This was not my first mathsconf but it was my first virtual one (along with everyone else who attended). It was brilliant to see people from all over the world tuning in. I saw ‘hello’ from countries such as the USA, the Philippines, China, just to name a few. With 3 000 people virtually attending it also meant the raffle raised an amazing amount for Macmillan cancer support. The total was at over £10 000 by the time I logged off yesterday.
Considering the conference was virtual you could still take part in the usual mathsconf activities such as the treasure hunt, the raffle, the tuck shop (although I believe that had to be pre-ordered), the cake competition and the usual lunch time activity involving pringles.
LaSalle did an amazing job with the transition between each workshop being flawless and the day so easy to follow. Not an easy thing to pull off with 3 000 delegates from around the world. The workshops I attended were as always full of great ideas and challenged me as a teacher.
Session 1 – Making up for lost time (Mel Muldowney and Christian Seager)
The question above has sparked some very interesting debate on my twitter feed since I have posted this. This student received 0 marks for this question due to the answer being on the answer line. The mark scheme does accept 15, 20, 25 as a method mark but the argument was that due to the answer being on the answer line this was not interpreted as a method. For this reason 0 was given as 20 is an even number and not odd therefore is not in the union of A and B. Apparently had this student written this answer higher up the page or adjacent to the words in the question they would have scored M1.
With everything happening right now in England and with covid19 closing schools and the students missing months of formal education the debate of whether to enter students into higher or foundation is probably raging more than ever for HODs. Below is information for 2019 for Edexcel:
You can see that overall 57.2% were entered into the foundation tier but within year 11 47.5% of students were entered into foundation. We need to remember that at re-sit students tend to be entered for foundation hence why the overall foundation entry is higher but GCSE is less.
You can see however that from 2018 to 2019 there has been an overall increase in the percentage of students entered into foundation. It was discussed that more schools may try to leave the overall decision of tier of entry until further down the line. This may however have implications for SOWs for some schools.
Mel has been doing some analysis of the topics that have been appearing on the GCSE exams (for the full analysis you will need to access the powerpoint from the session):
These may provide a starting point for some but as Mel and Christian both correctly pointed out, we can’t just plow ahead if the students do not have the necessary prior knowledge. It is going to be more important than ever to check this and pitch our lessons accordingly.
You may be excited to know that just maths are releasing a crossover revision workbook, ‘ready, set, go’. Head over to https://justmaths.co.uk/ to look at a sample and to pro-order. You can see the topics that are going to be covered in this below:
On top of this tutor time activities were also discussed. Not every school will be in the position were in year 11 the students are placed into groups by subject such as a maths group, an English group and a science group. They said they have formal session in tutor time so that they know what topics are being covered:
If you can’t do this in your school then we also discussed the importance of parental buy in. Next year will be a lot easier if we get parents to buy into what it is we want students to do. This may be handing out RAG sheets of mock exams to parents at parents evenings or posting them home to the parents that don’t turn up. It may be emailing parents each month with ‘a little bit of maths each day’ calendars. This is something I did last year in my previous school. Each month I emailed out the calendars and then the following month the next calendar and the previous months answers. Christian correctly said you will not get a thank you, but you certainly will get an email from parents if you forget to send the calendar out. At least you know that some students are engaging.
Mr Chadburn tweeted the other day that he is getting ready to release his calendars for the next academic year. Check out his previous calendars at: https://mrchadburn.school.blog/resources/a-little-bit-of-maths-each-day/
Next year making sure we have students in the right sets is going to be more important than ever. I am in total agreement with the statement:
‘attainment range not ability range’
This links back into the prior knowledge. We need to fight next year that the students targets are not what we should be setting on but their actual current attainment. Below are some other things to consider for setting:
For the team teaching point Mel shared that when they had spoken to their students about team teaching they found the students preferred when the teaching followed on from each lesson and not studying one topic with one teacher and a different topic with a different teacher. This may be something to consider. It does take a lot of communication and handing over planning etc but it might be worth finding out what your students prefer.
There were a lot of interesting points made in this session and I highly recommend watching the recording of this session. Below is the start of a possible timeline:
Our students next year are going to need all the support and confidence they can get. We need to make sure that we help build their confidence. Lets not start next year focusing on the time lost or that we are running out of time. Lets start by focusing on what our students can do, building their confidence and helping them to believe that they can do this. They don’t need us to have a ‘woe is me’ attitude, they need us to have a belief in them.
Session 2 – Method selection: Practical strategies to help students interpret problems (David Busby)
Does the below look familiar?
