flipped learning

My current Year Nine Maths class (MAT091A) must be like many around Australia. It’s very mixed. It has all sorts of critters in residence. Some of its students always find it easy to learn mathematics, are cognitively engaged and self-motivated. Others might be school-refuser’s, have personal disorders such as anxiety, or low literacy attainment. For some, the home environment is dysfunctional. A mathematics teacher’s role here is complex and full of challenges.

MAT091A marks the first case where I’ve flipped a class below Year 10 level, and the first time I’ve used this meta-strategy with a “challenging” class. We are fortunate to have 280 minutes per week contact time, so I’ve been able to implement several flipped learning strategies already in this class with its aforementioned characteristics and its absence of any prior student experience with flipped learning. The Good Stuff has been happening: my videos are watched, and if not, the in-flip is used. Flipped Mastery has been the staple, where I speak with every student, every lesson. Even though students have at times resisted flipping, the implementation is still progressing, as it should. There is much more work to do, however.

I have noticed, unsurprisingly, that there are substantial issues, to do with MAT091A student dispositions and skills in solving problems. I have thought that it would be great to be able to use the freed-up time due to flipping my videos to improve on the status quo. Problem solving is an immensely important element of a mathematics education, and in the twenty-first century, it is cited increasingly as a vital skill.

Problem Solving Teaching – A Background Narrative

My focus on student problem solving first started in a highly resolute manner back in 2006 when I first became a Mathematics HoD. I was concerned about senior student performance initially in the Modelling and Problem Solving criterion of the Queensland Senior Mathematics subjects. However, since then my interest has deepened, and I am active in teaching problem solving at all high school year levels, as an element of both Mathematics, the subject, and numeracy, the cross-curricula ability. One of the key junctures was as a HoD in 2013, when every faculty in my school had to action a mandate from the leadership team to implement Reciprocal Teaching authentically in their subject areas. Darn! As far as I was aware, no maths person was crazy enough to even try this. This mandate forced me to find a way to blend the Great Stuff: Problem-Solving Teaching (PST) – was not going to dump this! – with Reciprocal Teaching (RT) – what the English teachers did. Whilst I value RT and had used RT when teaching English myself, I was at a loss to find how in the world to make these two great strategies work as one machine. So, I used a truly unique plan one Sunday morning. Google.

My Google search of “Problem Solving Teaching + Reciprocal Teaching” yielded an immediate bulls-eye. Unbelievably, the first result listed was an article about RT in Maths, written by Yvonne Reilly, Jodie Parsons and Elizabeth Bortolot of Sunshine College, Victoria. This was Great Stuff! Later a team from my school comprising of the principal, three deputies and three HoD went on an expedition to some of the best schools we could find in Victoria. Sunshine College was one of these. We saw the aforementioned authors in action in their classrooms. This school seemed to have every excuse not to be producing great outcomes, with well over fifty different languages spoken in students’ homes, and an ICSEA index of well below 1000. However, the opposite was true. What the staff were doing there was amazingly successful – especially with regard to problem solving in Maths classes.

Reciprocal Teaching in Hattie’s Visible Learning, has a high effect size of d = 0.74. It is a renowned strategy for reading comprehension, and it is a collaborative group process.

Predicting
Clarifying
Questioning
Summarising

However, the key change Reilly et al made, and thus, my way of meshing PST and RT, involved replacing Questioning, which usually has little relevance in a high school mathematical problem-solving context. Questioning in RT is where students textually analyse, and interrogate an extended text and explore deeper meanings. The vital change was to use Solving instead:

Predicting
Clarifying
Solving
Summarising

This key change, plus refining the nature of the other three steps to suit a high school Maths context was what we needed. Now for the job of making it our own.

As a fan of PST (d = 0.61), and in particular the heuristic work of George Pólya, I set to work on modifying the ideas from Sunshine College for our needs. Over four years and a few iterations in collaboration with staff (past and present) from my current school, we have arrived at the following process (see Figure 1) which we call Reciprocal Maths Teaching (RMT), or just Reciprocal Maths. RMT dovetails Pólya’s PST steps with a reading comprehension strategy, in a collaborative context. Pólya’s steps are inherent in RMT.

Pólya’s steps:

Understand the problem
Devise a plan.
Carry out the plan.
Look back.

Figure 1: Reciprocal Maths Teaching (RMT)

By explicitly teaching students these RMT steps, as well as the “toolkit” of mathematical strategies in Solve, students gradually build an arsenal of tactics to tackle problems they may encounter in future. Our Maths faculty has spent up on physical resources to facilitate the implementation of RMT. Students from Years Seven to Nine have a trolley in their Maths classroom with laser-etched, ceramic-coated, tablet-sized whiteboards. On one side is a blank template version of Figure 1, where students may write their responses with whiteboard markers, and the other side is blank for rough working, of a temporary nature. We found from Sunshine College that mini-whiteboards give some students more courage to take a risk and have a go at the problem. We supply the stationery too. Additionally, we have a truly gigantic outdoor RMT template (as per Figure 1) with three RMT template full-size whiteboards.

