While I have worked as an adult educator, a youth violence prevention educator, and a social justice workshop facilitator, my only direct experience as a classroom teacher is one semester of high school math instruction. After this course, I will be finished with my masters degree and will be exploring various career avenues and one option I am certainly considering is to return to teaching secondary mathematics. I would therefore like to use this opportunity to investigate one of my curriculum options that might make my classroom more engaging.

In my first semester of teaching, most of my students were in Algebra 1 for the secord or third time and thus felt completely defeated by math. However, I also had a small group of honors students who had a history of excelling in math and science and were looking for new challenges. At the time, I struggled to meet all of their needs in one classroom and I found that traditional math instruction simply was not helping me succeed. As a result, I began searching for new and innovative ways to teach math. In my research, I was particularly inspired by the following TED Talk from former H.S. math teacher and Chief Educational Officer of Desmos, Dan Meyer:

As Dan describes, we need to design classrooms that encourage student inquiry and require students to collaborate, make arguments, define problems, and use critical thinking skills to figure out a solution. Instead, what we often do today is ask students to memorize and reproduce procedures or "plug and chug" numbers into given formulas. I think most math teachers would agree that this is not the most effective method. However, in order to abandon these practices and focus our energy on these more complex assignments, there needs to be a drastic classroom transformation. It is a huge challenge to take a traditional classroom and just try to add in these activities on top of traditional lessons. Therefore, I would like to explore an existing strategy that teachers are using to give themselves more time in the classroom to participate in these meaningful exercises.

In my other works, I have explored ubiquitous learning and project based learning, which I believe are ultimately the future of math (and all) education. However, I also recognize that it may be awhile before these are implemented more pervasively. Therefore, I am intrigued to see how flipped math classrooms are being utilized today and how they are helping teachers to create math learning environments that bring us closer to a ubiquitous learning model. I will preface this by saying that I do not believe that flipping the classroom will single-handedly fix the problems that Dan addresses. Like any technological application, it is only as good as its design and implementation. A flipped classroom can and often does look exactly like a traditional didactic teaching model. In these cases, there is nothing transformative about the approach. With that in mind, I am interested in exploring the following questions further:

• How can a flipped classroom approach effectively open up time and space for students to participate in more meaningful in-person learning?
• How can a flipped classroom be used as one of many tools to transform our math classrooms and possibly as a stepping stone to further classroom innovations?

"It is commonly accepted that the 'Flipped Classroom Model' was born, in the year 2000, by the hands of Bergmann & Sams, 2012" (Lopes & Soares, 2018, pg. 105) by two chemistry teachers in Colorado who decided to film their lectures and post them online to try and combat high levels of absenteeism and to then utilize their class time to explore more complex problems. (Lopes & Soares, 2018). Essentially, the flipped classroom is one in which students learn material at home, typically through online lectures and videos, and then use classroom time to apply their knowledge and skills to projects, activities, worksheets, etc. (Bhagat, et. al. 2016; Lopes & Soares, 2018; Lai & Hwang, 2016; Lo, et. al. 2017, Yilmaz, 2017) "The Flipped Learning Network (2014) offers the following definition: Flipped Learning 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 (p. 1)" (Lo et. al. 2017, pg. 53)." The theoretical strong point of this new pedagogy seems to be the combination of constructivist and behaviourist learning theories working together, in a constant interaction" (Bishop & Verleger, 2013). According to (Bishop & Verleger, 2013) the flipped classroom approach is “an educational technique that consists of two parts: interactive group learning activities inside the classroom, and direct computer-based individual instruction outside the classroom” (p. 5)" (Lopes & Soares, 2018, pg. 106). The image below demonstrates this concept:

(Lo et. al. 2017, pg. 52)

While the general design may be the same in all flipped classrooms, this can look extremely different from one teacher or school to another. (Lo et.al. 2017) For example, in a more didactic approach, one math teacher may have students watch  Khan Academy lectures at home and then have them practice on worksheets with some basic word problems in class, followed by traditional assessments when they reach certain milestones. In a more transformative approach, another teacher may have a completely project based learning classroom where online videos, etc. are only used for supplementary purposes. The classroom atmosphere, student engagement, and outcomes will likely be very different in these two environments but they would both be labeled "flipped classrooms." 

