(For a report on the morning session, click here.)
…onto the afternoon. Lynne McClure is a friend and mentor, and given that she is currently chairing the government’s curriculum review team, it was no surprise that there was a great sense of anticipation in the room.
Lunch was good, as hoped for, but as ever at these events, the real value lies in spontaneous conversations. I lost track of how many people I spoke with, many of whom I hadn’t seen for years. In fact, just as I sat down, who should come and sit beside me but Mike Askew, an old friend from BEAM days, with whom I happily reminisced for a while. It turns out that he is doing some interesting projects with a charitable foundation, and like me, not intending to ‘properly retire’ any time soon.
Time for Lynne’s talk, ‘Curriculum Design – notes from the chalk face.’ She started off wisely managing our expectations by explaining that she was unable to share much info (on DfE instructions!). Straight away, we got into some maths – specifically, this nice task from NRICH.
I was sitting next to Rob Eastaway, fresh from his stand in the exhibitors’ area with a range of fascinating things based around the history of maths, including the biggest slide rule you’ve ever seen! If you haven’t read Rob’s book on Maths in Elizabethan times, do check it out here – it’s excellent.
We enjoyed playing around with the problem, and Lynne suggested we might have done things like: Exploring, Conjecturing, Questioning, Explaining, Generalising, Convincing, Justifying or Proving.
Lynne argued that this was absolutely central to the way we should be doing maths.
We then looked at how we interpret graphs, specifically the ones shown here: can you work out which Olympic records each graph is showing?
Just when we were dying to find out, Lynne showed us another interesting puzzle, this time from Underground Maths. The point? Which were we using out of Lynne’s previous list: Exploring, Conjecturing, Questioning, Explaining, Generalising, Convincing, Justifying or Proving? Quite a few, naturally.
We then thought about the difference between fluency and recall. In each of the examples above, we were building both. The difference? Fluency is being able to use what we recall in a variety of ways. This is where the current curriculum perhaps falls down, so it was good to hear that Lynne’s Curriculum team was considering this as part of their review.
International data suggests that we are doing OK-ish in comparison with our neighbours, yet 26% of primary children did not achieve the national expected standard at Y6, and 41.7% of GCSE pupils do not get a grade 4 or higher. Worrying – and why?
Hence the Curriculum Assessment Review, and the DfE response. The two big ideas to come from this were:
- The Curriculum is simply too full. This was a huge shock to, well, absolutely nobody. The review team wasn’t allowed to take content out, so instead is trying to move some KS1 content to KS2, and some KS2 content to KS3. Hallelujah.
- Mastery: the review emphasised the need for mastery and secure learning rather than superficial ‘coverage’. The reality is that we need to go slower. Which dovetails with point 1, of course.
The other two points were a) the introduction of a Year 8 diagnostic test to identify and target gaps, and b) the need for financial literacy. The review team is also recommending NOT phasing out formulae sheets for GCSE, which some will agree with and some will not, but I doubt there were any dissenting voices at Lynne’s suggestion that a greater focus is given to Reasoning. Time will tell.
As a final thought, Lynne asked ChatGPT the interesting question: ‘What was the point of maths?’ It gave a surprisingly good answer, I thought. Do try it out! As ever, Lynne was engaging and well-received.
After a brief loo stop (I definitely drank too much tea and the room did not lend itself to slipping out the back), it was time to split into three small groups. Credit to the AMiE staff for being ready to guide us to the right places. My cohort started with Jenny Ingram, who took us through the current range of journals.
Here’s a scoop: currently, to keep things simple, ALL AMiE members have access to ALL journals – this represents an amazing amount of value (and no, they didn’t pay me to say that). I checked with Jenni later, and she said that this would continue to be the case until at least the first anniversary of AMiE; you heard it here first, folks!
Jenni ran through a few publications and then asked us to say which ones we used, or indeed, to identify gaps for resources we would like to see in the future. She mentioned that while some people prefer print resources (I’m in that group), teachers are now starting to engage much more with podcasts, etc., so perhaps AMiE’s offering needs to reflect this. Jenni asked us to discuss for 5 minutes.
