How on Earth do students learn?! Meaning making with manipulatives...

A quote from somewhere has been rattling around my head for a while. It gets rolled out every now and then by me when a colleague claims that they told their class something, that 'it was so basic' and that they 'have no idea how they haven't remembered it'.

"Students don't learn from what you say and do. They learn from their interpretation of what you say and do".

I've concluded from this that my job is to not only share the knowledge with students, but to then ascertain whether what I shared was understood in the way that I wanted it to be understood.

I've delivered, sat in and talked about lessons over the last 11 years whereby I and other staff have walked away from a lesson fully confident that they'd done a good job in sharing knowledge, where I and they have done no such thing.

I'm starting to understand why this occurs, and it all boils down to the Curse of Knowledge. An idea is shared by a person with a complex understanding of that idea and everything that connects it, but this complex web of ideas isn't shared. What is shared is the surface structure of the idea - but without the connecting ideas in place (the prerequisites), the idea cannot be understood, no matter how simple it may seem.

'Two negatives make a positive' makes sense to me. I am an expert at working with negative numbers. I've learnt the complex relationships between directed numbers and have developed a way to work more efficiently when subtracting a negative number, or multiplying/dividing using negative numbers. Unfortunately, Billy in Year 8 doesn't have the complex web of understanding that I hold, so when I tell him this, he learns that 'When there are two negatives, it's positive', so he applies it to -7 + -3, and writes down 10 as his answer.

Complete Maths has given me a banquet of food for thought this year and last - incredible CPD opportunities as well as an online platform that continues to go from strength to strength - and much of this is feeding the way that we shape our curriculum.

I am one half of the leadership team in our department and my role is the teaching and learning bit - the fun bit, the bit that's interesting and the bit that makes the biggest difference in the long term.
Our teaching has been very procedural for years (I've been at my current place of work for over 9 years, so I'm confident in saying this) and we need to shift to understanding and depth.

The biggest shift in my thinking has been the shift from 'Well, that task is pointless... It's nothing like what I'm asking them to do in the end...' to 'This task will make them think like this, which I need on the journey to make them think in a different way in the end...'.
This has largely come down to manipulatives.
I've never worked in a department where I've been given CPD on using manipulatives. With that in mind, for 10 years I've always seen them as a distraction, a behaviour management issue and an organisational issue in terms of minimising the disruption when organising them.
At the end of last year, I went on the look out for manipulatives around the department. We have LOADS of pairs of compasses for drywipe boards, but had no double sided counters. We have weights and weighing scales, but no geoboards. I did, however, find two almost complete boxes of Cuisenaire Rods, a whole lot of Numicon and lots of multilink cubes.

My job is to now order more manipulatives, add opportunities for their use to the SOL, direct staff as to when they can use them and how they can use them, and give CPD to our department so that they feel confident in using them and that their use will be worthwhile.

In the first eight weeks we've taught Place Value, Symmetry and Transformations and Averages. I've had some fantastic successes with the multilink cubes (to introduce the mean to students, especially giving meaning to those pesky 'Five numbers have a mean of 8...' type questions) and Dienes blocks (to compare decimals, hammering home what a 'tenth', 'hundredth' and 'thousandth' represents).

Onwards and upwards... Calculations, Angles and Sequences are up next!

Breakfast Boosters - A short post-mortem

This past academic year, we tried something different to what we might normally do with our Year 11 cohort - breakfast boosters!

Two mornings a week, Monday and Friday, we invited students in for an extra half an hour of contact time between 8:10am and 8:40am.

We identified a cohort of 31 students at the beginning of the year - all of whom who were a grade or more away from their FFT20 and that FFT20 was 4 or higher. 

Unfortunately the uptake was poor - only 5 fully engaged. They worked with myself and another TLR holder in the department on a casual basis and were making great improvements in lessons and making the most of what was offered to them. I was pleased that it was seemingly having impact.

In an attempt to have a greater impact across the department we got more staff involved and launched it again after their mock exams (based on their mock exams), inviting 97 students who were two sub-levels or more away from achieving their FFT20 - regardless of their current attainment or FFT20. Again, only 15 fully engaged, which was disappointing and led me to consider the time element of what we were asking staff, and ourselves, to do. Was it worthwhile? It might have seemed that way, but our only real measure was against the GCSE results.

With results coming out yesterday morning, I've been able to take a quick look at any impact we might have had by having students in a little earlier twice a week - working independently on booklets and worksheets (and that's all it was - some printed worksheets from Mathsbox in a booklet and the opportunity to get assistance from a member of staff).

Students from our whole cohort, on average, made 1.1 grades of progress between their Year 10 mock and their GCSE exam. The students who engaged with the breakfast boosters made 1.3 grades progress on average (with some as high as 2 grades - specifically, a girl who was only 4 marks off a 7 from a grade 4 in year 10) - compared to 0.95 for the students who were invited but didn't engage.

I'm concluding that the act of underachieving students engaging with the breakfast boosters had an impact - potentially not the boosters themselves, but the increase in contact time with a member of staff and the elevated focus on improvement of grades by simply knowing why they were there, and that someone cares enough to invite them in and spend time with them.

Was it worthwhile? 

I think I'll look at identifying this year's cohort over the next week.

With great power comes great responsibility...

Over the last term I've had the pleasure of observing our ITT student. I enjoy the times that I get to do this, as I get to see lessons from a student perspective, but also objectively look at use of language and teaching methods.

They said something (a real throwaway comment) which I've focused on a bit too much: "... and this is how they might try to trick you."

A few queries: Who are they? and Why are they tricking people?

I had this discussion with them and other colleagues about the use of the word 'them' and them 'trying to trick you'. I realised that I've done this a lot. In fact, most of us owned up, and those who didn't almost definitely lied.
But, why did we do it? Why do we do it?
We also found this to be the case in other aspects of life, but let's keep this to work stuff...

As a teacher, I got into education to help others. Once in the system, I want and have wanted to remain in circumstances where students have high levels of disadvantage. I quickly realised that I, and many others, began their educational journey with, or developed during their journey, a hero syndrome.

The hero syndrome is a phenomenon affecting people who seek heroism or recognition, usually by creating a desperate situation which they can resolve.

My origin story is my GCSE English exam when I was sixteen. That's when I realised I wanted to be a teacher. That's when I was bitten by the spider, arrived on Earth from Krypton and witnessed my parents' murder (both parents are very much alive, for concerned readers).

In almost seventeen years since then I've taught classes at the borderline who I've trained to overcome the villainous maths GCSE and I've mentored higher attaining students to become the heroes that they're capable of being, but in the last week I've spent time in refuge (a caravan park in North Yorkshire) and have started to recognise that I've been the villain (plot twist!!).

I've previously dipped in and out of various sections of Craig Barton's 'How I Wish I'd Taught Maths', but found a chunk of time in which to fully engage with the narrative of the book. I've been making notes of really small changes, and 'headlines' to share with the department, which I hope will be as impactful as promised. The thing is, all I can think of is 'How on Earth have I managed to get by over the last 9 years without considering these things?!' and 'What might have happened with my classes had I known this sooner?!'. Ultimately, I'm trying to see this as my second coming as a superhero, my second origin story, as I lead a team through what could be a holistic change in teaching methodologies and department-wide ethos.

If students develop real understanding and are able to apply their schema to other areas when asked, the exam surely becomes much more of a test of ability than the villain many currently perceive it to be.

I have one more week off, in my cave whilst my wife goes back to work, but at the end of it I think it might be a case of Maths team : Assemble!