At Highgrove Education, we have an approach to teaching and learning which is more individualised than in a traditional school and gives students more agency in their learning. Our Head of Mathematics, Harry Williams, shares his take on how our flipped learning approach supercharges progress in his subject.
There are three major stands to learning mathematics at Highgrove Online School:
1) live lessons with a mathematics teacher;
2) working through independently through self-study materials;
3) seeking out help outside of lessons via live interaction in open or bookable office hours, and/or seeking out help via exchange of Teams messages.
In this blog post, we’re going to consider the experience of students in live lessons with their mathematics teacher.
In our live lessons, students meet via videoconferencing software using their laptops or desktop computers. Students are expected to turn their cameras on throughout the lesson, as it’s surprising how helpful it can be to their teachers to pick up on subtle facial expressions as to how a student is feeling about a question they’re working on. Students also connect their microphones so that they can answer questions, or discuss problems in breakout groups with their fellow students, but leave their microphones muted otherwise so that everyone can really focus on the learning.
In our Maths sessions, we invite all of our students to collaborate on Miro online whiteboards, so that their Maths teacher can see what they’re writing in real-time, and give near instant feedback. This is a complete game-changer for mathematics instruction; in a normal physical classroom, a Maths teacher might be able to do the occasional bit of over-the-shoulder glancing at what a student is writing in a practice-phase of the lesson, and they might make use of physical mini-whiteboards to give quick feedback to individuals, but there are physical limitations to just how much mathematics can be comfortably read at a glance and can be written and read from across a classroom on such a mini-whiteboard. In our online Maths classrooms, however, our Maths teachers can comfortably read through several lines of algebra and diagnose any specific problems in real-time; every teacher knows that such personalised, real-time corrections and feedback is the most effective tool in leading to impactful learning.
Students might choose to connect relatively inexpensive graphics tablets to their laptops or computers to write digitally in real-time on the whiteboard using a single laptop or desktop computer, or some might choose to join the video call via their computer but to write on using an external tablet (and iPad or otherwise) using the free Miro app in conjunction with a stylus. We strongly believe that the best way to write mathematics is by hand with a stylus; indeed, this is the best preparation for the way that students will be writing their mathematics in their real exams. This is a major point of difference between our Highgrove online maths classrooms and other online classrooms: there is only so much that can be done via multiple choice questions and typing in the chat – writing mathematics is the most effective way of practising mathematics.
In our online lessons, we can see that students aren’t “busy tricking” as is surprisingly common in physical classrooms: all too often, students in physical classrooms who are uncertain or poorly motivated silently disengaged from their work, often without it being immediately obvious to their teacher: they might waste time copying out the question or underlining the title. This is not the case in our Highgrove online maths classes: we know that all students are engaged, because we can see exactly what they’re writing at all times, and indeed what they’re looking at on a Miro whiteboard. Efficiency is king in our online Maths classrooms; there is no time wasted with students copying down notes from a board, no time wasted handing out sheets and gluing them into exercise books, and there are none of the issues with low-level disruption that cause such a pernicious effect in so many physical classrooms.
From the moment students enter our virtual classrooms, they are learning and it is very apparent to us if someone has got distracted: we can see if their pointer isn’t moving and we can gently intervene to re-focus the student. For students with personal issues, it is very easy for a student to privately message us to let us know how they’re feeling, without their classmates knowing that there is any problem at all, and students that are struggling with a task can ask for help privately in this way without having to worry about feeling judged by their classmates.
Our small group sizes mean that every student can benefit from individual feedback in every lesson in real-time; in a usual physical classroom with much larger classes, such individual feedback in real-time in lessons is much more difficult for even the most skilled teacher to achieve. Having taught in both environments, I definitely feel that I know my online students’ academic strengths and areas for development in much more refined detail than those I have taught in physical classrooms – and crucially, I can intervene to help my students before they’ve accidentally practised doing it wrong, so that they spend more time practising correct methods and are therefore more likely to do the right thing when it really counts in the exam! With use of screen-sharing, we can easily demo interactive graphs via Desmos, or show students exactly what buttons to press on their calculator via the use of virtual calculator emulators.
The use of our interactive collaborative Miro whiteboard allows us to do things that are not possible in a physical classroom. We can start a problem together as a group, and then we can duplicate that exact starting point for every student to finish off for themselves; there is no wasted time of students copying (or miscopying) from a physical whiteboard. Our use of class time is maximised for learning.
Our positive classroom culture is absolutely key to our students’ success in Mathematics. We tell our students that we welcome mistakes during lessons, as these are the opportunities for learning; it is not uncommon for our teachers to thank students for making a particularly insightful mistake, that we can then discuss as a group so that everyone can benefit from the learning opportunity that this provides. Via our use of virtual Miro whiteboards, our default way of working is that every student can view what every other student is writing by moving around the board to check out what their peers have been working on; in this way, it is very easy for our teachers to spotlight the very best mathematical thinking and clear communication, so that all students know what mathematical excellence looks like. Students can easily collaborate and work as a group on the same virtual piece of paper in a manner which would just not be possible in a standard physical maths classroom. When we need to ensure that students cannot see what others are writing, we can make use of Miro breakout frames so that students can only see their own work and not that of other students; this can be useful for short phases of exam-style timed practice to keep students on their toes.
Another huge point of difference between our Highgrove Maths classes is that we engage in a flipped learning model, so students are expected to work through self-study materials in advance of our lessons. This was the most surprising thing for me when I first started teaching in this way: students would actually come to my classes expected to know the fundamentals! Therefore, though of course we will spend time reviewing these if necessary, the proportion of time that students spend in our live lessons practising and problem-solving is far higher than a traditional classroom, where in many cases the bulk of the lesson will be a case of teachers interleaving instruction with practice. In traditional classrooms, there often just isn’t the time for teachers to assist their students with grappling with complex, nuanced and particularly tricky problems. Instead, due to the constraints of class time and through no fault of their own, teachers in other contexts often have to hope that students are able to put the pieces together for themselves when undertaking independent exam practice for homework.
In contrast, in our online lessons at Highgrove, we’re often able to progress onto these meatier, trickier questions at a much earlier stage of the learning, so students have the opportunity to be supported by their teacher when tackling these more demanding questions. The experience is much more personalised than in a physical classroom. Students can work at their own pace through the problems, with those who are progressing rapidly encouraged to engage with trickier extension questions, and those who are finding the work more difficult receiving the individual support that they need to help them to keep pace with the group. It is very easy for us to open breakout rooms in an ad-hoc manner, so that I can give individual support to students who are struggling without distracting others, or to open up small group discussions without students wasting time moving around a physical classroom.
I teach my online classes using three monitors: one for monitoring our video conferencing software, where I can see all of my students’ expressions as they are working through problems as well as the chat and Q&A (where students can message privately), the second for seeing what students are writing in real-time on their Miro whiteboards and the third for my OneNote software, where I have my lesson plans and detailed model answers ready to help guide me through the lesson to reduce my own cognitive demand, and to monitor Teams for urgent messages and to take the register. It is often the case that I will take a quick screenshot of an excerpt of a mark scheme and paste this onto the Miro whiteboard, so that students can see for themselves exactly how the marks are allocated – and might even be challenged to tell me how many marks they think they deserve. In this way, we can train students to understand the nuances of the mark schemes, and they can see for themselves why maths teachers around the world always urge their students to ‘show their working’!
I hope that this gives you a bit of taste of what our online Maths lessons are like at Highgrove. If you’re curious and want to learn more, why don’t you get in touch? You’re always welcome to join a taster lesson to experience learning online for yourself.
