
“What the hand does the mind remembers.” – Maria Montessori
You want your children to master their learning. But you aren’t sure what you are doing at home is working. One minute they seem to know, the next they have forgotten. d Working with concrete materials is the powerful way you can ensure that their little brains retain the information they have been given. Concrete to abstract learning is the way to mastery!
This is probably the most powerful thing I learnt in my Montessori training. As a teacher, I would spend hours wondering why some children just didn’t ‘get’ what I was trying to teach them. I did everything I was supposed to do, and yet so many didn’t understand. The concepts that really stand out in my memory are: continents of the world, planets and times tables.
How many times have you been trying to learn something new, it wasn’t clicking and then eventually – PING! You get it. I know this is often the case if I am being shown something vs. actually being able to have a go myself.
Now, I know exactly where I was going wrong in my teaching. On each one of these subjects, we were expecting the children to understand these things, when they had no real understanding of what they actually were. How can a small child understand and remember the names of the continents when they had zero context behind them? How can we expect older children to learn their times tables if they have had gaps in their previous learning, and they are now expected to do everything on paper?
Everything in a Montessori classroom is set out like this: concrete materials THEN abstract, only moving onto the abstract when they are ready. Concrete to abstract = mastery.
Montessori talked about material abstractions. Which is really just a fancy way of saying that someone now understands something so well that they can imagine it in their head without the object in front of them to see and to touch.
I’ll give you a simple example. Think of a baby around 12 months old. They like looking at books and regularly choose one with some farm animals in. They have learnt that every time you point to that same illustration you say ‘duck’. Then you take them to the pond to see some ducks and they have no idea what is in front of them. You wonder why?
The image in the book was very abstract. It was a cartoon, it was much smaller than a real duck, it was 2D. It is quite far from reality. This is how we could have introduced ‘duck’ instead.
Start by going to see the ducks at the pond. I appreciate you can’t really go and pick a duck up to allow them to feel one for real life unless you have a petting zoo nearby that enables you to do this. However, seeing how one moves and the understanding size of it will really help.
You could then show the child some model toys of ducks. The real life looking ones, avoid cartoony ones. This is moving to the abstract as it is much smaller, and doesn’t move like a duck, but does show the shape of a duck and the colours will be realistic.
Then, it would be a good idea to look at some real life photographs of a duck. This is taking another step into the abstract as it is now a 2D image. Not a lot like a real duck, but at least the colours are real. At each stage, it is important that the child gets a chance to feel these things in their hands… maybe I could have come up with a better example as I think we should probably discourage them from picking up wild birds at the pond! But I think I’ve illustrated the point well.
How can this be applied to your older child with times tables?
Well they have to know what is going on behind the maths before they can really use is effectively. When we start teaching about times tables, we teach children about arrays, skip counting and repeated addition. 3×5 turns into 3+3+3+3+3. We use lots of grouping to make sure the child really understands before even thinking about showing them a times symbol. It seems like we are good at doing this in early years and KS1, but forget the importance of it in later year groups.
But what if the child needed more time in year 1 to understand these concepts than was given? What if covid or other illness disrupted their learning and they now have a gap there? And now they are in KS2 they are expected to do a lot of this in their head? We need to go back to the concrete materials before the abstract to help them to master a concept.
So if you’re ever unsure about why your child or children you are teaching are not grasping a concept, reflect. Have they got enough concrete understanding of this to show real mastery? If not, give them the concrete. Let them use their hands to explore. This will build up their understanding so much easier. Concrete to abstract learning really is the way to mastery.
I talk more about this on my Instagram and Facebook pages so go and have a look today! You can find see some examples of how I do this here.