ satisfaction in pre-test stage.

Variables	Sum of squares	df	Mean square	F	Sig
Between groups	1612.312	2	776.332	79.851	0.062
Within groups	1873.432	197	9.553
Total	3321.775	199

Note: Significance determined at (p ≤ 0.05).

The results of the satisfaction survey at the post-test stage as reported in Table 6 shows students’ satisfaction level enhanced when they were taught by the teachers under strict vigil of the researchers but notably students taught in the BF mode felt the highest satisfaction followed by the groups pursuing in F2F and FO. This finding can be presumed more clearly in mean plot analysis presented in Figure 4.

Figure 4.

Mean plots of students’ satisfaction level (post-test stage).

Now, to unearth statistical significance of these differences in satisfaction another one-way ANOVA was conducted and the results are presented in Table 8 that shows this difference is statistically significant (p = 0.000 << 0.05) indicating having rationality behind differences than being a mere scenario of chance. Investigating reasons were not under the preview of this study but the discussion will be made based on existing literature in the next section.

Table 8.

One-Way ANOVA comparing students’ satisfaction in post-test stage.

Variables	Sum of squares	df	Mean square	F	Sig
Between groups	1215.335	2	607.668	72.569	0.000*
Within groups	1649.620	197	8.374
Total	2864.955	199

Note: * Statistically significant at (p ≤ 0.05).

The Levene’s Statistics in Table 9 indicates having homogeneity of variance in the post-test satisfaction data that demands Tukey HSD test for post-hoc analysis to determine which of the three groups had the best overall performance.

Table 9.

Test of homogeneity of variances for satisfaction data (post-test).

Levene statistic	df1	df2	Sig
9.772	2	197	0.005^a

^aStatistically significant at (p ≤ 0.05).

The results of the post-hoc analysis is presented in Table 10 that shows the difference in satisfaction is the highest between BF and FO (having a Mean difference of 5.96 which is statistically significant, p = 0.000 << 0.05) followed by the differences between BF and F2F (having a Mean difference of 3.06 which is also statistically significant, p = 0.000 << 0.05), and F2F and FO (having a Mean difference of 2.9 which is also statistically significant, p = 0.000 << 0.05).

Table 10.

Post-hoc analysis of students’ satisfaction in post-test stage.

(I) Delivery mode	(J) Delivery mode	Mean Difference (I-J)	Std. Error	Sig	95% Confidence interval
(I) Delivery mode	(J) Delivery mode	Mean Difference (I-J)	Std. Error	Sig	Lower bound	Upper bound
F2F	FO	2.900^a	0.501	0.000	1.72	4.08
F2F	BF	−3.060^a	0.579	0.000	−4.43	−1.69
FO	F2F	−2.900^a	0.501	0.000	−4.08	−1.72
FO	BF	−5.960^a	0.501	0.000	−7.14	−4.78
BF	F2F	3.060^a	0.579	0.000	1.69	4.43
BF	FO	5.960^a	0.501	0.000	4.78	7.14

^aThe mean difference is significant at the 0.05 level.

Discussion

The results suggest that students learned better in the face-to-face classroom, followed by the blended flipped, and the fully online class had the lowest learning achievement. The face-to-face class had the highest mean final grade score, followed by the blended flipped course, and the fully online class had the lowest mean score. May be this finding a bit out of the track but considering the cultural context of the study this does not seem unmatched. Indian elementary students achieved best in the F2F mode since these students were almost unknown to any other mode of learning at least before the COVID-19 pandemic when this investigation was made as several past studies (e.g. Bozkurt and Sharma, 2020; Kundu, 2018; Kundu and Bej, 2020; Kundu et al., 2020) covering the same context also supports this. Naturally, they were accustomed to this mode and were alien to the other two options.

The statistically significant difference in learning achievement between the mean score of F2F and FO group suggest that students in the face-to-face class were more engaged with the course than the fully online group. Though the reasons were not deeply concentrated in this study but authors wish to attribute this as a result of long association with F2F mode.