For a more concrete example, this video shows one teacher's approach to flipped classroom math instruction, which I think is a combination of utulizing more didactic approaches and also utilizing his time in the classroom for more dynamic activities:

As you can see, flipped classrooms can vary drastically. Therefore, in order to provide some structure to the design of a flipped classroom, Lo et. al. (2017) "proposed a framework with a set of 10 design principles for mathematics flipped classrooms...based on the benefits and challenges identified in addition to the findings of (their) meta-analysis" (pg. 62):

(Lo, et. al. 2017, pg. 62)

(Lo, et. al. 2017, pg.63)

As I mentioned in the previous section, flipped classrooms can look very different from teacher to teacher or school to school. (Lo et.al. 2017) Therefore, it can be challenging to make a difinitive statement regarding their effectiveness. With that in mind, there have been many promising studies demonstrating an improvement in student learning in flipped classrooms vs. traditional classrooms with many outcomes related to student's perception of their learning (Lopes & Soares, 2018; Lo et.al. 2017; Lai & Hwang, 2016; Bhagat et. al. 2016). Specifically, one study found that using a "self-regulated monitoring system", which "is a platform on which the students can set their learning goals and evaluate their learning performance before and after their courses." (Lai & Hwang, 2016, pg. 128) "can improve students’ self-efficacy as well as their strategies of planning and using study time, and hence they can learn effectively and have better learning achievements" (Lai & Hwang, 2016, pg. 126). Regardless of implementation method, flipped classrooms have the potential to greatly improve in a few key areas; enhanced opportunities for student autonomy, improved differentiation, and more time and space for in-class collaboration, communication, support, and connection. 

One of the most celebrated benefits of a flipped classroom approach is the ability to let students explore math topics at the pace and in the method that best suits their learning needs. If a student is advanced in math, they may only need to look over the material once to have enough background to participate actively in class discussions and projects. They may also be given additional online or in-class activities to challenge themselves. On the other hand, students who may need more repetition will be able to pause and replay videos and have extra time in class to ask for help. Ideally, they would not be forced to move beyond their skill level and therefore might be less frustrated and more likely to develop self-efficacy in math. 

Arguably more important than having students work at their own pace, using a flipped classroom approach also provides more time in class for teachers to explore other learning opportunities with their students. Again, this could look very different for different classrooms, but the affordance is the same. Rather than spending valuable time in class lecturing, teachers can use their in-person time to connect with their students and build relationships that will help them understand their student interests, needs, and learning styles. They can also design activities for collaboration and inquiry or even embrace a full project-based-learning approach.That way, when teachers see videos like this one:

they may feel as if they have more freedom and time to play and grow with their students in this manner. In general, I think this is the main problem that flipped classrooms can help address. They can give us the gift of time with our students, which is so precious and limited, so we can say yes to our students' ideas because there is time to walk alongside them down whatever path they want to explore.

Although a flipped classroom has the potential to help us differentiate and utilize our time in the classroom more effectively, we need to remain aware of the potential downfalls of this approach. As with any new technology, we need to ensure that we are not implementing a new method that does not improve our current teaching strategies, just for the sake of implementing it. In addition, we must address concerns related to usability, video quality, resource allocation, upfront teacher preparation, student preparedness, and other challenges. (Lopes & Soares, 2018; Lo et. al 2017, Yilmaz, 2017).

One risk that I can see with flipped classrooms is the tendency to rely too heavily on online videos and lectures and independent learning. It can be empowering for students to have the opportunity to work at their own pace, but it can also become mundane, irrelevant, and isolating, especially if the entire classroom model is still following a traditional didactic teaching approach (i.e. lectures at home, practice worksheets in class, traditional assessments online or in person, etc.). In general, all methods used in a flipped classroom will still need to be researched and validated; particulatly, "since the lecture is such a great portion of a class (even within the flipped classroom), it seems rational to observe whether pre-recorded lectures have any impact, negative or positive, on learning" (Lopes & Soares, 2018, pg. 106). In one study, results "indicated that students' e-learning readiness was a significant predictor of their satisfaction and motivation in flipped classroom model of instruction" (Yilmaz, 2017, pg. 251), therefore it is critical that we do not put all our faith in students' abilities and motivations to learn through online lectures and videos outside of class without first examining their readiness and the effectiveness of the lessons themselves.

Another key issue with a flipped classrooom approach is the time and access necessary outside of class to learn the material. As with any new teaching method or technological advancement, we have to be careful about who it is serving and who it is not. If we expect students to participate actively at home in an online atmosphere, then we need to be aware of any potential barriers to success in that realm (internet access, device access, time outside of school, family obligations, etc.). 

