Attending my first ever Maths conference (and virtual one) on Saturday was an absolute dream and I am still buzzing from it. I had a full day of geeking out, making tonnes of notes and being inspired by so many amazing Maths educators out there – the team at La Salle did a brilliant job of hosting this online to around 3000 teachers across the world and it was so well organised. There were sessions that really challenged my thinking and others where I was literally nodding along with the speaker because of the similarity in beliefs – especially was especially true with the Kris Boulton session on ‘always teach what before why’.
Session 1: Method selection: practical strategies to help students interpret problems – David Busby
“I can do it when you show me, but not on the test”. As a teacher, this is something I hear time and time again, year after year. It breaks my heart when I see students perform ever so well in class, then completely slip up in low-stakes class tests to high-stakes exams. In this session, David highlighted the importance of modelling techniques as well as talking about resourcing for interleaving practice.
It is not that the students do not know what to do when answering questions, as I have found in my own practice, but sometimes they just do not know where to begin and how to unpack a question. What was really highlighted to me during this session was the detail in explicit thinking he suggested when modelling a question that I have never truly practiced. I have focused primarily on the calculations and often asking meaningless questions like “what is 60 x 50 x 40 ” if it were this question rather than focusing on the process and why I am using that process.
Going forward, something that stands out as an area for me to improve on is practicing the decision making skills and explicitly saying this when showing students worked examples. Instead of working through a question telling the students what I am doing, I need to say out loud why I am choosing to do what I do. This unpacking will then hopefully allow students to actively make their own decisions when working on problems like the above.
Another aspect David talked through was the use of examples and non-examples. Having recently embedded this into my practice following a great CPD day with Craig Barton in early 2019, I have seen the benefits of this and how important it is for students to be exposed to both. I really liked how a sequence of this was shared on angles in parallel lines first starting with showing students and then questioning.
Something that I have not used yet in my practice is flowcharts which was also explored in the session. I have found previously when teaching Trigonometry and Pythagoras that students end up mixing the two and over complicate a Pythagoras question by using Trigonometry. Although part of me feels that the students may become heavily reliant on a flowchart to make their decision on which to use, it could act as a good scaffold for those that require it. This can then be taken away slowly so they are able to do it without looking at one.
The last part of David’s session was on interleaving. Time and time again, I have found myself almost fuming at students for not having remembered something we covered a year, a month or even a few weeks ago. Often, the practice in class is blocked rather than interleaved and although interleaving has shown to increase the retention of students’ learning and ability to transfer it to other contexts, I just have not used it enough. One of my key takeaways was to introduce interleaving into class exercises and into assessments by starting with a resource and changing 1 question, 2 questions, bringing in 1 topic, 2 topics etc.
“Break the chain of thinking”
Speaker information/links for resources mentioned for this session:
- Twitter: @mrdbusby
- Blogs at: https://mrdbusby.wordpress.com/
Resources for interleaving can be found from - https://www.mathsbox.org.uk/index1.php (paid membership required)
- https://mathsbot.com/ (Brilliant resource, lots of manipulatives too)
- https://mrcartermaths.com/ (paid memberships required)
- https://www.drfrostmaths.com/
Session 2: Raising understanding and attainment – Siōbhán McKenna
One of the first things I will take from this session is to create a ‘Maths contract for success’ for the higher attaining pupils at A-Level to get them back on track. Siōbhán stated four of the terms the students sign to agree on, which are 1) I need to work hard consistently, 2) I need to ask the teacher or help when I am stuck in class, 3) I will spend 6 half hour blocks or 1 three hour block per week studying Maths over and beyond Maths homework and 4) I agree to attend study support on (day of the week).
The implementation of this that was suggested was to:
1) Choose the pupils
2) Meet with them to discuss and sign the ‘contract’
3) Send a copy to pupil support, year head and pupil
4) Track the pupils for supported study
5) Meet with them on a weekly basis if not adhering to the contract
I really like how this involves handing over responsibility to the students and allowing them to take ownership of their learning. From experience, I have often found in the past that with year 12’s and 13’s, they struggle to take ownership after having been ‘spoon fed’ and chased over the course of KS3 and 4.
“Everyone can do”
Another part of the session that I absolutely LOVED was the use of the area model to teach various aspects of Maths. From short division to completing the square using the model, my mind was opened. So far I had only used this model when teaching multiplication and expanding brackets, but after seeing ‘completing the square’ being done using this – so simply too – I will definitely be embedding this into my teaching in the future. Below, I have included a snapshot of my notes from the day to show the example Siōbhán went through.
Speaker information/links for resources mentioned for this session:
- Twitter: @ShivMcKenna55
- Blogs at: https://mathsmda.weebly.com/
- https://www.openmiddle.com/
Session 3: Always teach what before why – Kris Boulton
This was a session I sat through nodding along and agreeing with everything until it got to solving quadratic equations. That made me a little uncomfortable but I understand why. Kris started the session talking about indices and how his initial instruction looked like previously – very similar to how I have taught into the past:
710 = 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7
73 = 7 x 7 x 7
Which means , 713 = 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7
So, 710 x 73 = 73 + 10 = 713
Therefore, am x an = am + n
The problem with this, as I have also found in my practice, is that by the time the students get round to practicing the questions, they are not even practicing the ‘why’, the practice does not match the instruction and it is frustrating for those who can see how to get the answer without going through the process. There lays no purpose for the proof at that point.
“Attention is the currency of learning”
So instead, what Kris suggests is to teach the ‘what before the why’. This means showing students a few examples just asking “what did I do here?”, them having a go at questions on mini whiteboards as an initial assessment ask and then going through an expansion sequence.
