Cosmic Math made easy from preschool to high school

Ask a child what school subject he fears. MATH! would be the usual reply. The tendency of educators is to solve the problem by making children study less (DepEd terms it "minimum learning competence") or allot more time for the subject.

The constant redistribution of the program of studies obliges the teacher to hassle the students to achieve the desired results at a fixed date, setting a "forward-looking tension" for both.

A call for UNESCO debate on quality education

I sincerely hope that major teacher training institutions on Math and Science will accept my invitation to the forum debate on the pros and cons of existing strategies so we can cooperate on a curriculum that will provide quality in education — the missing item that causes poverty, which UNESCO stresses in all developing countries. The need to use the alternative educational system based on the developmental psychology of the child instead of traditional pedagogy is urgent.

Since 1946, UNESCO was established to provide the forum for intellectual debate of professionals from different disciplines of education, science and technology, social and human science, culture and communication. Time has almost run out in constant replanning and getting nowhere. It would require the scientific minds of NISMED (National Institute of Science and Math Education), teacher training institutions of UP, UST, PNU, CEU, La Salle, Assumption, Miriam to unite and work together.

Pride and prejudice often impede collaboration. This is the test of selfless commitment to lift up the lives of the 70 percent underprivileged and disadvantaged Filipinos.

Capturing the present power of the child

Every child from infancy has a natural drive to be self-sufficient. This "call to independence" stimulates the three-month old baby to first roll his body and raise his head, sit up and crawl by the fifth month, make his first step with help around the tenth month and walk without help by the first year.

A century ago, Dr. Maria Montessori discovered the "new child" and with him, the "new teacher." She observed the "sensitive periods" for each stage of growth: birth to six years (infancy), seven to 12 years (childhood), and 13 to 18 (adolescence). She defined the "sensitive period – SP" as "a" period of power" to comprehend with special facility, speed and thoroughness. The present power will not last. To make full use of this, we must let the child "live wholly in the present."

The mathematical mind

Dr. Maria Montessori so excelled in Math that she attended the so-called liceo scientifico or the six-year Italian high school. This gave her a baccalaureate diploma of a junior engineer. However, she pursued higher studies in Medicine at the University of Rome. Her mathematical and scientific discipline led her later to write the book, Psico-aritmetica, the basis of her Math and Geometry continuum curriculum from preschool to grade school until high school.

In this book, she stressed that Math arts must link numeration (Number Rods, Spindle Box to introduce zero, and Counters to learn odd and even numbers), and arithmetic operation. Then, memorization must follow using Memory Charts. These are all developmental.

From Numeration and Arithmetic operation to Geometry

Dr. Montessori identifies the psychology of preschool education as sensorial and activity-oriented, therefore requiring not visual materials, but hands-on apparata. Pictures and posters will not allow the preschooler to arrange and re-arrange objects, which frustrates his desire to absorb a whole range of concepts with movements.

For numeration, a box of the Golden Decimal Beads can initiate the preschool child to numeration. Dr. Montessori provided golden unit beads, bead bar, bead square, and bead cube. This hands-on experience will be stored in the preschoolers’ subconscious. The fundamentals of Geometry – the point, line, surface, and solid – would come in handy when his intelligence matures in grade school.

Whatever is stored in the preschool sub-conscious through the sensorial experience will sharpen the enormous reasoning power of the seven to 12-year old gradeschoolers. Therefore, it is necessary to equip the Montessori preschool with the tri-dimensional bag of wooden Geometric Solids and the wooden Geometry Cabinet with six trays.

Linking preschool to grade school

While I was doing my Montessori Elementary School Teacher Training Course in Bergamo, I requested Signor Grazzini, the training director, to give me a plan of how Math and Geometry is given to each grade level. At that time in 1969-70 their school at Vittorio Emmanuele did not have a precise quota of lessons per grade. He said that he would still have to work on them.

I could not wait for that so I decided, however, to let Grade 1 children master the Memorization Tables of Addition and Subtraction while focusing on Geometry of Lines (straight, curved, divergent, convergent and parallel). By Grade II, they focused on the Memorization Tables of Multiplication and Division. Geometry lessons were on the study of two lines forming ANGLES. With the right angles as the measuring angle, the children used their individual protractors and compasses to make acute (angle less than 90 degrees), obtuse (more than 90 degrees), straight (double 90 degrees), reflex (more than 180 degrees), and the whole angles (equal to 360 degrees – a circle). These lessons also use the Geometry Illustrated cards with definition labels. By Grade III, the study of TRIANGLES resurrects the wooden Constructive Triangles used in preschool.

Squaring and cubing with the Board of Powers

Visitors and parents who regularly come to the OB Montessori schools at Greenhills, Sta. Ana, Las Piñas and Angeles, Pampanga always wonder why we display multi-colored "rosaries" in our grade school classrooms. What impresses them as "prayer beads" is actually the Montessori Board of Powers, which is in every Grade II and III classrooms, as well as in Grade IV to VI classrooms. There are two chains representing the squaring and the cubing of numbers 2, 3, 4, up to 10. They hang lengthwise.

Each chain has a matching fixed square and fixed cube. Grade II children use them for multiplication by skip counting by 2s, 3s, 4s, etc. Grade III and Grade IV children are introduced to squaring of a number placing a fixed square marked by a golden ring on the chain. For example, the square of 3 is within the cube of 3. The cube chain of three would look like this: 0-ooo-ooo-ooo-0-ooo-ooo-ooo-0-ooo-ooo-ooo-0.

The fragmentation of Geometry in basic education

The concepts of EQUIVALENCY must be reinforced by the concepts of SIMILARITY and CONGRUENCY. With barely any mention of "equivalency" in the traditional elementary school, the traditional Filipino high school student is traumatized by this lesson since it is only introduced to the high school freshman class.

Psychologically, the seven to 12-year olds have more intellectual power while the teenagers weaken intellectually. Dr. Montessori, thus, wisely satisfied the power of abstraction in grade school when she provided drills in "equivalency" making use of metal insets not only of a triangle, but also of rhombus, trapezoid, pentagon and decagon as convertible to a rectangle.

The dreaded PYTHAGOREAN THEOREM is introduced in traditional schools by first year, and applications are done by the third year. In contrast, the Montessori Grade VI, well-prepared since preschool, can easily "draw out" the Pythagorean Theorem using three sets of insets of which gradates the difficulties of the EUCLIDEAN THEORY. Phythagoras initiated the theorem but Euclid proved its validity.

The urgency of establishing the launching pad for learning Math

Dr. Maria Montessori improved very much the Math and Geometry syllabus of Italy by developing a continuum program based on the psychology of preschool to high school students. Italian engineers and architects count among the best in the world.

Do you understand now how we can make Math Arts easier for Filipinos?

We have underestimated the power of preschoolers. Love for Math and Science is the foolproof result of using Cosmic Math and Cosmic Science with very young children instead of waiting for the intermediate grade school or high school. I wish I could pilot a bridge program for the sixth graders who failed and do not qualify for secondary education.

(For more information or reaction, please e-mail at exec@obmontessori.edu.ph or pssoliven@yahoo.com)