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Volume IV, Issue 1 | November 2012-September 2013

EDITORIAL

CHANGE IS INEVITABLE.
For any organism to survive, it must
adapt to change. Teachers as the vital
organism in a dynamic curriculum
should be adaptable and lexible to
remain as the surviving species in the
educational jungle. Such survival of the
teachers is very much timely in today's
era.
The introduction of K-12 curriculum
in the Philippine educational system has

over experiences, sharing of best practices,

honing pedagogical approaches, and
taking further studies are just some of the
options for teachers to update themselves
with change, adapt with change, and even
initiate change.
Hence, as an endless process, change
must be taken by the horns, so that the
teacher can stay relevant and competent.

IT IS deinitely humbling to take over the cudgels of the MTAP-IC presidency

knowing that the shoes to be illed are unfeasible to ill.

Dr. Herman M. Lagon

President, MTAP-IC, Inc.

For the past ive years, the organization

was led by the ever-inspiring Dr. Alona
Belarga, who happens to be my teacher in
Advanced Modern Geometry. But, it is also
under her wing that I learned the tricks of
the trade. With the help of the self-denying
members of the board, we have managed to
steer the organization to the way we want it
to course through.
Our thrust this year is simple: Going
beyond limits. We intend to make sure that all
the fundamental activities of the association
will go on, then cross organizational
frontiers, and make some innovations (or
tweaking) along the way to stay relevant
and expedient before its members and the
greater community.
For the past nine months, we
aspired to strengthen the resolve of our
constituents by spelling out their beneits
and responsibilities, enhancing the tools
to connect with them, sharing expertise
for mutual advancement, and ironing out
organizational concerns.
We have translated into words and
actions the 15 beneits and rights of each
member. These include the discounts
in trainings, seminars, newsletters and
journals, the updates and free instructional

materials that can be retrieved from

our oficial blog and Facebook accounts,
medical or death aids, and the use of MTAP
equipment, among others. In the same
document, the ive responsibilities of the
members are also enumerated.
Vital updates such as the one above is
posted in real time at mtapiloilo.blogspot.
com and Facebook: MTAP-Iloilo Chapter
(with nearing 500 members and counting).
Also posted here are the plans, pictures,
features, and articles of the activities of the
organizations, not to mention the different
research papers and journals related to
assessment, pedagogy, K-12 curriculum,
and the like. This is also an effective
platform for members to communicate with
each other and to forge partnerships or
initiatives that would enhance their teaching
profession. Members are also emailed with
organizational updates through mtapiloilo@
yahoo.com account.
But beyond these cyber platforms,
we have also initiated more tangible
projects such as the Regional Mathematical
Investigation Seminar-Workshop on April
20, 21, and 27, 2013 at the Center for
Teaching Excellence (CTE) Building, West
Visayas State University (WVSU), La Paz,
Iloilo City as a conduit for expertise sharing.
Here, under the headship of Mr. Kim Jay
Encio, we have invited national experts
from the ield (Dr. Belarga, Dr. Emellie
Palomo, Dr. Myrna Libutaque, and Dr. Elvira

Arellano) to lecture on MI with introduction

to mathematical modeling before 85 math
teachers. This, we wish, has equipped our
teachers the necessary skills to inspire
students to plunge into non-traditional
math strategies that would later translate
into more adventurous and skilled math
learners.
This culture of sharing of expertise
continues as we are to hold the ambitious
Training of Trainers and Conference on
September 27-29, 2013 chaired by Prof.
Jonathan Glorial. We expect about 300 basic
education and tertiary math teachers from
at least 14 school divisions in Region VI to
lock the Iloilo Grand Hotel to be trained
how to train the MTAP and math teachers
in the ield. Invited as lead facilitators and
instructors are math education icons Prof.
Rechilda Villame and Dr. Ian June Garces,
and 10 other expert trainers from the MTAP
fold. The foci of this event are content and
pedagogy, two of the most important factors
that can make or break a student in the
classroom. Also incorporated in this event is
the Business Meeting where the election 7 of
the new members of the MTAP-IC, Inc. 2014
board of directors, review/amendment
of the constitution, Treasurers report of
the organizations inancial health, and
presentation of the Presidents report shall
be held.

