Montessori revolution in Math

(Part 1 of a series on Montessori Revolution in Education)

Anyone can be “MATH Smart”. Of all school subjects, Math is the most dreaded since the concepts are very abstract. But, children can easily fall in love not only with Math but also with Geometry, even at the early age of three to six when the child’s interest in learning is most intense.

Fortunately, it is from pre-school to primary school where parents are most enthusiastic and concerned with their children’s learning. When children reach the intermediate level of Grades IV to VII, parents’ interest in coaching or tutoring their children begins to wane.

Watch out, for this is the delicate period called Puberty. The intelligence begins to wane, evidenced by the closing up of their personality. The growth hormones are especially active particularly for the girls. This is a vital passage to adulthood which must not be ignored.   

A child need not have Math phobia

Dr. Montessori, more a scientist than a teacher, discovered that abstract or purely intellectual lessons, especially that of Math, need solid material which hands, eyes and imagination can work out. A Math computer program is purely visual and flat. It cannot take the place of rods, cylinders, beads which the child can lay down with precision. Feeling the height, width and thickness of the objects is necessary.

She also observed that every child need not have Math phobia if exposed to the following lessons and materials on numeration and computation as early as pre-school:

GROUP I: 1-10. The basic numeration seems easy but Math being a precise science demands that the child grasps 2, 3, 4, 5, etc. as a unit, as in red and blue sectioned Number Rods (see illustration), instead of the traditional loose counters, buttons or bottle caps that cannot be bound together.

The “zero” concept is injected in the Spindle Boxes (0-9) where the zero section does not receive any spindle.

The third materials of bingo chips called Cards and Counters enable the child to pair (see illustration) the counters as “even numbers”. Numbers which cannot be paired are separated as “odd numbers.”

Decimal golden beads and cards

GROUP II: DECIMAL GOLDEN BEADS AND CARDS. Dr. Montessori stressed that a concept should be placed within a large framework. For Geography, she used the Puzzle Map of the World, then Map of Europe, before Map of Italy. In numeration, she chose to present the Decimal System of whole numbers with the Golden Decimal Beads of loose unit beads, ten bead bars, 100 square beads and the cube of a thousand. The introduction to the Montessori Decimal numeration is shown above. The complete set of cards that is 1 to 9, 10 to 90, 100 to 900, and 1,000 to 9,000 is used to form complex numbers.

GROUP III – ‘TEENS’, HUNDREDS, THOUSANDS AND MISCELLANEOUS COUNTING. The Montessori system provides parallel materials and lessons to reinforce numeration concepts. Above, the Seguin Board, named after the French psychologist Dr. Montessori admired, introduces the ‘teen’ numbers after the child learns 10.

The “Chain of 100” is a string of 10 golden bars of 10. This is laid out by the child on the floor with numbered arrows 1 to 10, 20, (21-29), on to 30, 40, 50 up to 100.

The “Chain of 1,000” shown here is made up of 10 “Chains of 100”. Note that the 10 golden 100 squares appear as in the Decimal Beads. Otherwise, excited small groups of children lay out these 10-meter long chains along the empty school corridors and match them with number cards.

Quarterly P-T conference needed for children with ‘Math barriers’

Parents often resort to tutors to help their children after school. Sad to say these tutors end up doing the child’s homework. Thus, the child’s intelligence fails to strengthen and worse, he and the parents get the false illusion that the child is an honor student. In school, it is best to only allow one-month tutoring just to help the child help himself.

The ideal situation is to work together with your child’s teacher. Make it clear that you want to be a partner in your child’s education. You don’t mean to be pushy nor a meddling parent. Take advantage of the quarterly Parent-Teacher Conferences or request for this if the school doesn’t regularly hold it. PLEAE DON’T SHOW UP FOR IMPROMPTU CONFERENCES.

Fractions

Right after learning the Decimal numeration and static arithmetic operation (without remainders) the child can be introduced to the Fraction Family insets. Montessori conceived a numeration chart with number 1 in the middle: To its left are whole numbers 10, 100, 1000, etc.; while to its right are the decimal fractions .1, .01, .001, etc.

No wonder problems concerning fractions are quite difficult but science has to deal with the infinity of numbers. These will prepare them for advanced lessons for Grade I to Grade IV since there are numerous fraction problems by then.

Geometry

Italians do well in Math and Geometry. Their famous men Galileo and Marconi based their discoveries on this science. Even Michelangelo and Leonardo da Vinci sketched their works of art with Geometry skills.

Thus, as early as pre-school, Montessori introduces the Geometry Cabinet of six trays showing insets of the basic Geometric shapes of the world: the first tray introduces square, triangle and circle; The second tray shows triangles according to angles (right angle, acute, obtuse, etc.), and according to sides (equilateral, isosceles, scalene); and the rest of the trays show kinds of quadrilaterals, polygons and irregular shapes.

The mathematical mind

For Dr. Maria Montessori, the objective of Math and Geometry lessons was the formation of a Mathematical Mind. It does not only refer to the acquisition of numerical and problem solving skills. This special mind of a cook, salesman, engineer or nurse inputs personal exactitude and precision into one’s work.

People with mathematical minds stabilize the nation.

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