“Dr Maria Montessori took this thought that the homo has a mathematical head from a Gallic philosopher Pascal and developed a radical math larning stuff for kids every bit immature as 3 old ages old. Her mathematical stuffs allow the kids to get down their mathematical journey from a concrete construct to abstract idea” . With mention to the above statement please discourse how these kids utilize their mathematical head as portion of their natural patterned advance. to ground. to cipher and gauge with these Montessori mathematical stuffs in concurrence with their purposes and presentations? What is a mathematical head? The Mathematical Mind’ refers to the alone inclinations of the human head. The Gallic philosopher Blaise Pascal said that ‘every human being is born with a mathematical mind’ . Dr. Montessori borrowing this construct. further explained that the mathematical head is the “sort of head which is built up with ‘exactitude’” . “In our work hence. we have given a name to this portion of the head which is built up with exactness. and we call it the ‘mathematical mind’ .
I take the term from Pascal. the Gallic Philosopher. Physicist and Mathematician. who said that the man’s head was mathematical by nature. and that cognition and advancement came from accurate observation. ” – Maria Montessori. The Absorbent Mind. Chapter 17. Pg. 169 She said the qualities of a mathematical head was such that ever tends to gauge ; demands to quantify. to see individuality. similarity. difference. and patterns to do order and sequence. The constructs within the mathematical head do non merely mention to common associations with math. such as basic operations. Alternatively. Montessori believed that the human inclinations lead one to be mathematical in idea. That is. basic human inclinations such as order. orientation. exactitude. repeat. activity. and use of objects. all lead to the development of a mathematical procedure of idea. “The child perceives. without witting concluding. forms of relationships: things to things. things to people. people to people…
The mathematical head [ hence ] is a power to form. sort and quantify within the context of our life experience” Mathematics is non merely about add-ons or minuss a kid learns at the school. it is all around the kid from the twenty-four hours he is born ( or may be good before that ) . It is a good known fact that an embryo can hear its female parent. So the female parent says “the babe kicked me twelve times today” or “my bringing is within another two weeks” when he was in her tummy. And so after he was born he may hear ‘you were born on the second’ or ‘at eight you go to the bed’ or ‘one button is losing in your pyjama shirt’ or in the society he may be questioned ‘how many sisters or brothers do you hold? ’ etc. . A child’s twenty-four hours to twenty-four hours life is all connected with mathematics and all the basic conversations he has is really much involved with mathematics. In that instance the kid is born to a universe that is full of math. created by homo for their benefits and the kid needs to accommodate to it.
Children need math to screen. categorize and group things within his environment. They need to number. they need to larn the clip and so bit by bit they need to work with arithmetic’s. geometry and algebra in the school when they grow up. “We must convey to the kid the belief that we have made mathematics ourselves. and that we re-make it every clip we move. think. work or drama. We should assist the kid understand that it is merely portion of our being human to hold a mathematical mind” . – Gettman D. BASIC MONTESSORI. Chapter 1. Page 159. Teaching mathematics to a immature Montessori kid is non a hard undertaking as he is really much exposed to Numberss during his twenty-four hours to twenty-four hours life. By the clip they enter into the Montessori school most of them are able to number one to ten ( we call this “rote counting” . they merely count without cognizing the existent significance of the numeration ) . Even in the prepared environment. though the kid does non straight work with the stuffs within the math shelf as he enters. he nevertheless indirectly learns math constructs such as repeat. computation. exactitude. fraction. appraisal and categorization and most significantly order through the practical life activities.
A important find that Dr. Montessori made was the importance of offering indirect readying for the math stuffs while kids were in the sensitive periods for motion and the polish of the senses. It is through children’s work with the Exercises of Practical Life and Sensorial stuffs that they foremost encounter and see the constructs of measuring. sequence. exactitude. and computation Sensorial instruction is the footing of mathematics. Dr. Montessori said that kids are sensory scholars. They learn and see the universe through their five senses. So sensory instruction helps the kid to make a mental order of the constructs he grasps utilizing his five senses. “The accomplishment of man’s manus is bound up with the development of his head. and in the visible radiation of history we see it connected with the development of civilisation. ” – Maria Montessori. THE ABSORBENT MIND. Chap 14. pg. 138 Montessori steadfastly believed that the ‘hands’ are the female parent of accomplishments.
By supplying Montessori sensory stuffs to the kid she was convinced that right use with quality and measure would surely make a permanent feeling in the child’s head with the apprehension of mathematics. We place stuffs rather deliberately on trays. we color code activities. stuffs are displayed in a logical sequence. and we break down motions during presentations into series of consecutive stairss. The sensory stuffs merely present three mathematics constructs of completeness. geometry and early algebra.