to page 24

PRESIDENTS REPORT

brought dramatic change and will deinitely

bring more changes in the future. Instead
of settling in the cave of comfort and resist
change, teachers should explore the various
possibilities and innovations that the new
curriculum has to offer. Making them a key
element in the evolution of our educational
system is essential.
Collaborating with experts, building
process skills, conducting research,
participating in conventions, relecting

WHO'S WHO IN THE MATH WORLD

Volume IV, Issue 1 | November 2012-September 2013

CHIEVEMENT SEEMS ordinary in the career of Mr. Adonis Mosquera. He

graduated at the top of the class when he inished his elementary and high
school years at Apdo Elementary School and Moscoso-Rios National High
School, respectively. He graduated magna cum laude at West Visayas State University
in 2004 and became the topnotcher in the licensure exam in the same year. He trained
champions in various math contests and was awarded as outstanding teacher in
Region VI. This unassuming personality in the helm of DepEd Region VI is young and dynamic. Here is the excerpt of
the interview, conducted by Dr. Rosemarie G. Galvez and Dr. Herman M. Lagon, where he poured out his ideas on
educations changing environment.
glorious moments at my irst assignment
but it was really a challenge for me when
I transferred to another school. Will I
still produce champions in mathematics
competitions? To my surprise, our school
emerged as the top performing school in
the division and produced winners in the
higher level competitions. With the passion
and commitment that I put into my craft,
my coteachers were also motivated to
perform better and their pupils also became
champions in other academic competitions.

How does it feel being a supervisor at a

young age?
It is a dream come true but I didnt
expect my promotion to be this early. Of
course, I was elated when I irst knew it and
the feeling never subsides from then on. I
was the youngest among the applicants and
it felt good that the Regional Ofice had given
its trust and conidence to a young Antiqueo
teacher.
How would you describe your leadership
style?
It is a kind of leadership that inluences
others to perform better. When I was a
classroom teacher, I used to be a coach in
various mathematics competitions. Prior
to my promotion in the Regional Ofice, I
taught at the Antique SPED Center (San
Jose, Antique) and Hamtic Central School
(Hamtic, Antique) respectively. I had my

What do you hope to achieve this year for

DepEd-Region VI?
It is my fervent hope that DepEd-Region
VI will perform better in various performance
indicators especially in the National
Achievement Test and Participation Rate
in the secondary level. With the concerted
efforts of everyone, Im very hopeful that we
will succeed on this.
What is your typical day at DepEd?
I dont have a typical day at DepEd
because of the nature of our work. The
core functions of the Regional Ofice are
Policy Formulation, Quality Assurance, and
Technical Assistance. And with these, we are
often out of the ofice to provide technical
assistance to our assigned divisions and
monitor & evaluate the programs and
projects of DepEd.
Do you have any programs or activities
related to K-12 implementation? Could you
please tell us more about these programs/
activities?
I was appointed for the position on
January 1, 2013 and was assigned to the
Curriculum and Learning Management
Division (CLMD) taking charge of
Elementary Mathematics. Last July, I was
reassigned to the Quality Assurance and
Accountability Division (QAAD) to take

charge of Technical Assistance, being one of

the core functions of the Regional Ofice. In
terms of K-12 implementation, CLMD and
TDD (Training and Development Division)
are the two divisions that are involved
most of the time. Right now, DepEd is busy
for the Modeling of the Senior High School.
We have barely two years to prepare for
its implementation in terms of curriculum,
classrooms, teachers, equipment, etc. There
will be schools that will offer speciic tracks
such as Academic, Technical-VocationalLivelihood, and Sports and Arts. The very
unique feature of senior high school is that
when our students graduate, they will not
only gain a high school diploma but they
will also acquire Certiicate of Competencies
or National Certiication in their ield of
specialization which makes them ready for
employment.
What are the activities that you recommend
for professional organizations, such as
MTAP, to conduct?
DepEd is very grateful for the assistance
and involvement of various professional
organizations, such as MTAP, in all its
programs and projects. I would recommend
MTAP to conduct activities that will further
hone the skills of our teachers in teaching
mathematics. I believe that education is a
lifelong process and so there is need for our
teachers to constantly learn new trends and
techniques in mathematics education.
What is your message to the mathematics
teachers in the region?
Teaching, as we all know, is not a
lucrative profession but the joy it brings is
priceless. Let us continue to be the agents
of change. We have the power to change the
destiny of our country. Ours is the rarest
opportunity of moulding the kind of citizens
that Philippines will have in the future. So
behold and lets make a difference. /

