using ilokano in teaching basic number concepts and operations in arithmetic ernesto c. toquero,...

USING ILOKANO IN TEACHING BASIC NUMBER CONCEPTS

AND OPERATIONS IN ARITHMETICErnesto C. Toquero, Ed.D.

Professor, Isabela State UniversityEchague, Isabela

CP #: 09158601315ectoquero@yahoo.com

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 (Dekker, 2009)

• This paper 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.

• It shows how 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.

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 with the use of concrete objects which the child can readily manipulate to indicate a number concept

• At this point it might be good to also start introducing the number symbols as shown in the table.

Umuna nga Simbolo ti PanagbilangConsepto Bilang Simbolo

awan 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

Panagbilang manipud iti Sangapulo

consepto Bilang Simbolo o Numero

0000000000 SangapuloMaysa nga pulo

10

0000000000

0000000000 00

Duapulo ket

dua 22

0000000000

0000000000

0000000000 00000

Tallo pulo ket lima

35

Etc.

Deriving meaning from the Ilokano counting

Numero Basa kaipapanan

3 tallo 3(1)

10 (May)sangapulo 1(10)

26 Duapulo ket lima 2(10)+5

327 Tallo gasut duapulo ket pito

3(100)+2(10)+7

5289 Lima ribu dua gasut walo pulo ket siyam

5(1000)+2(100)

+8(10)+9

Formalizing the meaning of Place values

… ribu gasut pulo maysa

… 1000 100 10 1

8

7 9

7 5 6

3 2 4 5

• Addition

• 324 3(100) + 2(10) + 4

• 32 + 3(10) + 2

• 203 2(100) + 0(10) + 3

• 559 5(100) + 5(10) + 9

• Combination of Similar Terms & CPA

• [3(100)+(2(10)+4]+[3(10)+2]+[2(100)+0(10)+3]

• {3(100)+2(100)}+{2(10)+3(10)+0(10)}+{4+2+3}

• 5(100) + 5(10) + 9

• Subtraction

• 324 3(100) + 2(10) + 4

• -203 -2(100) – 0(10) – 3

• 121 1(100) + 2(10) + 1

• Combination of similar terms

• [3(100)+2(10)+4] – [2(100)+0(10)+3]

• 3(100)+2(10)+4 – 2(100)-0(10)-3

• {3(100)-2(100)}+{2(10)-0(10)}+{4-3}

• 1(100) + 2(10) + 1

Multiplication• Example 1

• 2341 2(1000)+3(100)+4(10)+1

• x 2 x 2

• 4681 4(1000)+6 (100)+8(10)+2

• Distributive Property of Multiplication & Combination of similar terms

• 2{2(1000)+3(100)+4(10)+1}

• 2{2(1000)} + 2{3(100)} + 2{4(10)} + 2{1}

= 4(1000) + 6(100) + 8(10) + 2

• Example 2• 1231 1(103))+2(102)+3(10)+1• x32 x 1(10)+2• 2462 2(103)+4(102)+6(10)+2• 1231 1(104 )+2(103)+3(102)+1(10)• 14772 1(104)+4(103)+7(102)+7(10)+2 • Distribution Property of Multiplication and

Combination of similar terms• {1(10)+2}x{1(103)+2(102)+3(10)+1}• [2{1(103)+2(102)+3(10)+1}]+[1(10)

{1(103)+2(102)+3(10)+1}] • [2{1(103)}+2{2(102)}+2{3(10)}+2{1}]+[1(10){1(103)}+1(10)

{2(102)+1(10){3(10)}+1(10){2}]

• [2(103)+4(102)+6(10)+2]+[1(104)+2(103)+3(102)+1(10)] • [1(104)]+[2(103]+[2(103)]+[4(102)+3(102)]+[6(10)+1(10)]

+[2] = 1(104) + 4(103) + 7(102) + 7(10) + 2

• Division• _____1(103)+2(102)+3(10)+1

• 1(10)+2/1(104)+4(103)+7(102)+7(10)+2

-1(104)-2(103) • 0 + 2(103)+7(102)• -2(103)-4(102)• 0 + 3(102)+7(10)• -3(102)-6(10)• 0 + 1(10)+2