Dr. Montessori was convinced that there are two things to be introduced before working with mathematics. “Before get downing mathematics work. the kid must therefore make two things: explore and accept the impression of idealised things with stray qualities. and addition pattern in the needed rational. ” – MMI Mathematics Course Manual pg. 6 The child’s rational accomplishments are developed through both practical life and sensory activities. In practical life activities. kids pattern computation accomplishments when finding how much H2O to pour when transporting out exercisings like pouring H2O from jug to bottle with an index line. or spooning beans from bowl to bowl with an index line. or from jug to jug ; up to the more complex activities of brushing which have the qualities of repeat. computation and exactitude.
The Sensorial work is a readying for the survey of sequence and patterned advance. It helps the kid construct up spacial representations of measures and to organize images of their magnitudes such as with the Pink Tower. knobbed cylinder etc. These sensory stuffs besides provides the kid with the accomplishments of computation with the pink tower and ruddy rods ; as the kid Judgess the size and length of the regular hexahedrons and rods severally. every bit good as repeat with baric tablets etc. . All of the stuffs in the Montessori schoolroom have been specifically designed to pull the involvement of the pupil. while at the same clip learning an of import construct. The intent of each stuff is to insulate a certain construct the kid is bound to detect. The Montessori maths plan is divided into parts to ease a consecutive and gradual advancement in the maths constructs get downing from simple to complex.
During circle clip. informal activities or games are introduced to originate complex maths constructs like seriation. one-to-one correspondence. screening and more in the simplest manner. Without numbering or even expressing a figure name. the kid is really introduced to maths through preliminary maths activities. Dr. Montessori besides said. ‘what the manus does the head remembers’ . The really first math stuff to be presented to the kid is the figure rods. Number rods are really concrete and assist the kid to experience and understand meaningful numeration. It is besides non really new to the kid as he has already worked with the ruddy rods before. The lone difference is figure rods are coloring materials coded with ruddy and blue. which helps the kid to visually know apart the difference in length and so to number the rod. The instructor presents the stuff by a three period lesson. and by reiterating the same activity once more and once more. the kid understands that two agencies two things and three agencies three things and so on and so forth.
The purpose of the figure rod is to assist the kid Learn the names of Numberss 1-10 and visually tie in the Numberss with the measure every bit good as to demo that each figure is represented by a individual object. as a whole. separate from others. The figure rods help the kid memorise the sequence of Numberss from 1 to 10. When the kid counts one rod as a individual unit. he instantly notices an increase in the figure rod “2” even though it is still a individual unit thereby assisting him to tie in the Numberss to the measure. “Rarely. nevertheless. can he number with certainty the fingers of one manus. and when he does win. in making this. there is ever the trouble of cognizing why. …The utmost exactitude and rightness of a child’s head need clear and precise aid. When numerical rods are given to kids. we see them even the smallest take a lively involvement in numbering. ”……… . Maria Montessori. The Discovery of the Child. Chapter 18. pg. 265.
“The satisfaction of find leads to an enthusiastic involvement in Numberss when the kid is able to show the cardinal mathematical operations. instead than merely being told apparently dull and nonmeaningful facts. He physically holds the measures that he sees represented by written symbols. He combines the stuffs. counts. offprints and compares them while visually hold oning and reenforcing the thoughts in a manner that is concrete. instead than abstract. ”…… . . Teaching Montessori at Home. Now the kid is working with the concrete stuffs to understand the measures of numbers one to ten and so he knows the written symbols excessively.
The following measure is to learn him how to unite the measures with the written symbols. This is done through a set of merriment games. The Teacher invites the kid to convey the figure cards and the rods to the mat and so gets the kid to place the concrete value ( the rod ) foremost and so happen and fit the figure card with the rod. Next the instructor requests the kid to place the figure cards indiscriminately and fit them with the rods. This activity helps the instructor to detect how exhaustively the kid is familiar with the Numberss. The following two games help the kid to understand the sequence of Numberss. When the Numberss and the rods are indiscriminately scattered on the mat. the instructor requests the kid to place the figure rods in sequence and so fit the Numberss with it and construct the step so in the following activity the kid identifies the figure cards in sequence and so lucifers with the several rods and builds the step.
