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!