It is likely that over the next few weeks that we will start having groups of year 10 students back in school and we will be teaching them some curriculum content during this time. It is highly unlikely that we will be teaching them in the same groupings that they were previously in, and they will have done a massively varied amount of work in the time that they have been out of school so far.
So what do I do with a small, but potentially very mixed class who I may not know or have built any previous relationships with, where I do not know what they can do in advance? How can I give them a worthwhile maths lesson?
I think that this is where the principles of Teaching for Mastery will be useful, and I want to be sure that this is a very different type of lesson from the usual “revision” lesson that we may have delivered previously. The NCETM (National Centre for Excellence in Teaching Mathematics) sets out some of the principles and pedagogies of Teaching for Mastery as follows:
- Mathematics Teaching for Mastery rejects the idea that a large proportion of people ‘just can’t do maths’. All students are encouraged by the belief that by working hard at mathematics they can succeed and that making mistakes is to be seen not as a failure but as a valuable opportunity for new learning.
- Facility with procedures and algorithms without a deep and connected understanding does not constitute mastery. Mastery is achieved through developing procedural fluency and conceptual understanding in tandem, since each supports the other.
- Significant time is spent developing a deep understanding of the key ideas and concepts that are needed to underpin future learning. The structures and connections within the mathematics are emphasised, which helps to ensure that students’ learning is sustainable over time.
We can bring these aspects into our teaching of “one-off” lessons to make them as useful as possible to the students in them, and they will also help us to plan these carefully in advance when there are so many unknowns. I will try to plan any lessons I teach around the following structure:
- Reassurance and motivation.
Our students have not been in a school environment for a long time now. They need to feel supported, reassured, and motivated to make the most of this time. I also need to remind them of classroom expectations and how these will work in the new environment. I will need to start with a task that gives them an early feeling of success. Tom Bennett and Tom Sherrington have recently written interesting articles on these topics.
- Low-stakes quizzing
I need to then gently assess what my students already know about the topic. I will most likely use diagnostic multiple choice questions, maybe with mini-whiteboards, and this will be very low-stakes testing. I need to keep the students feeling reassured. Misconceptions will be discussed and mistakes will be celebrated as ways in which we can all learn, and those students who perform well will gain a deeper understanding of the topic by considering these misconceptions – this is an important part of the lesson for all students, however much they already understand the topic.
Mini-whiteboards will be a vital part of this lesson as they allow me to see clearly from a distance the work the students are doing, very useful for social distancing purposes. I won’t ask them to hold them up (unnecessary clatter and potential copying) but will be able to get a good view of their work from the sides of the room. I have also found that students are often far more willing to take risks and try things out on mini-whiteboards than in their books – perhaps it is the impermanent nature of the writing.
- Keep the whole class together
My lesson will then progress in very small steps through my chosen topic. I will use “I, We, You” to model examples, but I only want my students to spend a very short time on the “you” stage at the moment. We will talk a lot about the thought processes required to find the solutions, and I will try to refer this back to how they work independently at home, hopefully helping them to become more self-regulated and successful when they are in that situation.
- “Reflect, Expect, Check, Explain” (Craig Barton) http://www.mrbartonmaths.com/booklinks/
I then want to move into some more independent “intelligent” practice. I am currently reading Craig Barton’s second book and I think the processes he outlines could work really well in our one-off lessons. He suggests instead of a worksheet of pretty much random questions on a topic, or ones that increase in difficulty but are otherwise unrelated, we think about carefully sequenced sets of questions with links between them. Thankfully there is a large collection of these sets of questions on Craig’s website https://variationtheory.com/. The students need to apply what they have learned to answer the questions, but also make conjectures about the links between them, by asking “what is the same and what is different?”, and trying to discern the underlying mathematics behind these links. Students will work in periods of silence so they get the chance to think deeply on their own, but will also have the chance to discuss their thoughts both in (socially distanced) pairs and as a class. This way of working has a real advantage in that those who are struggling with the method will have a chance to work through lots of similar examples for fluency practise, yet still hear the thoughts of others who have managed to do the same examples but also gain a deeper insight into the underlying maths. I can keep the whole class doing the same task, they will experience deeper insight at the point when they are ready, and through discussion they will all have the opportunity to think about these insights. I will not be giving them many colours of differentiated worksheets!
- Formative assessment
Once we have had a good look at the links and discussed what we have found I will need to see what they can now do. I will not at this stage presume they have learned the content we have been covering. To wrap the lesson up I will probably use more multiple choice questioning, on a carefully though-out set of specific misconceptions. I will also ask the students to each think of two questions to ask me about this topic – a great idea from Craig Barton that avoids that pointless “Does everyone understand?” question. I will probably give them some other questions to have a go at on their own at home, and give them a way of getting their solutions to me so that I can feedback to them at a later date. We will discuss the forgetting curve and how important it is that they don’t just go away and not think about this lesson again. I will give them some Hegarty Maths clip numbers for further fluency practise. We may even discuss flashcards if they might work for the topic.
If relevant we may look at some exam style questions, but this lesson is to be about promoting confidence, building lasting foundations and a deep understanding, not about getting them exam-ready. We need to make sure this is a positive experience for the students we have in at this strange time, and re-ignite their passion for learning and maths, rather than cause them more anxiety.
It will be strange having very small groups of students in this fashion, but even writing about it has made me itch to get back in the classroom and be teaching students properly again, and to see that lightbulb go on when they finally make the connections that I have been trying to impart to them.
Deb is a Maths Teacher and Research Associate for Maths at Durrington High School. She is also Secondary Co-Lead for Sussex Maths Hub. She tweets as @runningstitch