This method also allows students to feel a sense of pride and success early on in the lesson which can lead to practicing the why independently later.
Now, what made me uncomfortable here was how we are encouraged to say “to find the solution, flip the sign of the second term in the bracket and put over the number in front of the x”. To me, this is purely a procedure without any understanding on what they are actually doing. However, as I was thinking this, Kris mentioned how important it is to understand that this is not ‘what without why’, it is ‘what before why’. Thinking about it this way makes complete sense and can be linked to Siōbhán’s session were we could start linking bits together, perhaps by introducing the quadratic graph to show the students what this all means.
Speaker information/links for resources mentioned for this session:
- Twitter: @Kris_Boulton
- Blogs at: https://tothereal.wordpress.com/
Session 4: Teaching exact trig values – Jo Morgan
When Jo broke down a higher question on Trigonometry, it hardly seemed like there was any Trig in there. The question was composed of the following components:
- Memorisation
- Substitution
- Surds
- Fraction work
- Multiplication
Trigonometry was a topic I loved at school and after finding out that the GCSE specification changes meant that all students had to ‘know’ more about Trig, like Jo, I was excited to see the level that will be tested. However I was a little disappointed when I looked at papers showcasing these questions – especially for foundation. To me, these questions just were recall questions with little or no conceptual understanding required for the students taking the Foundation paper. What was the use of just ‘knowing’ a bunch of numbers and values without context? As Maths teachers, we are always looking for meaty questions and those basic recall style questions hardly felt enough – until this appeared in the Higher paper 1 (Edexcel 2017) that fitted that criteria completely, for us.
But to teach a question of this level, the sequencing of sub-topics within Trig is so absolutely vital to get right and I liked the way Jo suggested sequencing it.
What stood out from this sequencing is that by teaching Exact Trig Values early on in, we should be embedding throughout the topic rather than seeing it as a stand alone topic. They should be embedded and interleaved into all parts of the topic.
Teaching memorisation is hard and seeing all the ways that Exact Trig values can be taught was refreshing, although I do still love to teach the method of deriving them using the triangles. This is what I was taught by my Maths teacher (oh, so many years ago) but I still remember them till date. I cannot get my own head around remembering a bunch of numbers in a table, drawing it on my hand, let alone teaching it this way. By using the method of drawing the ‘special triangles’, we deepen the understanding of Pythagoras and right angled trigonometry and show meaning and purpose behind these values.
The key takeaways were:
- Give Trigonometry time in the curriculum
- Recap and deepen understanding of trig and surds
- Order the lessons to maximise interleaving opportunities
Speaker information/links for resources mentioned for this session:
- Twitter: @mathsjem
- Blogs at: https://www.resourceaholic.com/ (don’t know how I would teach without this website!)
Session 5: Misconceptions in Mathematics: Angles – Craig Barton
The interaction element during this session was really enjoyable and it is something that is definitely worth exploring in a department meeting. We had to guess what the most popular wrong answer would be after being shown several questions on angles from his website Diagnostic Questions. These are absolutely fantastic questions that dive into the misconceptions students enter with and having used them over the last year or so, I highly recommend. What was really interesting was finding some misconceptions that I thought were misconceptions not to actually be true. This was particularly highlighted when I guessed the most popular wrong answer incorrectly for a scalene triangle, thinking almost too deeply about why this could be the case. Craig encouraged us to list and virtually discuss what might be the common misconceptions in sub-topics of Angles which I found really useful.
“Go deep”
Instead of showing students the ‘typical isosceles triangle’ as seen from a quick Google search above, we were shown unusual ones with the intention being of going deep from the start. Allowing students to engage with these versions of isosceles and embedding questions that use these orientations from day one, will mean they are used to seeing them and so will not be thrown off when they appear.
Something that really struck me and I believe has actually changed my teaching since Saturday is the idea of angles on a straight line, in particular the language used when it comes to this topic. For all my years in teaching so far (I’m going into my 6th year), I have always almost sung in class that ‘angles in a straight line add up to 180 degrees”. This has never struck me as a topic that can be really challenging. Until Craig’s session.
The minute a question like this appears to students, it is not surprising that many of them answer 96 degrees after having drilled into them that angles on a straight line add up to 180 degrees. What I found needs to change here is the language I use. Instead of saying “angles on a straight line add up to 180 degrees”, I now need to say “angles at a point on a straight line add up to 180 degrees. Even using something like “adjacent angles on a straight line add to 180 degrees” can be useful as it separates questions like the above from the more straight forward style of questions. This was a huge insight into this topic and how changing a few small elements in our teaching can really develop a stronger understanding for the pupils we teach.
Speaker information/links for resources mentioned for this session:
- Twitter: @mrbartonmaths
Resources can be found from: - http://www.mrbartonmaths.com/index.html
- https://diagnosticquestions.com/Account/Login (all the questions form the session we engaged with are on here)
- https://variationtheory.com/
- https://eedi.com/
- https://whiterosemaths.com/resources/
- https://donsteward.blogspot.com/ (absolutely brilliant!)
Finally…
Even after getting through over two and a half thousand words for this post, I have barely scraped the surface on what a fantastic day it was. It is especially exciting that La Salle are placing the whole conference online on their website for free – I can’t wait to dive into all the other sessions I could not attend. It also makes me super happy that there were delegates all across the world accessing this conference and I hope this is the start of the online sharing of such quality CPD. I can’t wait to share all that I have learnt with my department and also to see what this looks like in practice with the kids in front of me. I look forward to attending my next Maths conference, online or in person.
Conscious Teaching 
Loved the post very insightful
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