USING ILOKANO IN TEACHING BASIC NUMBER CONCEPTS AND
OPERATIONS IN ARITHMETIC
Ernesto C. Toquero, Ed.D.
Professor, Isabela State University
Echague, Isabela
CP #: 09158601315
ectoquero@yahoo.com
ABSTRACT
This paper explores what primary school teachers can possibly do to make use of the
children’s indigenous culture and the richness of their mother tongue as an effective medium in
teaching mathematics following the MLE framework of Listening, Speaking/counting, Reading
and Writing/Solving. It attempts to show how the mother tongue can be used as a bridge, not only
to learn the language of mathematics, but to build a strong mathematical foundation that can be
used for life long learning in mathematics. It demonstrates how cognitive development in
mathematics is based on the language the child understands best – his/her mother tongue. This is
done by making use of the mother tongue as a medium in building useful mathematical concepts
that run through from arithmetic to algebra. Concepts such as grouping by tens, place value,
exponents, addition, subtraction, multiplication, and division, combination of similar terms and
other mathematical concepts and operations are derived from the way children count in their
mother tongue.
INTRODUCTION
The current educational system
submerges learners in not just one, but
two foreign languages, postponing
strong achievement in school until
those languages are well enough
developed to support learning. This
situation favors a relatively small
percentage of intellectually gifted
children beyond those who don’t speak
either Filipino or English as a mother
tongue.
Multilingual Education (MLE)
offers an alternative approach to
education where children begin their
education in a language they
understand and develop a strong
foundation of cognitive development in
this language. It assumes that a
properly sequenced and planned
curriculum following sound principles
of learning including second language
learning, can successfully enable
young learners to learn how to learn, to
master curriculum content in school,
starting in a familiar medium, and then
learn all the classroom languages, and
use those languages for life-long
learning, in all subject areas.
Children know and speak
fluently their mother tongue when they
begin school. Using that language
allows them to continue to develop that
language and use that language to
develop critical thinking skills needed
for school, and to learn other subjects.
With a language which they
understand children can easily master
concepts taught even in mathematics.
If we bypass usage of the child’s
language in teaching early learning
skills,
we
immediately
delay
comprehension of curriculum contents
including mathematics. Using the
language that the child knows enables
immediate comprehension from which
new concepts can be built – going from
the
known
to
the
unknown
(Dekker,2008).
The success of MLE in the
Philippines, therefore, will largely
depend on the creativity of teachers to
make use of the richness of their
mother tongue to convey meanings that
facilitates learning. Young children or
babies begin learning their first
language (L1) with listening, and then
move on to speaking. Reading and
writing are more complex and are
introduced in school. Learning
mathematics should proceed in the
same way, beginning with listening,
then speaking, when they are ready.
Reading and writing numbers should
only be taught once good oral number
abilities have been developed. The
comparison is shown below:
Language
Development
Listening
Speaking
Reading
Writing
Development of
Number
Concepts
Listening
Speaking/Counting
Reading and
understanding
numbers concepts
Writing and
manipulating
numbers using
basic operations
The following presentation
explores how the richness of the
Ilokano language can be used in
teaching the basic concepts of numbers
and the fundamental operations in
arithmetic.
2. LISTENING AND COUNTING
IN ILOKANO
The teacher can start counting
using Ilokano words, connecting each
number word to the idea/concept
which the word represents, while the
pupils listen, if they still do not know.
The counting can be done through
stories familiar to the child. At this
point it might be good to start
introducing the number symbols as
shown in the table.
Listening/Counting: Basic Symbols
Konsepto or
Idea
Ilokano
word
awan
Numero/
Bilang
0
0
maysa
1
00
dua
2
000
tallo
3
0000
uppat
4
00000
lima
5
000000
innem
6
0000000
pito
7
00000000
walo
8
000000000
siyam
9
0000000000
Sangapulo
maysa a pulo
0000000000
Duapulo
0000000000
Dua a pulo
0000000000 0000 Duapulo ket uppat
0000000000
Dua nga pulo ken
uppat
0000000000
Tallopulo ket lima
0000000000 00000 Tallo nga pulo ken
0000000000
lima
Etc.
