Proem

Every language has a pattern or syntax. The thinking process of the pupil (Bis: alabay) is influenced by the syntax of his language. Therefore if you will adapt your lessons to the thinking pattern of the pupil, he can learn easily and fast.

Jes Tirol's Theory

In the hierarchy of asking questions, the English language usually starts with the question "what?" It is then followed by how, when, where, etc. Seldom is the "why" being used. If it is used, it will be at the last.

The Sugboanon Bisayan language usually starts with the question "why?" It is then followed by what, how, when, etc.

My theory is, if you will coach your lessons to always answer the question "why," then the pupils will be interested and their brains will work to investigate further. It will facilitate learning because your lessons cater to the natural inquisitiveness of the pupil.

The problem is, all our textbooks in the elementary grades are structured to answer the question "what?" It is patterned upon the English language. The schoolteachers do not know how to structure his lessons to answer the question why?

Class Demonstration

Last Sunday, October 7, 2007, I conducted a demonstration class in mathematics specifically structured to answer the question why?

Sixteen Grade II pupils were randomly selected from Cordova, Cebu Central Elementary School. In attendance were the teachers I trained in Sugboanon Bisaya and some administrators. A crew from the ABS-CBN Television was on hand to record the event.

The teaching method used was the Integrated Approach. The language used was pure Sugboanon Bisaya (Not the colloquial).

I started with a review of the ten numerical symbols. I started with "usa, duha,…".

When I wrote the symbols on the blackboard, the pupils started counting in four different languages. To hold the attention of the pupils, I wrote the counting words separately in Sugboanon, English, Spanish, and Tagalog. I wrapped up the situation by letting the pupils count from one to fifty in turn, using Sugboanon, English, Spanish, and Tagalog.

Mayor Adelino Sitoy of Cordova, Cebu was so surprised at the facility of the Grade II pupils in counting from one to fifty in four languages. I told the observers that by nature children can learn up to eight language at the same time. However, at the age of puberty, that facility would be lost.

I called the attention of the pupils to the numerical symbols. Why are there only ten numerical symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)? I told them that it came about because it was adopted from the ten fingers of the hand. That is why we use the decimal system (Bis: yabâ). It should be noted that I was always talking in pure (lunsay) Sugboanon. The observers were surprised why the pupils could understand.

Subtraction

The primary lesson was subtraction (Bis: kuhà) of two digit (Bis: halitang) numbers. I distributed small tiles of one-half inch size. It was colored white at one side and the other side was black.

We assumed that the white side represents positive (Bis: dayag) and the black was negative (Bis: dihag). I wrote two digit numbers for subtraction on the blackboard. To answer the question Ngano (why), I let the pupils verify by using the tiles. Since their Ngano (why) was answered, the pupils were still attentive. After many exercises in subtraction, the pupils mastered the lesson. However, I did not stop there.

I asked the question, "Ang napulò kuhaan og napulog-lima, pila man ang tubag? (Ten subtracted by fifteen, what is the answer?). In unison, the pupils and some teachers answered, "Dili mahimo (It could not be done)." I answered, "Mahimo (It could be done)." [Note: All our elementary school textbooks do not show a subtrahend (Bis: tagkuhâ) that is larger than the minuend (Bis: kuhaanan).

The Explanation

"Ngano nga mahimo man? (Why could it be done?). I let the pupils arrange ten white tiles (for +) and fifteen black tiles (for -). I told them to change the concept (Bis: taghunâ) into debt (utang) and lack (kulang). I let them pair off (Bis: siing; Sp: pares) the ten white tiles with ten black tiles. How many tiles are left? What is the color?

Answer: Five black tiles. Since we assume that black is negative (dihag) the answer is "dihag lima (negative five). I then went into a discussion of what happen when your payment for a debt is not enough; you still lack something or a negative situation. The pupils understood very well.

I heard a teacher-observer that the lesson was already in Grade V. I countered that is what will happen if you will cater to the ngano (why) of the pupils. They can already understand. And beside, why will you stop the momentum of the thinking process of the pupils?

A Notch Higher

To drive home the lesson in subtraction I did not stop at the level. I went on to teach the concept of "+10 - (-25)". In High School Algebra you are just taught to memorize the rule, "change the sign of the subtrahend and proceed to addition." The question is why?

I told them, the minus sign of subtraction indicates a process while the positive and negative signs of the numbers indicates a property of the number. The opposite (sukwahî) of positive is negative. Therefore the subtraction operations means subtract the opposite of the negative (Kuhaa ang sukwahì sa dihag). With the use of the white and black tiles, the pupils understood why "+10 - (-25) = +35". Of course the teachers were complaining that the lesson was too advance, the pupils could not understand it. I told them, go to the limit and find out if the pupils could understand the concept. I tried giving a problem, and there was one pupil who really understood the concept.

My Comment

The lesson is only subtraction of two digit numbers. We went on to other concepts. The procedure is to use "reinforcement" of the mental process. During the next session, you repeat the lesson and advance further. By so doing you will strengthen the mathematical ability of the pupil. All of you teachers thought that subtraction with a negative sign is too advance, but you see, we have one pupil who understood it.

Therefore you cannot really know when is the proper time for a mathematical lesson especially that we are using the pupils mother language and answer his curiosity by asking ngano (why).

At this level of the lesson I already noticed that the pupils were restless. It was really too advance for them in a first encounter lesson. However, I am confident that a few repetition of the lesson will make them understand. In fact one of the pupils has already crossed the threshold.