I'm not sure I should write this blog post but anyway! I taught for 3.5 hours 10 adults GCSE Foundation Maths where we looked at shape, space and measure topics. I had planned to do this lesson last week but due to a family emergency I was absent. As my class are adults I was nervous today that I may get a rough ride for the inconvenience of skipping out on them last week. Not true, they were wonderful. One lady said, "never apologise for putting your kids first". I thought, wow that's really powerful. I'm hoping to hold onto that when I am saying no to the million CPD lates I'm asked to do but I realistically can never deliver.
So I have to admit there was a very free and easy approach to my planning, I had a tonne of activities photocopied for a variety of SSM topics as I was out of sync with my scheme of work. I took a look and thought we will start with circles and see where we end up. We had just finished statistics and graphs as a topic a couple of weeks before so I quickly rustled up a retrieval grid on that, set that out as they arrived whilst I checked over my Google Slides presentation on circles. Just at that moment in walked 2 colleagues to do a peer observation. I have an open door policy. As an experienced teacher I feel it is my duty to offer an open door policy. Generally staff ask ahead of time out of courtesy if they can come in. I always reply with "come anytime, I won't be doing anything special" today's lesson couldn't have been more true!
Off we go then with circles in Google Slides. I have my learning intentions displayed and I write them on my board with my keywords to remain for the whole lesson. I also write the date in words. I'm a bit of a stickler on this one as good habits help make better teachers I think. I was once taught by a head of department that if you write the date in words you are showing learners that there is a quick way to write the date but have pride and high standards and wrote it fully. I quite like writing it in words and it upsets me when it is missing from classroom boards and when it is written as 1/2/20 I always flash back to my old head of department.
In the slides presentation I have inserted slido. Now Slido is a great polling tool that pops in really easily. It is an add-on to Google Slides (I am a Google Certified Trainer so most things I do are in GSuite) I have used Pear Deck before but due to connectivity issues at the remote campus I find Slido works better. I break down the learning intentions by grade, a grade 3 student should be able to do this and a grade 5 student can do this. I give my class my same old speech: "if we teach to a 4 and we fall short we will get a 3 so no apologies I teach to a grade 5 to give you the best chance of achieving a 4." This is high expectations in its simplest form. The Slido then appears and the learners rate themselves out of 5 stars where they are against the grade 5 broken down intention. We get a split of ratings, and some questions about what a sector is. (The grade 5 intention was about calculating area of sectors!)
I begin with labelling parts of a circle. Reminding them of correct spelling. English isn't the first language for many learners, for some it's not even their second or third language. This takes some time and is dull. I am worried I am losing them. I planned to do a mini quiz on the parts of the circle and a card sort but the mood in the room is, we have notes, you will out this on Google Classroom so we have your notes too, what time is break? Picking up the pace I jump in with the circle song! You can watch the one I use here. I know there are others but this is my favourite and I encourage them to sing it to themselves in their exam!
Back to the lesson... I can then see joy at the song but confusion at pi. No surprise, who actually knows what pi is? I quickly grab the elastic bands from my photocopying and ask them to measure the diameter whilst a partner holds the band in a circle shape. I then cut the bands and ask them to measure the length of the chopped band. They then tell me that they are measuring the circumference and that is. We record the 2 measurements from each pair on the board and discover that the circumference is about 3 times bigger than the diameter. We then look at where pi is on our calculators. There is the inevitable conversation of borrowing calculators, we can debate high standards and correct equipment vs financial situation vs local demographic vs adult learners another time.
I then come away from the presentation and project some circles onto my board with varying measurements of radius and diameter. I then give the learners the option to go through area first and then circumference. I highlight that in my experience the thing people get wrong in this topic is doing the wrong one in the wrong question. Calculating area when they needed circumference. Or I give the learners the option of my default every time way. They choose my way. Everyone I see a circle I write CARD. We look at this example where we are asked to find the circumference of this circle:
The question gives us 4cm as a radius. We can write into CARD that R is 4cm and D is 8cm. Quickly singing pi r squared sounds like area to me… we can write in that the circumference would be pi x 8 and area would be pi x 4 squared. We then look back to the question and see what it asked us to calculate. In this case it was circumference so we circle that one and work it out. I like this method as it build solid repetition of the skill of recalling and applying the formulae. I also like it as it encourages the learner to reflect and choose is it area or circumference before diving in.
In my class today the lower level group struggled to start but once CARD had been repeatedly applied they had rapid progression through the tasks. My top end learner decided his way was better and off he went. I always say, I don't care how you get here, just get here if you can. Meaning here is the correct answer! All the learners have access to the answers of all the tasks, they are marking as they go along. Suddenly my top end learner becomes frustrated. He has got most of the work wrong. I take a look and he has done the classic mistake of circumference when it wants area and vice versa. I remind him of CARD he gives it another go and signals to me 5 minutes later that he is being more successful now!