• -1(10)- 2

• 0

Transferring knowledge from the mother tongue to second and third language

• Dua a ribu tallo gasut uppat a pulo ket lima

• Dalawang libo tatlong daan apatnapu’t lima

• Two thousand three hundred forty five

• All means 2(1000) + 3(100) + 4(10) + 5

• All Written in the same way as: 2,345

Implications for Life Long learning • Transforming Arithmetic to Algebra

… ribu gasut pulo maysa

… libu daan sampu isa

… thousands hundreds tens ones

… 1000 100 10 1

… 103 102 10 1

… x3 x2 x1 x0

… 2 4 3 5

• From the foregoing table 2435 can otherwise be written as:

• 2(1000) + 4(100) + 3(10) + 5; • 2(103) + 4(102) + 3(10) + 5;• 2x3 + 4x2 + 3x + 5.• This transformation clearly shows that the

polynomial 2x3+4x2+3x+5 represents the number 2345, where x = 10 (base 10).

• Giving several examples of this kind will finally convince the pupils that algebraic expressions represents actual numbers and therefore behaves or follows the properties of numbers.

Monomials and Polynomials • Arithmetic-Algebra connection• Hence monomials, binomials,

polynomials are number resentations such as:

• 20 = 2(10) = 2x is a monomial;• 35 = 3(10) + 5 = 2x + 5 is a binomial;• 346 = 3(102)+4(10)+6 = 3x2 + 4x + 6

which is a polynomial (trinomial);• 2,579 = 2(103) + 5(102) + 7(10) + 9 =

2x3 + 5x2 + 7x + 9 which is a polynomial• etc

Addition of Polynomials is actually the same as Combination of Similar Terms

• Since polynomials are representation of numbers their addition follow the properties of addition with numbers. This is shown below:

• 324 3(102)+2(10)+4 3x2 + 2x + 4

• +32 + 3(10)+2 + 3x + 2

• 213 2(102)+1(10)+3 2x2+ x + 3

• 569 5(102)+6(10)+9 5x2 + 6x+ 9

• The examples shown in the previous slide can be written as follows:

• 3(102)+2(10)+4+ 3(10)+2+ 2(102)+1(10)+3 which can be rearranged (commutative) and grouped (associative) as follows: [3(102)+2(102)]+[2(10)+3(10)+1(10)]+[4+2+3] = 5(102)+6(10)+9 by addition or combination of similar terms.

• Hence: 3x2+2x+4+3x+2+2x2+x+3 by the same principle can be rearranged and regrouped as follows: [3x2+2x2]+[2x+3x+x]+[4+2+3] =5x2+6x+9 showing the commutative & associative properties of addition or of combination of similar terms.

MultiplicationNumeric Form Expanded Form Algebraic Form• 3431 3(103)+4(102)+3(10)+1 3x3+4x2+3x+1• 12 1(10)+2 x+2• 6862 6(103)+ 8(102)+ 6(10)+2 6x3+ 8x2+6x+2 3431 3(104)+ 4(103)+ 3(102)+1(10)___ 3x4+ 4x3+ 3x2 + x__ 41172 3(104)+10(103)+11(102)+7(10)+2 3x4+10x3+11x2+7x+2 30000+10000+1100+70+2 = 41172• Distributive property of multiplication and combination of

similar terms• 2[3(103)+4(102)+3(10)+1] + 1(10)[3(103)+4(102)+3(10)+1]• 6(103) + 8(102) + 6(10) + 2 + 3(104) + 4(103) + 3(102) + 1(10)• 3(104) + 10(103) + 11(102) + 7(10) + 2 = 30000 +10000+1100+ 70+2• = 40000 + 1000 + 100 + 70 + 2 = 41172

• [x+2][3x3+4x2+3x+1] = x[3x3+4x2+3x+1] + 2[3x3+4x2+3x+1]• x[3x3]+x[4x2]+x[3x]+x[1] + 2[3x3]+2[4x2]+2[3x]+2[1]• 3x4 + 4x3 + 3x2 + x + 6x3 + 8x2 + 6x + 2• 3x4 + 4x3 + 6x3 +3x2 + 8x2 +x +6x +2 = 3x4+10x3+11x2+7x+2

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.