Not only could this change be challenging or possibly ineffective for some students, we can also assume that teachers will have some significant hurdles as well. First of all, this shift requires an extensive amount of planning upfront and studies showed that students preferred online videos that were delivered by the teacher rather than through Khan Academy or another resource, which adds to the amount of preparation needed (Lo et. al. 2017). In addition to preparation time, this method also requires teachers to relinquish a significant amount of control over their classroom. In order to facilitate quality and meaningful learning outside of a typical didactic teaching method, educators have to be comfortable with some chaos. They need to be willing to put students in the forefront of the learning process and act as guides instead of leading the classroom in the traditional sense. It will likely be uncomfortable and will put teachers in a position where they don't always have the answers for their students and have to help them find resources instead of staying within the comfort zone of lectures, worksheets, and assessments.

Considering the many challenges above and the others that would certainly present themselves in such a drastic change, administrators, parents, teachers, and students would all need to be supported in the transition process in order for it to be successful. In addition, Lo et. al. (2017) suggest that teachers work in teams to develop material and/or transition their classrooms in stages and that they increase office hours at the beginning of the course to help work through any student barriers or technological difficulties.

Regardless of the benefits and challenges of a flipped classroom approach, we cannot deny that the classroom is certainly going to become more and more reliant on technology in the future. I imagine that a flipped classroom would be utilized as one tool among many that could be used to transform formal education as we know it and to further explore the new affordances that education technology provides. The flipped classroom allows us more time and space to explore methods such as inquiry based learning, project based learning, ubiquitous learning, portfolio based assessment, etc. In my mind, these things would all be done simultaneously and the amount of material "taught" at home would continue to diminish as we moved closer and closer to a world of Ubiquitous Learning.

As I explored in my other work on Ubiquitous Learning, I envision a school much like Dr. Burbules' model where he described a school as a hub with spokes in all directions where students could participate in other learning opportunities (coffee shop, home, library, construction site, etc.). In this model, the school is a space to connect and collaborate and the teachers are available as guides and resources to help students filter through information, prioritize projects, expand their perspectives, challenge their biases, etc. The school would value all learning opportunities equally and the technology would provide the necessary tools to tie all these learning experiences together in a meaningful way. In my mind, this looks a lot like the graphic below and also mimics the concept of a flipped classroom but on a larger and more school-wide, integrated scale:

While this model may be further into the future and require more infrastructural improvements, I believe a subject-specific flipped classroom is one where we could see some of these practices in action and therefore see how they might be scaled in the future.

In general, utilizing technology to design a flipped math classroom has been demonstrated to be a useful new method of teaching. While there are still plenty of opportunities for further research and exploration into effectiveness with diverse learners, student readiness, and the most beneficial uses of class time, there are clearly benefits to continuing to limit the amount of time spent in class on lectures and procedural math activities. The flipped classroom approach provides students more time in class to focus on activities that inspire, engage, and challenge them. As Lopes and Soares (2018) state, "the flipped classroom seems a promising teaching-learning procedure that can take advantage of all the recent and available technological developments which shouldn't be underestimated, an innovative pedagogical approach that focuses on learner-centered instruction" (pg. 111). While I see this as a stepping stone toward eliminating lectures altogether, I can see the benefits of this approach as a current method that moves us one step closer to a learner-driven education.

Bhagat, K. k., Cheng-Nan Chang1, 6., & Chun-Yen Chang1, 2. c. (2016). The Impact of the Flipped Classroom on Mathematics Concept Learning in High School. Journal Of Educational Technology & Society, 19(3), 134-142.

Lai, C. & Hwang, G. (2016). A self-regulated flipped classroom approach to improving students’ learning performance in a mathematics course. Computers & Education, Volume 100, pgs. 126-140,
ISSN 0360-1315, https://doi.org/10.1016/j.compedu.2016.05.006.

Lo, C. K., Hew, K. F., & Chen, G. (2017). Toward a set of design principles for mathematics flipped classrooms: A synthesis of research in mathematics education. Educational Research Review, 2250-73.

Lopes, A. P., & Soares, F. (2018). Perception and performance in a flipped Financial Mathematics classroom. International Journal Of Management Education (Elsevier Science), 16(1), 105-113. doi:10.1016/j.ijme.2018.01.001

Yilmaz, R. (2017). Exploring the role of e-learning readiness on student satisfaction and motivation in flipped classroom. Computers in Human Behavior, Volume 70. pgs.251-260,
ISSN 0747-5632, https://doi.org/10.1016/j.chb.2016.12.085.