Whilst the learners are working I take 3 of them out one by one for a mini tutorial. They are my 3 at risk learners. I let them know I am putting in interventions for them and say that I believe with hard work they can improve. I am then taken aback realising my peer observers are with me in my final mini tutorial. I am mortified I left my class unattended with peer observers in the room. I apologise and my peers are great and they say, no we think it's brilliant you have taught them well enough to leave them for 5 minutes and these mini tutorials are equally important. I check on the class and they have all done a nice mix of area/circumference including semi circles and compound shapes. I give verbal feedback (should have written more down!) It's almost time for a break but not quite and I am just about to move on when one of the learners makes a safeguarding disclosure to me out of the class so I call a break for 10 minutes while I make notes and report it to my safeguarding lead. I bid farewell to my peers.
I grab 2 minutes to think about what we can do next. I had planned to do angles in parallel lines but I'm concerned that the secure circle knowledge is at risk if I go to angles. My other option is loci or bearings. I decide to go loci. I don't know why I don't teach loci particularly well. Actually it probably ranks as one of my worst lessons. I don't enjoy it and I struggle to visualise the boundaries of areas in the complex questions. Decision has been made now though, I am writing my new learning intentions up on the board before I remember how badly I teach loci!
We do a quick Slido to check our rating now on circles. Everyone has improved. We review the grade 3 and grade 5 learning intentions on loci and constructions and do another Slido, the class has no idea about the language of the topic. No one rates themselves higher than a 1. With a feeling of dread that this has been a poor decision we begin by drawing line and angle bisectors on blank pieces of paper. I demo them in my Slides presentation. (Someone years ago shared a nice demo where the compass moves and the arc appears, I would never have the time to make such a beautiful presentation so I am very grateful to still have it!) Cue difficulties with expanding compass widths in between arcs. Some are unable to keep their pencil in the compass. Some can't use the compass. I get round everyone improving their techniques I see no harm in spinning the paper rather than the compass if the learner struggles. We then take a look at some exam questions. They progress into not explicitly stating it is a line or an angle bisectors but a more worded question. All can do the explicit ones, most can do the more challenging ones. Progress is through skill repetition practise here.
I then put an x on the board (I have been rummaging in my bag for post it notes whilst they were working) and I ask each of them to put a post it note 20cm away from my x. They chat amongst themselves. Some want to do a line, someone twigs it would be a circle, then there's a competition on who can be accurate and exactly 20cm away. I am observing this active learning loving the conversation. I then demo a dog tied to a post would have a circle locus. Then a dog tied to a bar would have a running track shaped locus. (Handily there's a bar outside my window to help visualise) all are keen to get going and for some unknown reason I then decide to demo one of the complex garden planning questions. I draw a rectangle ABCD and ask them where I could put my path that is an equal distance from AB and CD. I start to get clammy I am about to jump in and answer my own question when one of the weaker learners contributes "would it be a line dissector?" We will skip over the incorrect language for now. I check the room and all are thinking the same. Another learner says "yeah this is fine but more than 5m away from the tree for the fountain that isn't any bisect or anything so what do we do there?" I am over joyed. The long phase about the path was because they had twigged that it was a line bisector and were struggling with the next part of the question. I demo an arc 5m from the tree and all are itching to get going. We do a quick Slido and no one rates themselves below a 4!
I circulate the room giving feedback. All have the answers so can tick and flick. I see little merit in me ticking and flicking their work. My role is to shape their learning journey and I do this through feedback not ticks and flicks. I can't believe it, everyone can do it! The lower level ones have some beautiful running track shaped around lines and even a running track around an L shape. The higher level ones are shading the correct regions in the town planning questions. One learner even attempts a create a shipping path question involving 5 elements. I look at the clock and 3.5 hours has gone! I pull them back for a final Slido, it stays the same. I recap our learning intentions and ask them to reflect in their fake iMessage sheets. See my blog post on feedback for these. They all thank me for a brilliant lesson.
I grab a cuppa and sit down to respond to their feedback iMessage sheets. Here are some of the responses:
"Why has no one shown me CARD before? Changed it all now"
"I will forget loci but I won't forget the lesson"
"Thank you it was epic, I learnt more than the last 4 years of studying for my GCSE"
I honestly think this was my best lesson ever. Yes I had pre planned presentations and my photocopying was ready but I made responsive decisions throughout and reflected on learner points. I don't think I did anything special, I certainly would never do anything special for a peer obs, and it all came good in the end. The peer observer emailed me a few weeks later and said she was trying Slido and some other bits she had seen me do, that is why I have an open door policy!