I imagine for a lot of us the above is very recognisable. Stand at the front, go through the question, point out why we are doing things whilst writing out the method. But what about a simple shift:
Both of these examples are above are known as explicit thinking:
I really liked this idea. I find that students can have a hard time trying to decide what methods they are supposed to use for questions, especially worded questions. They tend to miss the key words that give them the hints they need. By doing a few simple changes it completely transforms the practice. Instead of just talking through it and me pointing out what information has told me to do that method, it puts the emphasis back on the students to think and decipher the question all whilst having the teacher present to combat any misconceptions. Think, pair, share could be used with this or asking the students to respond on white boards.
David then went on to talk about the importance of using examples and non examples. This is something I have been using in my practice a lot more. Boss maths have some great slides for examples and non examples. Frayer models are also a great way to get students to think about examples and non examples. Below is an example of how David uses them:
Notice here how the students are not being asked to write down the value of any angles, they are simply being asked if the angles are corresponding or not. Reflecting upon my own practise I realise i am guilty of rushing through some really important basic concepts. For some reason students struggle with identifying corresponding angles, alternate angles or co-interior angles. Perhaps it is my fault for not spending enough time at the basic level of actually identifying the angles without actually finding a value. An excellent blog by Mr Rowlandson can be found at https://ponderingplanning.wordpress.com/2019/03/23/thinking-about-corresponding-angles/ on the exact topic of corresponding angles. It is definitely worth a read and will challenge you. I know it challenged me and made me go onto create a single lesson dedicated to the Hypotenuse. Lets use techniques such as examples and non-examples to ensure our students really get to grips with a concept.
Next up was the use of flow charts in lessons as a tool for scaffolding:
This is a concept I have not personally come across before but it actually makes so much sense to me. Bear in mind this is a scaffold, meaning the ultimate goal is to take this away eventually. But I think it gets to the heart of differentiation. Should differentiation be about different sets of questions for the pupils in our class or should it be about accessibility to those questions? As someone rightly said we will not build our students confidence by placing lots of questions in front of them but telling them to miss them out. We are sending the message they can’t do it. Differentiation should be about us as teachers putting things in place so that all of our students in the room can access the questions we have selected.
The final thing that David suggested was using interleaving in our every day exercises. He didn’t suggest the usual of using our starters for interleaving or homework etc no he suggested using interleaving as a way to prevent blocked practise in exercises:
If you look at that and think ‘how obvious is that? Why have i missed that?’ well that was my reaction. How simply yet effective is that? What a great way for the students to connect different elements of simplifying. It breaks the chain of thinking, it stops the auto pilot. David made some excellent points. Start off small.
Make this change with 1 class and change 1 or 2 questions in your lessons. Make those question easy wins. Once again building the students confidence. The most important part, stick with it. Sometimes as teachers we trial things for a week or two but because the students are still resisting and it feels hard we go back to our old ways. We need to remember we are the expert, we know what is best for our students. Some tough love is sometimes what they need in terms of us using techniques. I must say I got so excited, I went and changed 2 questions in the lesson I am delivering in a few weeks on the circumference of a circle, as well as made a flow diagram!
This session was full of so much wisdom and excellent practice that I cannot do it justice. You simply have to watch the recorded version of this session.
Session 3 – There is more to life than GCSE (David McEwan)
This session I chose with my HOD hat on. I always think it is important that as HOD i am aware of what is on offer out there. What other qualification are there that my students might benefit from? You will be pleased to know that AQA do indeed offer several other qualifications:
The best way to look into these is simply to visit the AQA website and do your research.
Having delivered the entry level certificate myself a few years ago I do highly recommend looking into this for your lower attainers. It is maths in its most simplest form but it is nice to be able to give your students an extra qualification to aim for. The best part is it can all be delivered in house. You can see from the data below the increase in uptake for this certificate:
If you are also wondering about the further maths at level 2 for your higher attainers than a very brief outline is below:
You will notice that only grades 5 to 9 are available (David did say they have a catch grade of 4 when it is needed but not that many students fall off the bottom) as it is expected that only high level students will take this certificate. It can be a really great way to start bridging that gap between GCSE and A-Level.
Like I say the best thing to do is to visit the AQA website and research the qualifications.
Session 4 – From Abacus to zero (Ed Southall)
This session was all about the origins of words. You may be surprised with where some of our words come from.
I liked the example of factor. Factor means to make. A factory makes stuff in the same way factors make numbers. I thought this was quite neat and a nice way to get students to remember what factors are.
The next one will blow your mind. The word average:
It comes from the french ‘Averie’. Fisherman would rent a boat and take it our fishing. The boat tended to return damaged and the damage would need paying for. The fisherman would equally share the cost of the damage between them.
Hence the word average (this received a lot of love on twitter). All of a sudden average makes perfect sense!
Lets take another word, Zero:
When we talk about place value we always talk about zero being a place holder and you need to put it in to show nothing is in that value. What if we taught our students it is actually Arabic for empty? It might actually help them understand more that those place values are empty so we are simply putting in the symbol for empty.
