Encouraging deep Maths thinking in Preschoolers

The Montessori Maths curriculum is rich and beautiful. I love how it goes from  symbols to introducing written numbers. I also love how equipment delivered in one cycle or age group is used in another age group in another way for example the binomial. Equipment in itself doesn't make for good Maths education. I have been doing some reading recently around Maths and have been thinking about this question: 

What makes for good maths education?

When I was brainstorming this from a Montessori Perspective I thought of the following:

-Hands on materials

-Self correction

-Order

-Sensorial experiences before teaching other experiences

-The spiral curriculum (things at one stage are looked at in more depth at another age span)

Recently I was reading an article by Sue Gifford in the International Journal of Early Years Education. The Article called 'A new mathematics pedagogy for the early years' pulls together international research on what makes for the most effective type of Maths education for young children .

I have looked at each of the ideas and have then thought about them from a Montessori perspective:

Children need many varied experiences from which to learn an idea and need the ability to also make links between mathematical ideas for example big is like the word long, where as small matches with little.

Adults need to provide examples which challenge a child's thinking and their misconceptions. Gifford suggests one way of doing this is having peers working together. This made me think of the importance of including group lessons often and how important questions are! Gifford also says that it is important that children are given opportunity to correct common errors found in maths too.

This involves children using language and visual images to record their mathematical knowledge in a way that makes sense to them.  I wonder how we can do this more in Montessori?

Vygotsky stated that learning from instruction was important. Research by Fuson 

in 1988 showed that children learnt to count through imitating puppets - Another reason to include nursery rhymes, finger plays and songs into circle time!

Vygotsky said that Metacognition is aided by talking - which means we also have to be having rooms where talking is encouraged. Additionally demonstrating to children how WE are solving a problem encourages problem solving skills. Often this may mean you have to 'act' to communicate what you are doing. For example let's say you are trying to demonstrate which is taller : the chair or the 10 red rod.  Here is a possible way you could show the children about how you are solving the problem of working out which is taller: 

Another way of encouraging Metacognition is to ask students how they got to an answer.

I have found this to be a fraught subject in Montessori. Some Montessori teachers say very little to a child about how they are doing. While we certainly do not want to be constantly standing over a child who is working out an equation we also do not want a child to continue practising an error. Gifford says that effective maths teaching for Preschoolers encourages children to know how they are doing.

I think it is always good to reflect on our teaching and more recent theories and studies in maths as it makes us refine our practise! Now onto the implementing of it! :)