Flipped RMT – Observations Thus Far

I’ve been using RMT since 2013, and I knew that this would never be an easy quick fix in MAT091A. And it hasn’t been! Just like when a teacher trains a new class over weeks in how to watch flipped videos, take Cornell Notes, and use the Group Space responsibly, Flipped RMT is a lot of work initially. Certainly, by flipping MAT091A, I have far more contact time available than traditional non-flipped Maths classes to train students.

Group norms comprise an essential set of skills and protocols that students must be trained in. In MAT091A some students take over, others avoid the tasks at hand, some disrupt other groups because they don’t like the group I’ve put them in, and some initially refuse as they still haven’t decided that problem solving is worth the effort. However, collaborative skills are essential twenty-first century skills. Students learn by hearing their peers explain mathematical concepts or strategies, and deep learning occurs when students teach other students.

Some students often like to immediately go to the Solve step (I’m looking at you boys!). After all it’s the answer that matters – nothing else, right? My students sometimes come from households where parents can be heard to say (e.g. at PT interviews) that “It’s maths. It’s only right or wrong…”. Whether we flip or not, teachers must be patient and never give in to students who balk at the other key stages Predict, Clarify and Reflect.

I note with great interest that the new SATE system in Queensland (the new senior schooling system for curriculum, assessment and tertiary entrance – the largest systemic change in decades) for Senior Mathematics will assess students against a process and rubrics which are remarkably consistent with our RMT modus operandi. See Figure 2. Hence, in terms of preparing students for the increased rigour and required levels of initiative and insight, we think we are on the right track.

An Approach to Problem Solving and Modelling - Mathematics — Figure 2: An Approach to Mathematical Problem Solving and Modelling

The amount of active learning has been great to watch during RMT sessions. It is also often the reason why some students initially resist. Groups are typically small (I like two or three), and provided the right questions are provided (we have a growing bank of problems that our numeracy coach has been assembling), students wrestle with collective reasoning, apply their mathematical concepts and strategies in partnerships, and justify the reasonableness (or not!) of their results. Higher order thinking is required, as are initiative and insight. Sometimes, we can get students to re-watch an Individual Space video if no students in the group can recall the maths underlying the problem. This is sometimes, my job as a facilitator – to intervene and diagnose “just in time”, what the blockers might be. Other times, I like to just fire questions at students to prompt them, in little ways. The thinking needs to come from the students, wherever possible. As a result, I get to speak to lots of my students and have substantive conversations about the maths during RMT. It certainly does not do working relationships any harm.

Flipped RMT – What Next?

I am very confident in the validity and effectiveness of this strategy. However, it is crucial that I do some formal diagnostic work to more scientifically measure the effect of RMT in MAT091A. This will be a future focus. Additionally, I’m still not quite satisfied with some of the finer elements in our RMT process. For example, I want to “beef up” Predict, as students demonstrate some uncertainty around how to respond to this phase. We need to provide training that is more meaningful to students to help them understand and value this part of the process.

Note that we don’t use the same collaboration dynamic as English classes often use with RT. In English classes four students each take, or are assigned, one role: Predictor, Clarifier, Questioner, or Summariser. We have not pursued this dynamic in RMT, as we value that each student is participating in every step. However, perhaps I should do more investigation regarding these mechanics. At this stage, I’m interested in mimicking the “one role” mode from RT and using a system of rotation, so that students become experienced in all processes. No doubt, what I find will be interesting.

Finally, I’m beginning my journey in gamifying RMT. I’m calling the groups “tribes” and have devised a points system. Apart from checking out basics of Classcraft, I have not yet explored digital resources to support gamification. If any reader of this blog has some gamification strategies which they feel may work well in an RMT class, please contact me. I am all ears for this Great Stuff!

References

Hattie, J. (2012). Visible Learning for Teachers: maximizing impact on learning. London: Routledge.

Palincsar, A. S. (1984). Reciprocal teaching of comprehension-fostering and comprehension-monitoring activities. Cognition and Instruction, p. 59.

Polya, G. (1945). How To Solve It. New Jersey: Princeton University Press.

Queensland Curriculum and Assessment Authority. (2017). 21st century skills for senior curriculum: a position paper.

Queensland Curriculum and Assessment Authority. (2017). Specialist Mathematics 2019 v1.0: General Senior Syllabus. Brisbane: QCAA.

