So it’s been a while since I’ve written anything on here. For anyone interested in my educational life between mathsconfs 6 and 10, my Twitter feed covers it fairly comprehensively.
After trips to Kettering, Birmingham, Sheffield, Peterborough and Kettering for previous mathsconfs, we’d finally made it to London for round 10 – two of us from Ninestiles were on the train just after 6am for our adventure, and this blog post summarises the highlights of the day.
Session 1: How to Teach Problem Solving – Kris Boulton
Kris kicked off his session with a couple of interesting problems for us to solve – some fun with isosceles triangles, and some more fun with circles inside a square. I managed to solve them both eventually, which was mildly pleasing.
If we want to help our pupils to effectively solve problems using something more than Polya’s ‘be ingenious’ strategy, we should probably focus more on getting the basics right. If pupils have a solid grasp of their key skills, it leaves more room in the working memory to actual deal with the problems at hand.
Using the analogy that people don’t run marathons to practise running marathons, Kris suggested that just giving pupils ‘problem solving’ tasks probably isn’t the best way to go about teaching problem solving.
In amongst some consideration about the deep structure vs. the surface structure of problems, and the importance of amassing a catalogue of problems organised by deep structure, Kris shared the following idea on the topic of simultaneous equations:
Teach pupils to add and subtract equations as an explicit skill on their own, using minimally different examples.
It’s not something I’d really thought of doing, other than as part of a step in a longer simultaneous equations question, but it’s definitely worth a try.
Session 2: A Brief History of Mathematics Education in England – Mark McCourt
This was the sort of session which I expected to find interesting, but not necessarily applicable to my everyday lessons. It’s sometimes nice to learn about the past. Mark spoke knowledgeably about nearly 1000 years of education, in spite of being much younger than 1000 years old, and we heard tales of Oxford, Cambridge, Henry VIII, humanist curricula, private-public schools, progressives, traditionalists, free schools and the rest. Hopefully Mark will write up the whole story at some point for anyone interested.
Session 3: Cambridge Mathematics Espressos – Lucy Rycroft-Smith
This was a session that I was really looking forward to – I love a bit of educational research, and the opportunity to look through summaries of research which we could share with the rest of our teams back at school seemed like a great idea.
Unfortunately, the session focused more on the fact that these ‘espressos’ existed, and sharing a few key facts, rather than actually going through them in detail. My colleague and I discussed this one after, and we would have much preferred the session if we’d had a brief ten minute introduction to the project, then forty minutes to actually delve into the research. I actually looked up a couple of the research summaries on my phone during the session, and I did find them really interesting, but I felt that it was a bit of a missed opportunity for the group. There were, however, some interesting discussions on early number sense and approximate number systems formed by very young children.
I think the session was good for raising awareness of the existence of this project, and some time was given for individual questions, but I personally would have preferred a different balance. Maybe others would disagree?
The espressos can be found at cambridgemaths.org/espresso and current topics include:
- Learning and assessing times table
- The impact of assessing confidence
- Applying traditional and progressive models to maths teaching
- What is number sense?
- The effects of attainment grouping
- Maths anxiety
Session 4: Digital Resources for the New Curricula – Douglas Butler
Douglas’ session was the sort of thing I wouldn’t normally go to, as technology-based sessions from others in the past have often offered awkward, yet expensive, non-solutions to problems I didn’t have. This one was much more enjoyable.
We started with a journey through Google Earth, finding hexagons, pentagons and equilateral triangles in the wild. From there, we moved onto the tsm-resources.com website, plotted Pythagorean triples in 3D on autograph, and found the equation of the heart.
While all of the above was interesting, the bit I found most useful covered the use of Autograph for statistics. The plotting of bar charts, histograms, box plots and the normal distribution is something which could be very useful for my GCSE statistics class, who are fairly confident with each topic individually, but often struggle with interleaving them.
The final session of the day came with an Ofsted stamp of approval, in that both Dani and Rose’s schools have recently received Outstanding judgments. As both presenters made very clear, none of their work was done for the benefit of Ofsted, and the Ofsted judgment doesn’t make their ideas good, but it’s useful to allay fears that reducing marking could be met with the wrath of the inspectorate.
Both schools featured essentially use a system of regular quizzing, rather than traditional book marking, to assess progress over time. The quizzes mainly featured a mixture of questions from the previous week’s lessons, with a section for recapping previous knowledge. At Michaela, pupils would get a practice quiz with different numbers the week before, with the opportunity to go through questions in class and revise over the weekend. At Dixons Kings, pupils would do any corrections during DIRT time. In both cases, hours of time have been saved on traditional marking, with pupils gaining more immediate and impactful feedback at the same time.
Dani argued clearly that there is no need for extensive written feedback. The quizzes on their own show that the pupils have received impactful teaching and feedback, as the pupils couldn’t answer the questions without being taught the content, and they wouldn’t have improved between quizzes without receiving feedback.
Teachers from both schools claimed that their pupils both enjoyed and looked forward to the quizzes, with the only ones to not like them being the ones who didn’t work as hard. Pupils also felt better prepared for their real exams, and parents and tutors could easily see where to help their children.
The quizzes in both schools were centrally prepared, with room for teachers to adapt slightly for low/high achievers, and designed to take no more than twenty minutes to complete. Pupils would then stick their tests in their books, so they could be reviewed over time.
While Dani opposed the idea of marking exercise books at all (while obviously checking books during lessons), and proposed staff marking the quizzes, I’d like to try a slightly different system:
- Checking through books roughly every two weeks for effort, completion of work, and pupil checking/correcting of answers.
- Noting pupils’ names in three columns – exceeding, meeting and working towards standards (or something), with public praise for the exceeding pupils, and quick, individual conversations with the ‘working towards’ pupils in the next lesson.
- Noting any common misconceptions and going through those with the whole class, fully reteaching topics if necessary.
- Running fortnightly quizzes for pupils to swap and mark, which could then also be checked during the book reviews. (But what if they cheat?! Just insist that all pens apart from the green (red/purple/sparkly) pen are away before the answers are revealed, and keep an eye on the class while marking).
The main issue with the WWW/EBI-style systems is that, generally, the WWW comments will cover whatever you’ve just been teaching, and the EBIs will cover the things you were about to do next anyway. The repeated, deliberate practice after careful modelling of a topic (which pupils should generally be getting correct) shouldn’t be the same work you’re assessing for memory and long-term understanding of the topic. The only thing you can tell from this is whether pupils have done the work correctly at the time, hence the need for quizzing later.
I’d definitely be up for the maths marking revolution. Every hour spent marking one pupil’s book once is an hour which could have been spent planning and producing reusable resources (or balancing the work/life), so any marking we do really needs to be worth the time cost.
Other Miscellaneous Things
‘Same signs sum, different signs difference’ can be used to help pupils quickly decide the magnitude of the answer to questions like -3+7 and -3-7. The sign of the larger number then gives you the sign of your answer. When moving on to -3+-7, use the same idea to deal with the double sign first, before going from there.
‘Underline, circle, decide’ can be used for rounding to either decimal places or significant figures (and truncating, although the decision there is somewhat easier to make).
Peter Mattock suggested that we should use ‘angles which form a straight line’ to avoid the ambiguity of ‘angles on a straight line’.
I also discussed finding exemplar GCSE Statistics controlled assessment work at A* grade with someone from Edexcel. I’m currently in the position where even my best pupils (95%+ on the exam), after following all of the printed guidance, still only get A grades on the controlled assessment, and I’m still not entirely sure where they’re going wrong.
Overall, it was a great conference. Thanks again to Mark and the La Salle team for organising, and I hope to see everyone again soon!