Furthermore, there was statistically significant difference in student achievement between the F2F and the BF group was found. But there was no significant difference of achievement was observed between the BF and the FO group though they achieved better in BF mode. This implies that, with respect to students’ achievement the blended flipped class was an improvement over the fully online class. But students’ achievement was found highest in the F2F mode this may be context specific and having roots in the lack of technology integration for a technology enabled education (Mukhopadhyaya. 2021).

The results of the satisfaction survey indicated that the students preferred the BF mode of course delivery the best, followed by the F2F, and they enjoyed the FO class the least. The authors attribute this to students’ spontaneous involvement in learning and having teachers’ support as evident in prior studies like Kundu et al. (2020) and Kundu et al. (2021a). It also supports the finding in Kundu et al. (2021b) that concludes students’ view as “we have efficacy but lack infrastructure.”

This also hints at the future good days for technology-enabled learning if its integration is properly shaped even in a school so far has been far away from techno-pedagogy, thus supporting Bergmann and Sams’ (2012) claim that the flipped classes speak the language of today’s students. Specifically, a mathematics class at the elementary level even in a premature context in flipped mode is found more satisfactory than traditional F2F delivery mode supporting past studies made in higher level (Chen at al., 2017; Fazal and Bryant, 2019; Greer et al., 2014; Lo and Hew, 2018). These results have several implications for the design and implementation of mathematics curricula at the elementary level. Students’ individualities and satisfaction level are two vital parameters to recommend an effective mode of course delivery especially in the context of developing countries.

Selecting the best mode

This study concludes elementary students of an unequipped school for a mathematics course were more satisfied with the flipped model than the rest two which is an important finding. This shows when they were given adequate opportunities to select one of the three alternatives- F2F, FO, BF- they select BF. This is a good sign for such millions of students spreading across several developing countries like India struggling amidst teacher-dominated orthodox F2F pedagogies with a shortage of adequate integration culture, scope for creativity, interaction, and individuality. The flipped model could be the best mode of math course delivery for elementary level in these countries where infrastructure for online teaching-learning is still unequipped and premature. Provided teachers were assisted with adequate skills and material supports BF model could be effective for such underdeveloped schools as well the only. This finding is in tune with the finding of Lo and Hew (2018) who said that the peer interactions inside the flipped classroom were critical in promoting students’ mathematics achievement and cognitive engagement, as opposed to online learning resources and gamification per se.

The elementary students exhibit the lowest achievement and satisfaction for fully online mode. In a face-to-face course, students have direct access to the instructor. This means that students can seek clarification immediately during the presentation of the material. This type of interaction is impossible in an asynchronous online course. In a flipped mode also, students must wait until the next time they see the instructor to obtain clarification on concepts they do not fully understand as they are not able to ask the question while watching the videos or interacting with the PowerPoint presentations. These advantages on F2F advocated in its favor and helped students to perform better.

This finding has also a broader implication in improving online delivery mode substantially based on empirical findings. This connotes that fully online courses that incorporate regular meetings using real-time video conferencing may mitigate the isolation students feel when taking online courses with no synchronous meetings. For example, in a face-to-face course, teachers using learner-centered principles may put students in groups to solve problems while going around the classroom to provide scaffolding. Some video conferencing software allows for this type of interaction virtually. Instructors can place students in separate rooms and allow them to interact while sharing a whiteboard. The instructors can then visit each room to answer questions and provide scaffolding. This type of interaction among students may foster students’ success and satisfaction better than the prevalent way educators usually promote interaction in online courses, the asynchronous discussion board.

Online learning courses often use a discussion board to promote interaction among students and between the instructor and the students. The asynchronous nature of this type of interaction may limit the quality of the encounters, especially in mathematics or statistics courses where students need immediate feedback to address potential errors and misconceptions. Incorporating scheduled synchronous sessions using a video conferencing tool may improve the quality of the interactions in online courses, and thus improve their performance in the course as well as their enjoyment.

Conclusion

The current study explored the differences among three teaching methods-face-to-face, fully online, and blended flipped. The analysis revealed that the participants in the face-to-face group achieved significantly better than the rest two groups. But students facing in the blended flipped mode had the highest level of satisfaction, followed by the face-to-face and the fully online class. Some studies published after the start of the Covid-19 suggest that students were dissatisfied with online learning in general (Aristovnik et al., 2020). Students were reported to be especially unhappy with the modes of communication in asynchronous learning (Kundu and Bej, 2020; Means and Neisler, 2021). The shortcomings of the modes of communication in asynchronous learning may have contributed to students’ dissatisfaction with distance learning, particularly in mathematics courses where direct interaction with faculty and among students is of paramount importance.