What do you think of when the word polygon is mentioned? Are you thinking of shape with more than 4 sides? That is indeed the imagery that should appear but the ‘gon’ part of ‘polygon’ actually refers to the angles:
This is why quadrilaterals do not fit in with the naming convention of polygons. The quadrilateral is the only shape that references the sides (lateral):
If you want to have a bit of fun and a challenge then watch the recording of this session to see how the conventions of naming shapes can be used to give a name to a 999 sided shape.
Ed then went out to talk about the relationship between certain words:
I really liked this. I can easily see myself using this in a lesson. How ate all of these related to circle?
A circus traditionally was in a ring.
Circumstance: events surrounding another evnt
Circuit: again reference to ring. The Formula 1 circuits.
The prefic circ simply means ring.
Final one from me, why is a Rhombus called a Rhombus?
Rhombus is Greek for anything that can be twirled.
The Rhombus is something that was used as a spiritual tool. They would attach objects to a cord and swing it around their head and it would make a large sound https://www.youtube.com/watch?v=2ODGE2f7gLQ
Apparently the shape looks like something that could be twirled.
I once again recommend you watch the recording of the session to get lost more brilliant information and things to make you think.
Session 5 – Teaching exact trig values (Jo Morgan)
This session was brilliant. Jo made some fantastic points so this is a must watch. You must watch the whole of the recorded session. I will give you what I took away but you need to watch this session.
Below are the changes between the old style GCSE (on the left) and the new style GCSE (on the right).
Anything in bold is higher only. Underlined on the new one is both GCSE and foundation:
You will see how the word know was not on the old spec anywhere. Students had to understand, recall and use them but not know. On the knew spec you will see the word know a lot more along with the word apply. Jo made an excellent point. Michael Gove said the following:
Did he misinterpret the research? Did he mean knowing is a necessary precondition of understanding? It is indeed possible to know something without memorising it. It is possible to know about the exact trig values without memorising them.
I think as teachers we all agree that we feel the exact trig values being on the foundation paper is unnecessary. As Jo correctly said our foundation students will not go onto study A-Level maths, their grades are capped at a 5 and I wager most, if not all, A-Level Maths programmes require a 6 or more (controversy lies around this as well as I am sure most of us agree a 7 or above is really needed to study A-Level). In which case then are they necessary for foundation students? Should we be spending time on them?
Below is how many times exact trig values have appeared on the foundation tier and the question that was asked:
Have even the exam boards realised that Exact trig values on foundation tier isn’t relevant? Is just a step too far?
It has appeared on the higher tiers a lot more and so the session focused on the higher tier. However even then, it can be argued that some of the questions don’t look at the application of the exact trig values and are more surds based:
We do see some questions where the application is more that of what we expected but knowing the exact trig value part is worth 1 mark. In part b the students are given that sin 60 = 0.5 and then asked to work out the value of x:
But what working out are students having to do for something like part A? Below is a similar question to a with different students working out:
Deriving the exact trig value takes quite a lot of work and arguably more than 1 marks worth of work. I, like Jo, teach only how to derive the exact trig values. I do not use the table or the hand trick I only teach how to derive from an Isosceles triangle or an equilateral triangle. If these are bright and able students then they should understand how to derive the trig values. It makes them use their skills for trig and Pythagoras which certainly has merit. The thing is I can understand the students becoming disheartened when they find out about the tricks. Why are they going to so much effort for a question that is only worth 1 mark? And is this maybe why we as teachers rush through exact trig values because we have also downgraded them as something that can only appear on 1 out of 3 papers and is probably not worth that many marks anyway? (no guilt or judgement here, I am as guilty as the next person). But we could interleave them into our trig practise as Jo suggests.
Below is what Jo perceived a comp to have on their SOW (for my school she is pretty much bang on the money):
So how much time does Jo suggest spending on trig in year 11? Prepare to be challenged:
4 weeks! 4 weeks to do trig justice and to look at it in depth. Now Jo does belong to the real world, she said in a perfect world this would be how she taught it. Personally I love it. I have really been challenged over the past few years by some amazing teachers. I remember Gary Lamb saying that he told his team to believe that all students who came through their school were capable of achieving a grade 5. Wow! What a bold statement to make. But as i sat in that talk and listened to Gary talk about how they taught lessons it made perfect sense. Like Jo he believes in teaching in depth, but from the start. As he said, if we teach it right the first time we won’t need as long for the revision. How many of us are guilty of rushing through topics so we can finish the SOW so we can revise? But what would happen if we shaped our SOWs so that all the way from year 7 we study each topic in depth, interleaving knowledge and skills as we go? I dare to say we would have students who would have a great understanding of Maths and would be capable of that grade 5 that Gary dares to say all students are capable of.
