Blended Learning: Re-Thinking the Mathematics Classroom
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Introduction
This paper will discuss findings from prior studies related to teaching in a blended learning model. One of the main things that blended learning allows for is instruction being student paced and student driven, however, this does not always ensure that students are absorbing or mastering the material rather than simply being able to replicate a process, especially in a mathematics classroom such as mine. Although investigating a variety of subject matters as well as grade levels may influence blended learning strategies, the core themes that I will be delving deeper into should provide much insight for the outlook of this plan.
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My goal every day I step into my classroom is for my students to develop the ability to think critically and problem solve. Reading through studies with various grade levels, early secondary through college level, it is evident that there is no one-size fits all method. Research shows that one method of a blended learning model, a flipped classroom, is most successful as a supplement, but must be paired with direct instruction (Lowe et al., 2016). However, the difficulty and abstractness of the content certainly plays a role when investigating impact of the format of the course (Reju & Jita, 2018). The research I reviewed is made up of both quantitative, mostly assessment results and numerical ratings from surveys, and qualitative data, consisting of student and parent surveys. I will be investigating the impact blended learning has on motivation, achievement, comprehension, and collaboration inside the classroom.
Literature Review
Motivation
It is evident across all levels of schooling that motivation is key for student success regardless of the teaching method. The idea of motivation is often challenging to measure and although quantitative data can be collected, it is typically more authentic and meaningful in open-ended form. Blended classrooms have shown to have varying impacts on student motivation. A study done in a secondary mathematics classroom like my potential setting, noted “motivation can be defined as the willingness to attend and learn material in a development program” (Muir, 2016, p. 488). While the measurability varies from scenario to scenario, qualitative data may paint a more vivid picture of what the teacher is observing from students. In Gomez-Lanier’s (2018) case study, it was prominently noted that time spent working amongst peers increased, however, motivation did not increase as working with classmates with a lack of desire to success has adverse effects on group members desire to learn.
Accountability
To reach the level of mastery that all teachers hope their students achieve, student must want to learn. That desire often stems from how lessons are presented, and a blended learning model has the unique opportunity for students to take true ownership of their learning. A study done by Sookoo-Singh and Boisselle (2018) in a chemistry class found when lessons were prepared in a flipped setting asynchronously, the student motivation increased significantly. The student participation and ownership of the work escalated as the four-week study took form and students felt more responsible for participating in online activities as their work was more traceable than a lecture/worksheet setting. Another study found that implementing an interactive e-book as a supplement to provided videos “not only promoted the students’ self-efficacy for learning mathematics, but also improved their learning achievement” (Hwang & Lai, 2017, p. 193). Additionally, Hwang and Lai (2017) found that typically lower motivated students showed a greater overall increase than students who were initially motivated.
Individual Pacing
Horn et al. (2015) defines blended learning as “any formal education program in which a student learns at least in part through online learning, with some element of student control over time, place, path, and/or pace” (p. 75). In parallel, Muir (2016) discussed the affordance that a blended classroom provides students with, most prominently including self-pacing. All learners are different, and in classes that are often process based, having the ability to move at your own speed allows teachers to meet students where they are without feeling scattered. Additionally, more time can be spent mastering the necessary prior knowledge components to ensure that a solid foundation is built before moving forward. With the technology that many education institutions have access to, utilizing a course management system can provide the organization that students need to move through lessons independently.
On the other hand, Reju and Jita (2018) found that often students felt they spent more time sorting through materials to find what they were supposed to be doing than truly interacting with the content. In a blended learning setting, which may be unfamiliar to many students early on, this lack of efficiency could lead to frustration. This suggests the importance of ensuring the processes are understood by all parties prior to implementing them into the classroom. Gomez-Lanier (2018) found that having the ability to work with peers in a blended classroom setting during certain activities allowed students to compare pacing and work habits and, in turn, led students to believe that their time management skills increased.
Achievement
Achievement can be measured by grades, of course, but the qualitative side can be quite open-ended, especially depending on the types of students being studied. The same can be said for what we, as teachers, define achievement as. However, when evaluating data, we typically look for growth, often quantitatively. In a blended learning setting, achievement can be measured a variety of ways including scores on formative or summative assessments, participation, meaningful contributions to discussions (both online and in person), or even a student taking initiative to advocate for themselves when struggling with their work. Additionally, Tong et al. (2020) speaks of the natural connection that project-based learning has with blended learning, providing more real or authentic assessment, however, acknowledges that a true model has not been developed.