3. READING AND UNDERSTANDING
NUMBER CONCEPTS
Once the children can count
orally, the reading and understanding
of number concepts can be introduced.
The pupils read numbers in Ilokano
and tell what the number means by
writing the numbers in expanded form
(e,g 325 read as tallo gasut duapulo ket
lima which is written in expanded form
10
20
24
35
as 3(100) + 2(10) + 5). A suggested
activity is shown in the table.
Number
3
10
20
35
123
95
etc.
Reading
tallo
sangapulo
duapulo
Tallopulo
ket lima
Sangagasut
duapulo ket
tallo
Siyam a
pulo ket
lima
etc
Meaning in
expanded form
3(1)
1(10)
2(10)
3(10)+5(1)
1(100)+2(10)+3(1)
9(10) +5(1)
etc
The table clearly shows that the
Ilokano counting already spells out the
expanded form of numbers and that the
Ilokano word ket/ken signifies addition
while the phrase “siyam a pulo”
signifies multiplication (nine times ten
or nine tens) making it clear that when
we count we are actually counting by
thousands, hundreds, tens, ones.
Hence, the Ilokano counting language
already spells down the concept of
grouping by tens (decimal) and the
concept of place values in the base ten.
This makes the Ilokano language an
easy bridge to the teaching of place
values and exponents.
4. Formalizing the meaning of place
values
Place Values
… Thousand Hundred Tens Ones
10(10)
10
1
… 10(102)
7
5
3
8
4
8
5
6
9
The table shows that the place
values are formed by grouping by tens:
10 means 10(1); 100 means 10(10);
1000 means 10(100) or 10(102), 10,000
means 10(1000) or 10(103) and that the
numerals under their columns actually
tells how many of the place value is
taken or counted. The Ilokano counting
actually spells out what the numeral is
counting: 75 is read as pito pulo
[7(10)] ket lima [5]; 384 is read as tallo
gasut [3(100)] walo pulo [8(10)] ket
uppat [4]; and 8,569 is read as walo
ribu [8(1000)] lima gasut [5(100)]
innem a pulo [6(10)] ket siyam [9].
The Ilokano counting clearly states the
place value counted.
A clear understanding of the
meaning of numbers as illustrated in
the way it is read in Ilokano and in the
way it is written in expanded form is
the foundation of understanding and or
learning addition and subtraction as
combination of similar terms and
understanding/learning multiplication
and division as a combination of
distribution (distributive property of
multiplication) and combination of
similar terms.
5. Addition
The clarity of the meaning of
place values in the indigenous counting
makes it easier to teach the concept of
addition as the combination of similar
terms, a concept that defines addition
and which runs through from
arithmetic to algebra. It is clearly
shown in the following example that in
adding we are actually combining the
similar terms and that similar terms
means the terms that counts the same
thing such as 2(10) + 5(10) = 7(10) =
70. This is the reason why the digits of
the addends are arranged according to
the place value which they are
counting. This is shown in the example
that follows:
324
3(100) + 2(10) + 4
32
+ 3(10) + 2
203
2(100) + 0(10) + 3
449
5(100) + 5(10) + 9
6. Subtraction
The same principle that is used
in the combination of similar terms is
also used in subtraction. The digits that
count the same value are also placed in
the same column but the signs of the
subtrahend are all changed to
subtraction (which is what is done in
algebraic operations) as shown below.
324
-203
121
3(100) + 2(10) + 4
-2(100) – 0(10) – 3
1(100) + 2(10) + 1
numerals then moving up to tens,
hundreds, thousands, etc., as follows:
Number
1
2
3
…
10
20
30
45
7. Multiplication
In multiplication the principle
of distribution and combination of
similar terms governs the arrangement
of the sub-products. As long as the
child knows what similar terms are,
s/he will have no problem placing the
sub-products to where they should be
placed. The illustration is shown
below.