Jo gave us some insight into the resources that she would recommend for a topic such as this. Below are some wonderful questions by Don Steward. I love his website median, there is great stuff on there for so many topics.
Jo also recommended the website Mathspad which she says she uses regularly in her teaching. You won’t find many maths pad resources linked on resourceahlic as you need a subscription, although some resources are free. The subscription for maths pad however is very reasonable.
brilliant.org was also suggested for stretch activities.
Jo went on to say that if we teach this topic right our students should have no problem with the following question:
To use this probably looks basic, but if we have taught trigonometry procedurally our students probably would be flummoxed.
Some final thoughts on the higher vs foundation debate:
As ever wise words from the amazing Jo Morgan. You have to watch this session!
Session 6: Misconceptions in Mathematics: Angles (Craig Barton)
Before I start i must mention 2 things:
- There are lots of CPD opportunities from Craig at the following address: https://craigbarton.podia.com/
- Craig is releasing an ultimate SOW from September 2020 (definitely keep an eye on that!).
This session really made you think as a teacher about where the misconceptions for our students lie. Craig showed us many questions from diagnostic questions (all on angles) and asked us to vote for which we thought was the most popular wrong answer (this is more difficult than it sounds). He then showed us responses from some of the students which highlighted where their misconceptions lie:
Laila clearly understands the difference between an equilateral triangle, an Isosceles triangle and a scalene triangle yet she thinks the triangle is Scalene when the answer is Isosceles. If you look at the question carefully notice how only 2 angles have been labelled. Has Laila not realised that to answer this question she needed to work out the third angle? What if the question had said find the value of the missing angle? Would Laila have had more success?
Look at this next question:
Only given the right angle, asked to find one other angle. The student has clearly missed the point that the annotations means Isosceles. Had the question in writing said ‘this is an Isosceles triangle’ would they have had more success?
Compare these two questions to the type of questions you ask in lesson. If you asked your students these questions would they get them correct? Craig raised an interesting point:
How many of us are guilty of not doing this? I know it struck me when before lockdown I was doing completing the square with a top set year 10 group. We were expanding a bracket with a fraction and they just could not do it! They froze. They protested, they didn’t understand and oh my was it a hard lesson. But then when we expand brackets how many of us throw in fractions? Or decimals? Or a negative fraction? Had these year 10s seen the unusual from the start they may have had a better understanding. And its the same here, had these students seen questions such as these on triangles from the start they may have had a better understanding.
What about angles on straight lines? Get ready for this:
How many of us display a question like the above when we do angles on straight lines? How many of us only ever display half of this question? Again, we need to include the unusual but we also need to be aware of our language and explanations. This student knows angles on a straight line add up to 180 degrees but he has a misconception here. Craig suggested we change the language we use:
I personally like adjacent angles on a straight line. You may be thinking ‘but that causes more problems. We need the to understand adjacent’. But if you use it from year 7 all the way to year 11 they would know what adjacent means. Its that spending time on these points. Once again its:
I could picture myself creating a lesson dedicated to simply recognising angles in triangles. NOT GIVING THEM A VALUE, recognising them. How many of our students cannot select the correct pair of base angles in an Isosceles triangle? Again, did we use the unusual from the start? Did we go deep?
The set of exercise below that Craig recommended by Don Steward are brilliant:
Notice how these are dedicated to isosceles triangles and then go onto develop the general case. I remember sitting in a course on how to teach proof at A-Level when we got onto the crux of it, we don’t teach proof enough at lower levels. Not just GCSE, but further down at KS3. Could you imagine going deep by trying to get students to generalise the case. Maybe our students would be better at proof by the time they studied A-Level. We need to stop boxing proof off as its only little topic and again include it where we can.
Lets make sure that we are really thinking about what questions we are setting our students. What do we want them to notice? What do we want them to think about. Below is an example from Craig’s website variation theory:
You can see how the orientation of the triangle has changed along with the angle that is being found. There is so much content already that a whole lesson (or even more) could easily be dedicated to Isosceles triangles.
And Craig’s final point was also that of using examples and non-examples in our lessons. There are lots of these that you can find already made on https://variationtheory.com/
Once again to really get the most out of this you need to watch the recorded session.
As always mathsconf did not disappoint. I am very delighted to say this as I encouraged mt 2nd in department to take part in her first maths conf yesterday. When i asked what she thought, she said she loved it and can’t wait for a face to face mathsconf. YES!
So if you are reading this and you have not experienced mathsconf then follow lasalle on twitter and keep up to date with them to find out when the next mathsconf is due to be on. Do not miss out. The tickets are an absolute bargain for the best CPD you will get as a maths teacher. Hope to see you in person at the next one.