Academic
In Sookoo-Singh and Boisselle’s (2018) case study, although student motivation significantly increased, academic achievement remained stagnant. The results of this study can be interpreted different ways. Although the achievement in the short-term did not yield significant results, one may feel that the increase in motivation on a long-term scale could lead to a deeper understanding of content and therefore an increase in achievement. On the other hand, in a side-by-side experiment comparing using a Khan Academy platform as a flipped classroom support system versus a textbook, the Khan Academy group yielded a higher increase from pre-test to post-test (Zengin, 2017).
Islam et al. (2018) found in a controlled experiment comparing student achievement in a blended learning versus direct learning model that the blended learning group showed a statistically significant increase in achievement. Unlike many, this study was particularly attentive to the lurking variable of student motivation and attempted control it as much as possible to loosely find a cause-and-effect relationship between learning models and achievement.
Differentiation
Differentiation is a hot topic in education nowadays but can look different from class to class. Muir (2016) found that the students benefited from being able to move ahead when they saw fit. In a secondary/professional setting where behavior problems are typically not an issue, this can be a real asset, however, may not translate as seamlessly to an early education setting. Again, implementing Khan Academy videos as a supplement naturally differentiations in mathematics classroom. This has shown to be a very powerful tool, especially due to its interactivity and accessibility (Zengin, 2017).
A blended model provides the opportunity for teachers to differentiate instruction more efficiently. With differentiated lessons based around technology, particularly a course management system students are familiar with, students can find empowerment as they move through lessons (Winter, 2018). Jong (2017) conducted research from three different schools using three different subsets of students: a high-achieving group, a mid-level achieving group, and a low-achieving group. While teachers differentiated the lessons for students as needed, Jong (2017) found that the high-achieving group’s self-efficacy remained stagnant, while both the mid- and low-level achieving groups improved. Given materials at their own level in the mid- and low-level groups, students found it easier to be able to work at their own pace outside of the classroom and take more ownership of their learning. This bridged that gap for students not only mastering the procedural skills necessary but also gaining a deeper understanding of the underlying concepts (Jong, 2017). When students can master a skill at their own pace outside of class, the pressure and stress that come with the setting largely dissipate.
Comprehension
In a mathematics classroom, conceptual understanding is key. It is one thing to be able to replicate a process and simply change numbers/variables around, but to be able to take a concept and apply it to something new is where real learning is exhibited. In a blended learning setting, particularly when asynchronous, measuring the levels of comprehension is not as straightforward as quick check-ins when circulating the room do not exist. Reju and Jita (2018) highlight the difficulty students have when reading textbooks and e-book, especially due to the emphasis higher mathematical terminology. However, depending on age level and maturity, self-advocacy skills may not be present for all students. If a student is not communicating with their instructor when struggling, their lack of understanding may not become evident until the end of the unit. This relates back to Lowe’s et al. (2016) study emphasizing the need to communicate with students when implementing any type of blended model.
Conceptual Understanding
Muir (2016) found that when students had “greater autonomy over their learning it enabled them to attain their goal of mastery over their learning” (p. 493). Students striving towards their goals speaks volumes to the power of self-assessment. Building from this, Hwang and Lai (2017) found implementing the typical flipped classroom strategies restricted comprehension but found that partnering it with an interactive e-book made a significant difference. Having an e-book that is interactive provides the instant feedback that is typically available in a direct class setting while continuing the allow students to move at their own pace.
In acknowledgement of the contrary, prior knowledge is a crucial element of critical thinking and problem solving. Much of critical thinking involves applying previously learned information. One danger of students driving their own foundational learning is if they have it “wrong”. Kirvan et al. (2015) found in their math classes if students were struggling to complete the independent learning outside of class, their problem-solving skills during the student-centered activities suffered as a result. In a scenario of this sort, teachers then must step in to reteach.