Yvonne Reilly, e. a. (2009). Reciprocal Teaching in Mathematics. MAV Conference 2009 (p. 8). Melbourne: The Mathematical Association of Victoria.

I sat in a taxi in Sydney last year, on my way to indulge in another large helping of steamed dumplings in my quest to try all of the top 8 dumpling restaurants Sydney has to offer. (as voted by website Concrete Playground). The taxi driver was a middle aged gentleman of Greek origin. I asked him about his opinion of Uber. Did he hate them? Had business slowed since their inclusion into the market? etc. He told me to open his glove box. To my surprise, within the glovebox was his Uber identification tag. He had a foot in each camp! He had accepted that Uber was here to stay and slumping in his seat and complaining about it wasn’t going to get his bills paid. To cut a long story short the main learning I took away from this interaction is that we can choose to take one of two options. Embrace the trends or fight the trends.

This train of thought is something I have always sort of followed but never really embraced. The taxi driver had inspired me to not only embrace the trends but to accelerate them. Make them my own and use them to my advantage in an educational setting. Things like the bottle flip, dabbing, fidget spinners, memes etc. have been banned in some schools, whereas I see them as an opportunity to teach projectile motion, angles of a triangle, reflection or a relevant way to bring up and discuss social inequity, assumptions and bias.

An example of an educator who is not embracing trends. (used with permission from Mr. Jones online from Teachers pay teachers)

This is where social media comes in. Do we embrace it, or do we fight it?

For me it is a no brainer. After meeting this motivational taxi/ Uber driver I set myself the goal to use Social media as a means for assessment, both in a formative and summative manner.

These are some of the success stories.

Formative assessment:

This was an important one for allowing me to check the students understanding of the content. It was an excellent way to transition the move from the ‘individual’ to the ‘group’ space of the flipped classroom.

I instructed the students to use Snapchat for this. I asked them to summarise or take key points from a video, complete a two truths one lie, do a three level reading guide on a text or any sort of activity where they needed to think about and exhibit an understanding of the content. Once they had created a video using Snapchat they were to save it to their camera roll and then post it onto our class Facebook page. The buy in from students was excellent. Feedback from the class showed that they didn’t mind putting themselves out there for others to see when there was a fun element to it, when they could use a filter to disguise their faces and their voices, and when they could quickly check any notifications they had.

Some examples of students who have used Snapchat filters to record their responses. (used with permission from the students)

Facebook obviously allows you to post videos and other content to your classroom group. I will often put up a video or a link to an article and ask the students to leave a comment which shows their understanding. This allows the students to learn off each other, especially if you have the students in some sort of ability grouping. Students who are lower ability might only need to make a literal statement directly from the text or video whereas someone of a higher ability may be asked to write a comment from a much more critical lens. Going ‘live’ and the new ‘watch party’ feature on Facebook have opened up other avenues of viewing content as a class and could prove to be very useful in the future. Colleagues of mine have set up a Facebook chat for homework where students have had to meet online at a certain time and talk about a specific topic. Although this was optional, it had excellent buy in from the students and some valuable learning came from it.

Summative assessment:

Many sportsmen and sportswomen are setting up “athlete” Facebook pages. Even people who have only been going to the gym for a week or two are setting up fitness based Instagram and Facebook pages too.

This made me think about how I could use the same format for my students. Being a PE teacher who is teaching contextualised courses which are based around improving a students own ability in a sport, it was easy to follow the “athlete” page model. Students had to create a profile, using their school email address as their login. They could make it a page or group depending on whether or not they wanted to keep it private. They could also choose not to make it public or not to publish it at all. This worked particularly well for an assessment where the students had to reflect on their participation in an activity and discuss the factors involved. Typically they would have done this in a diary type format but Facebook allowed them to post their response immediately and also gave them the option of adding in video and photos as evidence. I have seen the same standards being assessed in a similar way on Instagram. Any sort of assessment that requires a portfolio of evidence could be used here.

An example of a post from a students “athlete” page. It is a reflection of their use of interpersonal skills throughout a lesson.

Some of my colleagues from the English department followed suit and allowed their students to set up a Facebook page on which they critiqued the books they were reading and completed reading responses.

I have also seen public pages created by students which contain information about a set topic. The page itself is the assessment and the student needs to have a certain number of resources, posts etc. Making a page designed to create change in a community is a possibility for a number of Health based topics.

These are just a couple of ways that you can use social media to enhance your classroom practice. At the end of the day student buy in is a very important part of being successful on a day to day basis. Using tools, techniques and technology that students are familiar and comfortable with can be a big positive. When a new trend comes along think about how you might be able to use it to your advantage, don’t be scared of it. Go with the trends and don’t concern yourself with what cannot be controlled. Embrace the trends and make them your own!