Montessori Math
Montessori is an approach which many have adopted these days as a teaching method for children in preschool. The materials which they use create an environment that is developmentally appropriate for the children. Montessori believes that with the helped of trained teachers and the proper environment which the children are placed in, intelligence and different skills will be developed in the child (Casa Montessori, 1997-2009). In addition, one of the main aims of Montessori is develop children to become life long , independent learners.
Instead of following the tradition teaching methods whereby teachers would present the students with all the facts and information that they need to know, the teachers trained in Montessori teaching would ask questions and direct the children in a way where they have to look for the answers themselves. In the learning process, the teachers would basically motivate the children to be actively engaged in their learning and to think independently (Seldin, 2010).
The basis of the Montessori approach is that learning through experience and going through the process of investigating and discovery is one of the most effective ways for a child to learn. Montessori also believes that children do not learn by memorising information given to them but from concrete experiences that interests them. This is why Montessori focus on different creating different developmentally appropriate concrete learning tools and materials that stimulates the child into logical thinking and discovery for subjects such as mathematics, sensory development, language and so on (Seldin, 2010).
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With regards to mathematics, the Montessori approach sees sensorial training as a very important platform which aids in the learning of basic arithmetic. The wide variation of materials Montessori has to cater to mathematics allows children to familiarize themselves with numbers at an early age (Modern Montessori International, 2006). They focus on using sensorial materials because they are precise and exact. They believe that it is important for the children to work with materials that are exact and so that they can be exposed to isolated concepts, learn through repetition and rom there draw the main principle of each and have a clear abstraction. All these concepts would help the child to order his mind and enable him to classify different experiences. This is because having a clear perception and the ability to classify things help the child to learn how to be precise in their conclusions. Working with sensorial materials prepares the children for the study of progression and sequencing as it builds up spatial representations of quantities and form imagines of magnitudes (Montessori Primary Guide).
Montessori believes that before a child can start learning mathematics, he or she must explore and accept the notions of idealized things with isolated qualities and to practice the requisite intellectual skills (Modern Montessori International, 2006). First of all, exposing the child to early sensorial activities is used to introduce the idealization of things and isolation of qualities to them. This is because allowing the child to work with sensorial materials gives them the opportunity to deal with isolated qualities physically and hence acquire the sensibility of what mathematics is all about.
Secondly, the child must be introduced to the intellectual skills needed for mathematics such as exactness, calculation and repetition. Practical activities such as pouring beans into a jug or sweeping the floor can help children acquire such skills. It is believed that when children reach age four, they are ready to start learning mathematics. However, prior to that, the children have to establish certain things such as internal order, precise movement, work habits, the child must be able to complete a work cycle, follow a process and are able to work with symbols (Modern Montessori Guide).
That is why there are developmentally appropriate ways for the children to explore arithmetic. The material first begins with concrete experiences such as the number rods and cards where the children are able to work with such materials to learn the different concepts of numbers. This would also help the child as they work towards the abstract stage of solving mathematical sums. The mathematics in Montessori is organized into six groups. Group 1 is Introduction to Numbers, group 2 is the Introduction to the Decimal System, group 3 is the Introduction to Teen Board, group 4 is the Operation of Decimal System, group 5 is the Introduction to Recording and Arithmetic Tables and group 6 is Abstraction. Firstly, group 1 which is the Introduction to Numbers introduces the units of quantity up to 10. The focus group for this group is for children age 3 and a half onwards and the main aim of this group is to help children learn the names of numbers, understand the value of each number and to memorise the number sequence.
Secondly, for the in group 2, The Introduction to the Decimal System, the children are given concrete experiences with units with tens, hundreds and thousands as tools to introduce them to the decimal system. As for the third group which covers the Introduction to Teen Board, it helps the children to understand the different numbers within a hundred. Fourthly, group 4 which covers the Operation of Decimal System gets children to work with beans when doing the operation and is usually done at a sensorial and group level.
The fifth group is the Introduction to Recording and Arithmetic Tables. Children at this level work individually with the materials and area also introduced to recording at the same time. The children will use strips, boards and beads that help in giving them material demonstration of addition, subtraction, multiplication and division. In addition, these board games do help them children to memorise tables. And lastly group 6 is covers Abstraction. This level is a transition to abstraction which helps the children to internalize the different functions of arithmetic.
The materials used by Montessori are of progressing difficulty. The child would first be introduced to a quantity in isolation and then a name would be given for it. After which, the child would be given the opportunity to associate the quantity and the symbol. Using an example for the number rod exercise, we can see that the children are first introduced to the numbers by itself when they are asked to count the rods. Subsequently, the teachers would go on and teach the children how to match the numerals to its values by matching the number cards to the rods.
The focus group for this group is for children age 3 and a half onwards and the main aim of this group is to help children learn the names of numbers, understand the value of each number and to memorise the number sequence. With regards to Montessori, sequence is always given in all of the work and the children are taught to establish a sequence in everything they do. I believe that is how the children learn how the numbers go in sequence (Modern Montessori Guide). The advantage of this exercise is that the units of each number rod are fixed.
Therefore, this reduces any possibility of confusion that might arise. Moreover, the children will be able to absorb the concept into the unconscious easily and hence teach them the names of the numbers before the child grasp the abstract conception (Montessori Mom, 2009). The materials by Montessori give the children the experience that they need to arrive and progress to begin working independently. Some of the activities are directed by teachers but all these activities would have to be followed up with activities which allow the children to work on their own.
The children are only allowed to progress to the next level when they have fully understood the previous stage (Modern Montessori Guide). Thus, the children will only be able to progress to the decimal stage when they have finished the first level. As mentioned above, the children will start to learn about the decimal system in group 2. This teacher directed exercise is done for children age 4 years and above. What the teacher will do first is that she will put beads on a tray and place it on a table with the unit on the right and the thousand on the left.