Example 1
2341 2(1000)+3(100)+4(10)+1
x 2
x
2
4681 4(1000)+6(100)+8(10)+2
Example 2
1231
1(103))+2(102)+3(10)+1
x32
x 1(10)+2
3
2
2462
2(10 )+4(10 )+6(10)+2
1231 1(104)+2(103)+3(102)+1(10)
14772 1(104)+4(103)+7(102)+7(10)+2
8. Transferring knowledge from the
mother tongue to second and third
language
Once the child is well versed
counting in Ilokano, the numerical
knowledge can now be transferred to
English and Filipino. This can be done
by showing how the same number is
read first in Ilokano then in Filipino
and English, starting with the basic
267
...
Ilokano
maysa
dua
tallo
…
sangapulo
duapulo
tallopulo
Uppat a
pulo ket
lima
Dua gasut
innem a
pulo ket
pito
…
Filipino
isa
dalawa
tatlo
…
sampu
dalawampu
tatlompu
Apatnapu’t
lima
English
One
Two
Three
…
ten
twenty
thirty
Forty
five
Dalawang
daan anim
napu’t pito
Two
hundred
sixty
seven
…
…
The understanding of this
transformation can even be made
easier by showing the similarity of the
words and their meaning in expanded
form, emphasizing in the process that
the numerals/digits that compose the
numbers are actually counting the
value of the place (place value) that
they hold. This is shown in the
example below:
 Dua a ribu tallo gasut uppat a
pulo ket lima
 Dalawang libo tatlong daan
apatnapu’t lima
 Two thousand three hundred
forty five
 2(1000) + 3(100) + 4(10) + 5
 All Written as: 2,345
9. Implications for Life Long
learning
Mathematics teachers usually
teach Algebra apart from Arithmetic.
Many fail to help students realize
that the properties or principles
applicable to numbers in arithmetic
operations are indeed the same
principles that make Algebra work.
Because of this, students cannot see
the logical connection between what
they know in Arithmetic and what
they need to learn in Algebra. They
cannot use their knowledge in
Arithmetic to find meaning in the
abstract variables and the operations
involving them. Very often they
learn the rote procedures without
understanding the concepts and
principles that make it work. Mother
tongue based teaching arithmetic in
the primary grades makes the
necessary connections making it easy
to
introduce
and/or
teach
mathematics
in
the
higher
levels/years.
9.1 Transforming
Algebra
Arithmetic
to
Using what the students know
with place values, as learned from their
native counting system, is a very
powerful bridge to the understanding
of Algebra. Through the place values
students can be made to realize that the
algebraic
expression
such
as
monomials, polynomials are actually
algebraic representations of the
numbers that they knew in arithmetic.
This is shown below:
Place Values
… ribu
gasut
pulo
… libu
daan
sampu
thousands
hundreds
…
tens
1000
100
10
10x10x10
.
10x10
10
. 103
102
101
. X3
X2
X1
3
6
5
4
7
2
maysa
isa
ones
1
1
100
X0
3
5
9
6
9.2 Monomials and Polynomials
From the foregoing table, 3 can
be written as 3(1), 3(100) or
3(x0); 45 can be written as
4(10)+5(1), 4(101)+5(100), 4x1 +
4x0, or simply 4x+5; 679 can be
written as 6(100) + 6(10) + 9,
6(102) + 7(10) + 9 or 6x2 + 7x +
9; and 3,526 can be written as
3(1000) + 5(100) + 2(10) + 6,
3(103) + 5(102) + 2(10) + 6 or
3x3 + 5x2 + 2x + 6. From these
we can now show the
arithmetic-algebra connection
from which we can introduce the
meaning
of
monomials,
binomials,
trinomials
and
polynomials, as follows:
Arithmetic
3
45
679
3,526
Algebra
3
4x + 5
6x2 + 7x + 9
3x3+5x2+2x+6
9.3 Combination of Similar Terms
and Addition of Polynomials
As representation of numbers,
the operations of polynomials follow
the properties of numbers. The
concept of addition is actually the
same as combination of similar
terms. The arrangement of addends
in columns according to place values
is actually placing similar terms
together and the act of adding them is
the same as combining similar terms.