Realizing that the global orders in general and education, in particular, are in constant change hence, it would be prudent to address critical issues on the educational landscape from our past and present experiences and by applying our learning insights to ensure a solid future (Bozkurt and Sharma, 2020). The Covid-19 pandemic makes online education inevitable to the educational institution may have to limit the number of students they allow on-campus and entire groups of faculty, staff, and students may have to go to quarantine when a positive case is reported on campus. This empirical research along with past studies (Yen, 2020) suggest that combining the flipped classroom model with the appropriate technological tools may improve students’ overall performance and satisfaction level in online courses.

To conclude the current study suggests that the blended flipped classroom model may be a viable alternative to the traditional classroom, especially in mathematics courses at elementary level. As educational institutions may have to wrestle with the unprecedented nature of the Covid-19 pandemic for a long time to come, the blended flipped classroom model may provide an adequate way to mitigate the consequences associated with the pandemic. It could help building a resilient education system that could stand fearless amidst future calamities and institutions don’t need to shut their operations. This activity-based BF model offers a highly interactive and engaging environment that may bring a fresh air of self-paced learning making a significant improvement to students’ achievement and overall satisfaction. This will help the observed limitations as found in a pandemic by bridging the gap between achieving learning outcomes, while invoking virtues deemed universally effective for young children across all segments of society.

Limitations

This study had some limitations and further studies are necessary to validate these claims. It was a case study conducted within a single school among 200 students of an elementary class and hence the results may vary in another study with larger samples or the different contexts or done in different cultures or states. The convenient nature of the sampling method may limit the generalizability of the study.

The study used DBR in a specific school purposively chosen by the researchers at their convenience having teachers sincerely searching for ways to up-bring quality education responding to their national thrust and hence, these findings are not generalizable to all schools. The results may be influenced by the emotional impulses of uncommon and exclusive experiences of the participants.

The unavailability of demographic information such as the age, race, and gender of the participants may limit the generalizability of this study as the sample may not be characteristic of the students enrolled at the university and the general population of undergraduate students. Another limitation is the difference in proctoring. Students in the online course were not proctored while proctoring was required in the face-to-face and blended flipped courses. It is interesting to note that students in the online distance learning group had the lowest mean final score even though they received the assessments without proctoring.

Another limitation is the fact that researchers were there in the overall monitoring and guidance of this study because without their involvement this study was not possible since the school was unequipped to conduct technology-integrated learning. Hence, the researchers fear that the study could bring different results if the researchers were not there.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Arnab Kundu

Tripti Bej

Gourish C Mondal

Author Biographies

Arnab Kundu, Ph.D. Student, Department of Education, Bankura University, India. He has received a Master of Arts (M. A) in English and in Education, M.Phil. in Education, Post-Graduate Diploma in Educational Management and Administration (PGDEMA). Arnab’s research focuses on several issues regarding teachers’ work specially to promote literacies in online/digital environments. He authored 20 research articles published in SCOPUS/WoS/SCIE indexed international journals. He is the main and corresponding author in this research article. He may be contacted at: arnabkundu5@gmail.com

Dr. Tripti Bej, Assistant Teacher, Department of Science Education, Maniklal Singha Smrity Madhyamik Vidyalaya (H.S.), Bankura, India. She has received M. Sc. and Ph. D. in Mathematics from Vidyasagar University, India. Her research interest includes algebras and elementary mathematics. She wrote 25 research papers published in ESCI/SCOPUS/WoS international journals. She is the co-author of this paper and may be contacted at tapubej@gmail.com

Gourish Chandra Mondal, Ph.D. Student, Department of Education, University of Kalyani, India has received M.Sc. (Physics), M.Ed. and M.A. (Education). He has authored in several national and international journals including IGI-Global. He may be contacted at: mail2gourish@gmail.com

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