The conversation at our table ranged from the suggestion of an audit to identify overlaps and gaps; the idea of short-form videos (TikTok, etc.) to model particular teaching strategies or skills; and the discussion around the room appeared to have followed similar lines, as well as podcasts and better website navigability and functionality.
Time for the second of our 20-minute sessions, this time around Professional Development, led by Ashley Compton. Another Menti to vote on- how do we personally learn about maths? Trying things out, listening to others, and lesson-study (time-permitting), all came up.
Unfortunately, this room was very long and narrow – I was right at the back in the cheap seats, and found it very hard to hear Ashley (not her fault, she was trying to proect, just a layout issue). I did, however, get into a very interesting conversation with my old friend Cherri Mosely (she’s not old, obviously, I am) on whether it was even possible to learn passively, or whether this was probably an oxymoron.
Ashley talked about what AMiE should offer – from what I could make out, it seemed that a majority of people felt more positive about things like conferences, podcasts, and webinars, but less so about hybrid events, for example.
Next, we were asked to rank what we felt AMiE’s priorities should be. These were research, networking, conferences, webinars, podcasts and, um, another one – I missed it at the back, apologies to Ashley.
Next – content: we were asked to put our ‘top three’ interests. I had a bit of a blank, but in the end, I went for Interactivity, Examples and Joy. I think Ashley liked that one. I was deadly serious too.
Next, we were asked (somewhat ironically): What sort of venues should we use? Here’s a thought – not this room. (The rest of the venue was great, to be fair, but by this time of day, I was clearly a bit grumpier and less forgiving.
Sorry – grump over. Finally, Ashley advertised the BCME conference coming up in October – here are the details. I will be there, I hope.
Onto the third and final mini-session: Sue Madgwick and Charlie Stripp shared their thoughts around Policy and Advocacy, and External Relations. I enjoyed their ‘old married couple’ presenter vibe as they argued about who did what! All very good-natured.
Charlie made the obvious but important point that AMiE represents a huge opportunity for the profession- no longer is there a need for anyone to ‘choose a team’. He said that maths education has arguably never been more important; again, I found myself thinking that he was unlikely to find any dissent in this particular audience. He has a vision to be a voice for the profession and to influence government. Again – Amen to that.
Charlie posed the question: in which areas should AMiE seek to shape and influence policy, and which partners are most critical to this work? Well, obviously, Maths Week England is the correct answer. We’ll get there.
Sue’s turn. She asked a second important question: which external stakeholders should AMiE prioritise in developing and sustaining strong, strategic relationships? Again – MATHS WEEK ENGLAND!
We had a few minutes of discussion – I sat with Lynne McClure, who showed me this amazing diagram from the Nottingham Observatory. Quite an impressive list of who’s who in maths education, and I guess the answers to Sue’s question will be on there somewhere. Apart from MATHS WEEK ENGLAND, which for some reason appears to be an inexplicable omission ;-)
Also at our table was Karen McGuigan, from Maths for Life. I had not heard of them before, but I enjoyed learning more. Check out their impressive work here.
Ok – time for another short break. Flagging now!
…and back…after some fabulous cake, providing a much-needed sugar boost, and more fabulous company (I have to say that, Ruth is watching me type, but as it turned out, she wasn’t wrong!)
Final session – respect to Jenni Ingram for taking on the graveyard shift. The session is entitled ‘Coherence in mathematical communication – Aligning talk, symbols, and representations’. And yes, the Oxford comma was in Jenni’s title slide, in case you were wondering. She promised it would be interactive and that we would be doing most of the work. Spoiler alert – she held the room very well. And I predict that many people will soon be ‘stealing’ her lovely ‘animal eyes’ idea. Sorry, but if you weren’t there, you may never know.