Abstract Concepts
Although many of the findings around blended classrooms are positive, there are certainly limitations. One study that took place in an undergraduate mathematics level course found that the absence of live lecture/teaching complicated abstract topics (Reju & Jita, 2018). Although there are countless resources available for mathematics courses, a discussion board between teachers and students can never truly take the place of being able to have a group discussion about the whys. As the content gets more and more challenging, supplemental resources for support become few and far between. In qualitative data collected by Hwang and Lai (2017), students stressed the helplessness they felt when not comprehending a concept. They mention how often times tutorial videos cover procedures and walk students through the process but lack the deeper explanation that is provided in a classroom.
Collaboration
Collaboration is a buzz word in the 21st century education system, both for students and teachers. While full remote learning restricts the small group discussions between students that typically occur in a normal class period, blended learning can provide it. Many course management systems have discussions boards built it and slides can now be made interactive. Lowe et al. (2016) showed how students used Blackboard Collaborate to share their screens with one another and to create visual representations of geometrical concepts, similarly to what a teacher would do on a whiteboard. As for collaboration among teachers, Spillane and Shirrell (2018) emphasized that teachers prefer “physical proximity,” however, many of these meeting are informal, while more formal collaboration is often tech/web based (p. 68). Web-based course management systems and cloud-based file sharing can quite seamlessly take the place of after school meetings and with the integration of video chatting and screen sharing, we can be more efficient than ever.
Asynchronous vs. Synchronous
In a secondary chemistry setting, the approach of asynchronous teaching showed to be the most practical regarding time, however, this varied from class-to-class constraints (Sookoo-Singh & Boisselle, 2018). Lowe et al. (2016) discussed the idea of synchronous teaching in virtual setting as well as recording these synchronous lessons to be posted. After collecting qualitative data on two occasions, they found that both students and staff “valued online sessions to face-to-face” due to their flexibility but felt that they were more helpful as a supplement to live teaching rather than as the primary source of instruction (p. 7).
Gomez (2018) found when researching the idea of building collaboration via blended classrooms the social aspect was strong when creating ways to “teach back” the learned information. This can be done by using numerous applications, one of which includes Flipgrid. Gomez (2018) found that having students interact with one another while learning new material further develops critical thinking and problem-solving skills. However, in an exclusively virtual setting, these collaborative meetings become more difficult to organize, especially with younger students and with self-paced lessons.
Teachers
Muir’s (2016) original motivation to investigate the blended classroom setting was the “optimize class time in order to cover the prescribed curriculum” (p. 489). This statement certainly encapsulates how many teachers feel as they progress through the year and shows the value of being able to collaborate with fellow teachers to create shared lessons, the idea of divide and conquer can go a long way. Teachers prep periods are typically a time for catching up on grading and meeting with students who missed class, however, the ability to stumble upon peers and share viewpoints/converse on education is irreplaceable (Spillane & Sherrell, 2018).
Conclusion
Based on the ample research that has been done on the blended learning model, it is evident the impact it can have on the world of education. Education looks different from class-to-class, grade-to-grade, and school-to-school, but the goals are consistent throughout. A student driven lesson can grow critical thinking and problem-solving skills. By self-motivating through adversity and working with students and teachers alike to achieve goals both inside and outside of the classroom, students will be better prepared for their diverse futures. Determining which components of the model should be taken to ensure that students are not only gaining the deeper understanding of the content but the ability to apply it moving forward is tricky, but an obstacle that educators thrive from
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References
Gomez-Lanier, L. (2018). Building collaboration in the flipped classroom: A case study. International Journal for the Scholarship of Teaching & Learning, 12(2), 1–9. https://doi-org.neumann.idm.oclc.org/10.20429/ijsotl.2018.120207
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Gwo-Jen Hwang, & Chiu-Lin Lai. (2017). Facilitating and bridging out-of-class and in-class learning: an interactive e-book-based flipped learning approach for math courses. Journal of Educational Technology & Society, 20(1), 184–197.
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Islam, S., Baharun, H., Muali, C., Ghufron, M. I., el Iq Bali, M., Wijaya, M., & Marzuki, I. (2018, November). To boost students’ motivation and achievement through blended learning. Journal of Physics: Conference Series, 1114(4), 012046.
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Tong, Y., Kinshuk,, & Wei, X. (2020). Teaching design and practice of a project-based blended learning model. International Journal of Mobile and Blended Learning (IJMBL), 12(1), 33-50. http://doi.org/10.4018/IJMBL.2020010103
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