In Montessori we are incredibly fortunate to have such amazingly thought through hands on maths equipment in particular for teaching place value.
From the golden beads through to the golden frame Montessori math equipment helps the child isolate and has the potential to teach place value concepts well - however I learned that maybe I wasn't helping teach it that well!
.
.
THE PROGRESSION
The first place value material are the golden beads. Activities with them include
- 3 period lesson of the hierarchy
- The 45 layout
- Making numbers: 'make me the number three thousand and twenty five'
- Operations such as adding and subtracting
I was always taught by my mentor teacher that when a child could start doing the operations in their head it was time to move on to the stamp game as they had a good knowledge of place value.
.
.
.
HOLD ON!
Teaching in a Public Montessori class I had to ensure the children in my class also met the state requirements for children their age. It was during this process that I began looking through the state requirements and seeing some things that I felt were missing from my use of the Montessori equipment and my manuals.
I came to realise that many of my children were not confident with questions like :
- How many tens are in all of the number 356?
- Make the number that is 39 tens and 4 units
- What is 100 more than 456?
In the last question for example I sometimes found if the child was given the question as an equation 456 + 100 they could solve it however the alternative wording and written question above would thrown them. This had me reflect on was I really preparing children for the real world if they only knew how to solve a pure maths question and not one with words?
Some of this was quite challenging for me as a teacher and to my ego. I was delighted to have young children in my 6-9 class learning about the checkerboard and felt superior when looking at what children in mainstream classes were doing, however did my children really know their place value?
I know that many Montessorians pride themselves on the advanced concepts the children in their class can achieve through the equipment however I was humbled by this learning that although we do have great place value equipment I was not teaching these concepts well enough and needed to put in place things to ensure that the Montessori equipment was truly teaching the richness of this vital math concept. Another way of saying this would be just because the child is 7 years old and is using the large bead frame this does not mean that they can answer or explain their thinking of place value.
For me I learned that while there is a scope and sequence to the Montessori equipment this should not be a fundamentalist style checklist that we are married to. Also we need to acknowledge and be able to come to peace with the fact that Maria Montessori was not a God like 'all knowing' person. There are gaps in our curriculum and we need to be able to think laterally to meet the needs of our children for example knowing what maths strategies students are using and why.
Teaching in a Public Montessori class I had to ensure the children in my class also met the state requirements for children their age. It was during this process that I began looking through the state requirements and seeing some things that I felt were missing from my use of the Montessori equipment and my manuals.
I came to realise that many of my children were not confident with questions like :
- How many tens are in all of the number 356?
- Make the number that is 39 tens and 4 units
- What is 100 more than 456?
In the last question for example I sometimes found if the child was given the question as an equation 456 + 100 they could solve it however the alternative wording and written question above would thrown them. This had me reflect on was I really preparing children for the real world if they only knew how to solve a pure maths question and not one with words?
Some of this was quite challenging for me as a teacher and to my ego. I was delighted to have young children in my 6-9 class learning about the checkerboard and felt superior when looking at what children in mainstream classes were doing, however did my children really know their place value?
I know that many Montessorians pride themselves on the advanced concepts the children in their class can achieve through the equipment however I was humbled by this learning that although we do have great place value equipment I was not teaching these concepts well enough and needed to put in place things to ensure that the Montessori equipment was truly teaching the richness of this vital math concept. Another way of saying this would be just because the child is 7 years old and is using the large bead frame this does not mean that they can answer or explain their thinking of place value.
For me I learned that while there is a scope and sequence to the Montessori equipment this should not be a fundamentalist style checklist that we are married to. Also we need to acknowledge and be able to come to peace with the fact that Maria Montessori was not a God like 'all knowing' person. There are gaps in our curriculum and we need to be able to think laterally to meet the needs of our children for example knowing what maths strategies students are using and why.
.
A quick check:
2 digit numbers
- Is the student aware of how tens relate to units?
- Can the student tell/show you different ways of representing a 2 digit number e.g. 65 is six tens and five units or sixty five units?
- Can the student understand a number in written form e.g. sixty five or six tens and five units?
- Can the student tell you ten more or ten less than the number or one more or one less?
3 digit numbers
- Is the student aware of how hundreds relate to tens and then units e.g. one hundred has ten tens in it. One hundred has a hundred units.
- Can the student tell/show you different ways of representing a 3 digit number (including unconventional ways) e.g. 245 is two hundreds and four tens and five units or two hundreds and forty five units
- Can the student tell you one hundred more or less than the number, ten more or ten less than the number or one more or one less?
- Can the student understand a number in written form e.g. 763 is 700 + 60 + 3 or seven hundred plus sixty three units
- Does the student understand groups e.g. 78 groups of ten is 780?
Are your students used to viewing numbers in different ways?
.
.
If you are looking for pre-made questions that cover this concept you might be interested in looking at my advanced place value cards resource that I made for this purpose!
To find out more about the progress of children's thinking with math strategies see this blog post that explains how children think about maths.
1 comment
Excellent article! Thanks! I think we may need your materials :)