Jenni referred specifically to a structure for thinking about communication that includes ‘Linguistic Demands’, ‘Listening and Feedback’, ‘Making Connections’, and ‘Reasoning and Explanations’. Interestingly, Jenni said that UK teachers spend less time than international peers explicitly relating mathematical ideas to the images they use in the classroom. She also reported that we are not very good at listening to each other. At least, I think that’s what she said…
First task: Jenni displayed a series of images and calculations. (such as 3 x 12, -12–3, etc), and asked us to think about how we would read/say/describe them out loud, followed by a brief comparison of thoughts.
This made it very apparent what communication might lead to or achieve. For example, there are a myriad of ways in which we might describe 3×12. We were invited to come up with a list of ways we might describe 12÷3.
Confession time: It was yet another Menti, and my brain decided it was all menti-d out, so sorry Jenni. But I will shamelessly blog on the shoulders of giants and report what others came up with. Actually, I won’t, as the responses appeared on the screen a bit too small for me to read. Sorry. Things are going downhill.
Next up – a triangle. English ‘tri-angle’, three angles. Spanish: Triangulo. Mandarin; ‘Three angled shape’ Turkish: Three-sided figure. German – Three corners.’ Irish: ‘Three parts; Urdu: ‘Three faces’. What?! This was fascinating – the names we give things think about how we describe them.
This is classic metacognition; where is your attention? In a nutshell, the way we describe things impacts how we think about them. Jenni gave further examples using Alternate and Corresponding angles.
Oops. I just said ‘Boom’ rather too loudly. And the room went quiet.
Why? Jenni mentioned the ‘vertically opposite’ angles are angles on the opposite sides of a VERTEX. To use an old cliché, I was today years old when I realised that.
Sticking with the theme of angles, we were given an interesting challenge. Jenni showed four different worded solutions to an angle-finding problem, and we were asked to critique them. This caused quite a bit of discussion on our table. Not from me at first, as I was still too busy enjoying what I’d just learnt about alternate angles (and writing this paragraph, obviously), though I did have a good chat with Ruth and Andy about it once I’d finished.
Jenni’s general point was that everyone looks at things we all take for granted (e.g. angles) slightly differently. Are angles things, amounts of turn, measures, slopes, rotations between directions, parts of wholes, or a relationship between lines? Arguably, all of the above. She argued that we therefore need to exercise more rigour when we are talking about or describing concepts. What’s the same? What’s different? Jenni referenced the work of previous contributors to this idea, including John Mason was was in our group, and with whom I had a fun debrief about ‘vertexally opposite angles’ later as we were leaving…
Another example from Jenni: we might legitimately think of negative numbers as debt, bookkeeping, counterbalance, relativity, translation, symmetry, directed quantities, or symbolic rules. The implication of this is that we need to think carefully, both about which representations to use, and how we describe them and relate them to the specific concept we are exploring.
We were then asked to think about how to explain -12 x -5 = 60. This led to some great discussions, and then an amusing intervention from a delegate. He is retaking his GCSE maths, and he was questioning the utter weirdness of multiplying -12 by -5, and the ways we tried to describe it. A good point, and well received by the room.
One thing I found myself nodding vigorously at was the need to communicate well, specifically to:
- reduce ambiguity through our representations – the use of ‘equals’ is a good example.
- help students make connections and distinctions.
So, a well-delivered and fascinating session from Jenni, who finished with a link to a research project on developing research-based communication in classrooms. It’s always a skill to manage energy levels at the end of a conference, and having been on the maths education circuit for a while, I can’t believe it’s the first time I have had the chance to listen to Jenni speak, but I thought she was really good, particularly as she had only just flown back into the UK the night before.
Wrap up – Helen Madeley gave thanks to the team, and then to Ashley, who thanked everyone else – it was starting to feel like a handshake problem, and not to be outdone, the laptop chose that moment to have a handshake problem of its own (in that it refused to shake hands with the projector) so with some relief I will sign off, at the end of what has felt like a very significant, positive and important day.
I hope those of you who were not able to attend will have found this useful. Time to head home. Sleep well.