This child is moving along through the math curriculum (she is a Kindergartner) and is ready for slightly more abstract materials. She has used the golden beads for the operation of addition and has now been introduced to the Stamp Game. Here she uses small tiles which represents units, tens, hundreds and thousands. In a similar way to the golden beads, two addends are written, here in colored pencil which coordinates with the tiles. She puts the first addend down on the table. (She likes to line up the tiles perfectly with the ruler- this is something she did on her own.)
The second addend is placed below the ruler. Once the addends are double checked, the ruler is removed and we slide the tiles up together.
The tiles are then counted by moving them down slightly. We always begin in the units. This way if we go up to ten, we change ten green unit tiles in for a blue one and put it in the appropriate column.
The sum is then recorded on the sheet.
For the older children, they have progressed through many of the other math materials and have moved onto golden beads. Again this is an amazing Montessori material that teaches units (ones), tens, hundreds and thousands concretely. We have many exercises that begin with teaching the quantity then the symbol and finally matching quantity with symbol. Once they understand this we move onto the operations beginning with addition without change.
Once the child understands this concept, we begin addition with change or dynamic addition. Here the child realizes they have to go to the “bank” and change 10 unit beads for a ten bead bar and carry it over into the tens column. From here we actually move to multiplication as it is really just “fast adding!” Stay tuned!
Once the child has gone through the sequence we call the “first five” of the Montessori maths materials, we move onto other aspects of math. The first five helps the child understand the concepts of 1:1 correspondence, the idea of zero and matching the symbol to the quantity of 1-10. One of the directions to go is to introduce the Short Bead Stair. This helps to reinforce the quantities 1-9 and to prepare the child for the operations of addition and subtraction. Many works are completed to familiarize the child with the short bead stair and the children enjoy working with the beautiful colorful beads.
We place a set of beads and the child counts with their fingertip or the tip of a pencil. They then write the number in the first slot. For some, as they can be only three, they need help writing so we use a dotted stamp for them to trace. For most, they love to stamp the numeral too. We then place the second addend on the green felt. They count this as well and write the number. We then show them how to put the beads together and add up with the fingertip or a pencil and write the “sum” in the box.
This is an example of how the Montessori math materials progress from concrete to abstraction in a specific sequence. The children really enjoy this activity and ask for it when they come to school. Many tell us, “I want to do math!”
Many of our children are very interested in math! They have entered their sensitive period for numbers and all things related (see post on sensitive periods). The Montessori materials follow the developmental sequence of the child when they become interested in math. We have heard many voices saying the numbers which is called rote counting. This is when a child can repeat the numbers because they have memorized them.
We have also seen some number recognition. This is when a child can visually identify the number which we call the symbol. (We use the sandpaper numerals.)
We are working toward 1:1 correspondence. This is when a child can match the quantity to the symbol, for example, the number four with four items. Once a child understands this concept, they are able to begin the mathmatical operation of addition.
1-1 correspondence up to 5- this is a good place to begin with those just entering into this type of activity
another 1:1 correspondence game with a die
table top number rods
Montessori cards and counters, matching quantity and symbol.
If your child is interested in numbers, take a few pinecones or leaves and count them. In the beginning we may need to touch the object with our finger or four can become six. The children are used to rote counting which can go faster than the finger can move. If we stop on each one as we count, it reinforces the 1:1 correspondence. Use refridgerator magnets as numerals and count pieces of fruit in the kitchen. Place the number next to the amount. There are many different activities you can do to help your child learn this concept. As always, we never push the child to do work if they are not ready or interested. If they are showing you signs of readiness, count away!