The purposes of these exercisings is to set up the kid in the acknowledgment of numerical symbols 1-10. . every bit good as aid him larn association of measure to symbol and besides assist the kid understand measure and sequence of Numberss utilizing manipulatives. Once the kid is really clear with numbers one to ten. the following measure is to learn the denary system. Decimal fractions are introduced to the kid with the concrete use utilizing the aureate beads. Through a three period lesson. the kid is introduced to one. ten. hundred and thousand. The kid feels and sees what one means by a little unit and so sees that 10 is a long saloon and so hundred is a level square of 10 ten-bars bound together and eventually the 1000 is a regular hexahedron made up of 10 100 squares. The kid can visually know apart the difference in the sizes of different value and so experience it excessively. ‘Counting through’ helps them to farther internalise the construct of denary system. The instructor counts up to nine units and so says ‘if we have one more unit we will hold a 10 bar’ . So this helps the kid to understand that to do 10 we need 10 units.
Then to do hundred we need 10 ten-bars and so eventually the 1000 regular hexahedron is made out of 10 hundred-squares. The great trade begins with the denary system operations. Here the kid is introduced to add-ons. minuss. generations and divisions. The kid learns the exact abstract manner of add-ons or minuss utilizing the aureate beads and big and little figure Bankss. All these activities are teacher directed and working with these activities. helps the kid understand that add-on means uniting two sums together and so hold a large sum at last ; that minuss means giving some sum off from what he had and so what remains is a little sum ; that generation means holding the same sum in to different Numberss of times and gets a big sum as the reply ; and eventually. that divisions are giving the sum off every bit or unevenly among two or three people. These operations are really concrete to the kid since he sees and manipulates the stuff. After pull stringsing with the concrete stuffs. the kid moves to the abstract numeration.
Using the big figure cards. the instructor introduces the written symbols of power of 10 ( the decimal system ) . Then moves to the ‘counting through’ with the written symbols. Once the kid is through with measures and the written symbols the instructor shows the kid to associate concrete with abstract doing the ‘Bird’s oculus view’ . Through the bird’s oculus view the kid can clearly see the procedure of the measure increases with the written symbols. It gives the kid the sensory feeling that when the symbol increases from one to ten. ten to hundred and hundred to thousand value of the measure besides goes higher. The purpose of presenting the denary system. is to assist the kid understand the construct of 10. larn the composing of Numberss every bit good as the topographic point value system and their equivalencies. After the denary system operations. the kid progresses to informal entering. By this clip. the kid knows the Numberss really good and he is familiar working with amounts excessively.
The informal recording introduces the kid to little figure rods. In the first presentation. he is concretely introduced to composition maintaining 10 as a usher and demoing him how to do 10 utilizing rods up to six. Decomposition is besides every bit concrete. foremost he makes ten and so takes one off the kid sees he is left with nine. During this presentation. the symbols of asset. minus and equal to. are besides introduced and in the 2nd presentation he is introduced to entering. The adolescent board is introduced to the kid when he is through with the denary system. It is besides called ‘linear counting’ . The short bead stepss changing in coloring material and measure ( one is red. two is green. three is pink. four is xanthous. five is light blue. six is violet. seven is white. eight is brown and nine is deep blue ) The coloured bead bars show clearly the separate entities from 1 to 9 and the ten-bars are the chief concrete stuffs involved with the additive numeration.
First of all. the kid learns to construct the short bead step and so combines the short bead stepss with 10 bars to learn the names of measures eleven to 19s. When the kid understands the names of values. the written symbols are introduced through the ‘sequin board A’ . Similarly the names of measures from 10 to 90 are besides introduced and so the ‘sequin board B’ is used to learn the abstract construct of written symbols. The hundred and thousand bead ironss reinforce the child’s numbering from one to a 1000 and besides helps the instructor to measure child’s criterions with understanding numeration. The colored bead bars show clearly the separate entities from 1 to 9. in combination with the 10s they show the kid that Numberss 11 to 19 are made of 10s and a figure 1 to 9 The intent of presenting the kid to the additive numeration exercisings is to develop the child’s ability to acknowledge and number to any figure.
Equally good as learn skip numeration. The child’s ain sound cognition of the Numberss 1 to 10 and their numerical order Acts of the Apostless as a usher “This system in which a kid is invariably traveling objects with his custodies and actively exerting his senses. besides takes into history a child’s particular aptitude for mathematics. When they leave the stuff. the kids really easy make the point where they wish to compose out the operation. They therefore carry out an abstract mental operation and get a sort of natural and self-generated disposition for mental computations. ” – Montessori M. . The Discovery Of The Child. Chapter 19. pg. 279
Maria Montessori. The Absorbent Mind. Montessori Pierson Publishing Company. the Netherlands. Reprinted 2007 Maria Montessori. The Discovery of the Child. Montessori Pierson Publishing Company. the Netherlands. Reprinted 2007 Modern Montessori Institute. DMT 107 Mathematics Students’ Manual David Gettman. Basic Montessori. Saint Martin’s Press. 1987 Elizabeth Hainstock. Teaching Montessori in the Home. Random House Publishing Group. 2013