MTS - Math Album

MTS - Math Album - Intro

Shu-Chen Yen's On-Line Montessori Albums

MONTESSORI MATH ALBUM

INTRODUCTION

When we think about Montessori's mathematics, we can not just consider math materials only because sensorial training is of great importance in Teaming the basics of mathematics. Those training allow children to become familiar with numbers at early age. For example, red rods, pink towel, brain stair, geometric solid, binomial cube, and trinomial cube can be a tools of preparation for mathematics. Montessori arithmetic materials and the conception of identity and difference in the sensorial exercises is built up from recognition of identical objects and gradation of similar ones. Also, in Practical Life, the development of "Order", "Concentration , "Coordination" and "Independence" are important for mathematics mind. Order is the basic foundation of Math because we can't do any Math without sequence. Concentration on the task is so important on Math to develop logic thinking and problem solving skill. Children need to eye- hand coordination to do the math works too. To develop independent thinking and problem solving skill is one of our educational goal to students.

Why so many children feel uncomfortable about mathematics because they seem mathematics like a cold and bored things with its abstract symbols. In traditional instruction, children are assumed to learn by internalizing knowledge; teachers simply correct the errors and present the right answer. Many teachers know that this is not what happens, but they go on correcting the same error day after day. It is true that is can't be done. Children need to see, without hurry or pressure, how numbers change and grow and relate to each other. They need to build up a mental model of the territory before they start next step. Like Piaget said "Knowledge is not a copy of reality. To know an object, to know an event, is not simply to look at it and make a mental copy, or image of it. To know an object is to act on it. To know is to modify, to transform the object, and to understand the process of this transformation, and as a consequence to understand the way the object is constructed." [1] On the other hand, even the wrong answer could be productive because any wrong answer could provide more in-depth thinking if children can try to work it out in areas where it didn't work and to figure out why is doesn't work. But it takes time.

In fact, mathematics is very important in our daily life because we can see that "Number are in everywhere." From The Absorbent Mind, Dr. Montessori wrote that " Children at early age are urged by the laws of their nature to find active experiences in the world about them. For this they use their hands, and not only for practical purposes, but also for acquitting knowledge." [2] Basic this idea, at Montessori classroom, math is presented in a fun and interesting way by using concrete materials during the school year, and help children develop concrete to abstract concept. Also, children have free choice to their own inner needs. At "The Secret of Childhood", Dr. Montessori stated that "The principle of free choice was thus added to that of repetition of the exercise. The free choice made by the children enabled us to observe their psychic needs and tendencies" [3]. Repetition is necessary for the child to refine his senses, perfect his skills and build up his competency and knowledge. Through free choice and repetition, children can acquire their knowledge step by step depending on their own needs, not on the teacher or parents. So, there is no pressure or hurry to build their knowledge by themselves. This is a good reason that Dr. Kamii's said "Teacher doesn't correct children from outside, but set up the situation that helps children revise from inside." [4]

The math materials at Montessori classroom begin with numeration from one to ten. These materials include: Numerical Rods, Sandpaper Letters, Printed Numerals, Spindle Box, Cards and Counters, Colored Bead Bars and the Memory Game. By manipulation these material, children build the basic concept from one to ten not only to memory the natural order of numbers, but also to recognize the relationships between quantity and quality. After master the basic concept, children need to understand the place value in math. The Decimal System introduce children the place value to thousand. Through working with the 9-Tray, the 45 Layout and the Formation of Complex Numbers, Teen Boards, and Ten Boards, children will develop mathematics concept beyond ten. When children recognize the written symbols and know their meaning, they need to perform the exercises in remembering numbers. From "The Discovery of the Child", Dr. Montessori said that "A child must therefore remember his number not only while he moves among his companions as he approaches the large table, but also while he is picking up his pieces and counting them one by one." (5) This skill is facilitated through the use of the following materials: Sequence Board, Addition Strip Board, Subtraction Strip Board, Multiplication Bead Board and Division Bead Board. The Bank Game will help children learn the concept of addition, subtraction, multiplication and division. Children will acquire mathematical operational principle in concrete way because they may have previous experience to go to bank with their parents. Also, There are four sections that have more materials to present these four operational principles.

After understanding Dr. Montessori's math materials, we can figure out that she did not present math as a terrible or boring lesson, but use the concrete materials and let children have their own step to build their knowledge. At this point, teacher plays an important role during Montessori's classroom. Teacher needs to understand that children will reveal himself through works. Do not insist by repeating the lesson and do not make the child feel that he has made a mistake or he is not understood. The teacher teaches little and observes much because only when the teacher has teamed from her observation, she can help children remove their obstacles and guide them to next step according their own needs and desires.

REFERENCE:

[1] "The Having of Wonderful Ideas and other Essays on Teaching and Learning", by Eleanor Duckworth, p.35.
[2] "The Absorbent Mind", by Mana Montessori, p. 173.
[3] "The Secret of Childhood", by Mana Montessori, p. 121.
[4] "Number in Preschool & Kindergarten", by Constance Kamii.
[5] "The Discovery of the Child", by Mana Montessori, p.268.