After which, the teacher will bring the unit of bead from the tray and put it on the mat and say “this is a unit”, and put the bead back on the tray. Subsequently, the teacher will bring out the tens bars and indicate to the children that “this is a ten”. And the teacher will do likewise for the hundreds and thousands. After all these have been taught, the teacher will follow up with the second period where she will place all four materials (unit/ tens/ hundreds/ thousands) at random and get the child to show her the unit she wants. In the last period, the teacher will take a random unit out and ask the child what it is.
So for example, the teacher will take a cube and get the child to name what it is. The main aims of this exercise is firstly, that the children will learn the terms “thousands, ten and unit”, that they can understand the decimal system and that the child will be able to understand the relative values of one, ten, hundred and thousand. Following that, in order to teach the children how to associate the quantities with the numerals from 11 to 10 and to teach the children how to count from 11 – 19, the teachers would use materials such as a sequin board, 9 ten bead bars and a set of short bead stair.
The different boards would be arranged on the floor and teacher would arrange the 9 ten bars to the right of the board. She would then ask the child to lay the out the short bead stair to the right of the ten bars. After which, the teacher would stack the numeral cards n order going from 1 to 9 and place the stack to the right of the board. With that the teacher will ask the child what the first number on the board is. When the child says 10, she will ask him to place a 1 ten bead bar to the left of the board and when she asks the child what comes after ten, the child will have to make 11 by adding 1 to the 10 bead bar.
After that, she will get the child to place the numeral card with the number. She will continue to do this until the number 19. In order to teach the children numbers up till 99, the steps that the teachers do will also be similar to what they do with teaching the children from 11 to 19. As we can see, just like what was mentioned above, the procedures that Montessori adopts is one that has sequence. The children would progress step by step slowing adding on to what they know. Many have criticized Montessori’s method of using strings of beads to teach numbers as being clumsy or materialistic.
However, they believe that it is necessary for the children to understand numbers because it would be easier for a child to work with concrete materials patiently if he or she is unable to get a clear idea of abstraction (Montessori Mom, 2009). The beads chain is used to give the child an understanding of the relative value of 1, 10 and 100. The teacher would place the chain and the 100 square next to each other, telling the child that the bead chain and the 100 square are the same.
She will then start the exercise by asking the child to pull the chain into a straight vertical line and ask the child to count every single bead in the first bar. When the child comes to the 10th bead, the child would be asked to place the first number label 10, next to the ten beada. He will continue for the rest of the tens (20, 30, 40) until 100. In the next level, the children would progress to the stage where the teacher will develop their understanding of working of addition, subtraction, multiplication and division.
For example, in the exercise for addition, the teacher will show the children how to lay the materials out. A large number card is laid out in column and the 2 sets of small number cards are laid side by side. The teacher tells the children that they are going to work with addition problems. After that, the teacher makes addends in small number cards and puts one in each tray. She will then get the children to go to the bank and get the appropriate beads. After the children have done so, she has to show the children how to put the beads and the different quantities on the mat.
The teacher will then explain to the children how she is going to add the different quantities and units that are there. She will get one child to place the large number card and show him where to place the card. A second child will be asked to bring down the 10s, count them and bring the large number card. She will repeat all the steps with the 100s and 1000s. Following that, children will start to learn composition and de-composition of numbers 1 to 10. This is for children age 5 onwards. The teacher will ask the child to build the stairs with the number rods on the mat.
She will bring down the rod number 10 and get the child to count it. After which she would bring down the rod number 9 and get the child to count it as well. She will then ask the child “how many more do we need to make the number 10? ” and the child will be required to go and take down the appropriate number rod. The teacher will continue this exercise using different combinations given to the child. The main aims of this exercise are to show the child the working of addition and to provide further practice in addition. In addition, this would also give the idea that two quantities added together make one large quantity.
At the last level, the children will learn individual sums using different materials. For example, in the addition without changing exercise, the children will be introduced to individual addition sums using the golden beads and work cards, they will learn how tor record answers as further practice, it serves as an intermediate stage in the progression from concrete to abstract and to practice changing whenever it’s necessary. For this case, the teacher will remind the children that the colored lines corresponds to the numbers of large numeral cards and get them to read the first number (e. 4675). The child will then have to look for the corresponding beads and place them on the mat. After which, the child will read the next sum and have to bring the corresponding beads out as well. The child will then be asked to add all the units and record his answer. The teacher will repeat this with the tens, hundreds and thousands. Once the child has down all 4 sums, he will have to check his answer at the back of the cards. It has been said that children will soon grow out of using manipulatives such as blocks and beads to learn mathematics.
Once they have reached the stage where they are familiar and are confident in using that method, they will want to go on to something of a higher difficulty level. This is when the teachers can start teaching them numbers with concrete objects (Montessori Mom, 2009). As the materials used for the different groups are developmentally appropriate, the children are able to learn the different concepts at a progressively level. At each stage they would learn something new which adds on to their prior knowledge. This is how the Montessori curriculum works.
We can see that it all starts with the children learning the concept of numbers with the number rods and number cards and soon start progressing to learn decimals, addition, subtraction and learning how to group numbers together into tens, hundreds and thousands (Montessori Mom, 2009). Therefore it is important to introduce the fundamentals of mathematics in the early years during preschool where it would be easier for the child to grasp the concepts easily using concrete materials. The foundation of mathematics would have impact the children’s academic growth in years to come (Montessori Mom, 2009).
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Montessori Math. (2017, May 12). Retrieved from https://phdessay.com/montessori-math/
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