Using the expanded form students
can easily see that adding all 103s,
102s, 10s and 1s is like counting the
number of 103s, 102s, 10s and 1s in
each of the numerical expression.
Showing that the terms of the
algebraic expression are actual
representations of the numbers in
column, one can make it easier for
the students to understand the
concept of similar terms, and
combination of similar terms. This
understanding facilitates their ability
to simplify algebraic expressions and
learn addition and subtraction of
polynomials. Moreover, students can
be made to realize that, for as long as
they know which terms are similar,
addends need not be arranged in
column. It is, however, more
convenient if similar terms are placed
or grouped together. This gives them
a better understanding of why the
digits of addends are arranged in
column according to place values.
9.4 Multiplication of Polynomials
To introduce the concept of
multiplication in Algebra using
arithmetic as springboard, the
students can be asked to multiply two
digits by one digit numbers, two
digits by two digit numbers, three
digits by two digit numbers in their
original numeric form, expanded
form and algebraic form and make
them explain how they got their
answers. Based on their answers, it
can be shown that in multiplying
numbers with more than one digit,
each digit of the multiplier is
multiplied one at a time to each of
the digits of the multiplicand and the
partial
product
are
arranged
according to place values to make it
easy to add the partial products.
Through the process the students can
easily be introduced to the fact that
multiplying polynomials follow the
same process as that in Arithmetic,
namely: each term of the multiplier is
multiplied to each term of the
multiplicand (distributive property of
multiplication over addition) to get
the partial products and then combine
the similar terms together to get the
final product. Using the expanded
and the algebraic forms it can easily
be demonstrated that, for as long as
they know how the distributive
property of multiplication works and
how to combine similar terms they
need not have to start from the right
most term. It can be demonstrated for
example that multiplication can start
from left to right and they still get the
same result.
9.5 Division of Polynomials
Arithmetic can also be used to
introduce and deepen the concept of
division of polynomials. Division the
arithmetic way, starts by dividing the
first digit of the dividend by the first
digit of the divisor to get a trial divisor
that will yield a product which when
subtracted from the first digit of the
dividend will give a difference of zero.
The process is repeated until the
difference is zero or a remainder is
obtained. The students can be asked to
divide three digits by two digit
numbers. The same numbers can be
expressed in their expanded form and
let them do the same procedure
following every step which they did in
arithmetic division. Then let the
students express the numbers in
expanded form and using their
experience in the process they can
learn how to divide polynomials.
What is good in using
arithmetic is the fact that the students
can verify the correctness of the
answers. They can actually multiply
the quotient with the divisor, add the
remainder and see that the result is
actually the dividend. This gives
them more faith in the process and
therefore has a better disposition to
learn it. So that when the expanded
form is translated to algebraic
expressions there is already a pattern,
which they believe, and can follow.
10. Summary
In summary, this writer showed
that using the mother tongue (Ilokano)
to teach the basic concepts of numbers
and operations helps build a strong
foundation for the understanding and
learning of higher mathematics.
Meaningful teaching reveals the
concept and the rationale of the process
and the relationship of the processes to
each other. Students learn most when
new lessons are taught in a language
which they understand and when
lessons are logically connected with
processes which they already know,
and/or to situations and/or experiences
that are familiar and interesting to
them. The approach is effective not
only in getting the interest of students
in the lesson but as a springboard in
teaching new mathematical concepts
and principles and in deepening
student
understanding
on
why
mathematical operations or processes
work.
Asking leading questions to
allow them to discover, internalize
and/or articulate the things they
learned and their insights on the
process can deepen the interest and
involvement of the students. The
individual needs of students with
difficulties in following/performing
the activities can be helped by going
to them to respond to their needs
individually. The more intelligent
students can be challenged to explore
alternative ways of solving to deepen
their understanding. For example in
multiplying a trinomial by a
trinomial, some students can try
starting from the leftmost term going
right and see if they can arrive at the
same thing. The fast learners can also
be of help to tutor slow learners.