Volume IV, Issue 1 | November 2012-September 2013

The mathematics experts

DR. IAN JUNE L. GARCES
Dr. Garces grew up in Cabadbaran City, Agusan del
Norte, where he inished his elementary and high schools. He
graduated with the degree Bachelor of Science in Mathematics
from Mindanao State University, Marawi City in 1992 as magna
cum laude. He inished his Doctor of Philosophy in Mathematics
degree at Ateneo de Manila University in 1998.
He was the Leader of the Philippine Team in the
International Mathematical Olympiad from 2007 to 2010. He
was the Convenor of the Mathematics Learning Area Team of the K-12 Basic Education
Program of the Department of Education. His mathematical interests lie in graph theory,
integration theory, mathematics education, and mathematical olympiads. Currently, he
is an Associate Professor at the Department of Mathematics of the Ateneo de Manila
University.

PROF. RECHILDA P. VILLAME

Prof. Villame is an Executive Board

Member of the Mathematics Teachers
Association of the Philippines (MTAP).
She actively participates and assists in the
planning and implementation of MTAPs
programs, and when necessary, collaborates
with agencies/institutions/organizations for
the improvement of mathematics education.
She was MTAPs Vice-President for Private Sector and is currently
the Coordinator of NCR private schools. She has taught in Adamson
University, Philippine Academy of Sakya, Miriam College, and the
University of Sto Tomas. She also served as Math Consultant of
PAREF Southridge School for Boys.
In 1991, she received the Exemplary Teachers Award from
MTAP and the then Department of Education, Culture, and Sports
(DECS). In 1999, she became the National Winner in the Dr. Juan
Salcedo Science Education Award by the Department of Science
and Technology (DOST), Commission on Higher Education (CHED),
and Department of Education, Culture, and Sports (DECS). She
co-founded Deeco Technological Institute and Dee Hwa Liong
Academy.
She earned the degrees BS Chemical Engineering and Master
of Science in Management Engineering in Adamson University and
earned units in PhD Development Education in the University of
Sto Tomas. She is the associate coordinator and co-author of the
21st Century Mathematics, preschool to high school series. She was
also the project director and coordinator of the math series of Sibs
Publishing House, Integrative Math 1 to 6. Just recently, she coauthored Math Challenge questions for Grades 4, 5, and 6.
She is one of the four founders of the Mathematics Trainers
Guild (MTG), Philippines and is currently its Executive Vice
President. As MTGs active trainer and Center Coordinator, she
has coached and led numerous young Filipino math wizards to
international mathematics contests held in various countries
such as Hongkong, South Korea, India, Singapore, Indonesia,
China, Thailand, Taiwan, USA, Czech Republic, Italy, and Bulgaria.
In June 2008, she received the Samuel L. Greitzer Distinguished
Coach Award conferred by the American Regions Math League in
the University of Nevada-Las Vegas, USA. In summer of the same
year, she was hired as Instructor in the Center for Talented Youth
Program of John Hopkins University held in Stanford University,
California, USA.

IN THIS years regional

conference, MTAP-IC brings
renowned personalities in
mathematics closer to
Ilonggo teachers.
Get to know Dr. Ian June
Garces , Professor Richelda
Villame, and Sr. Iluminada
Coronel the experts who will
guide mathematics teachers
in the region in dealing with
the changes brought
by the K-12 Curriculum.

SR. ILUMINADA C. CORONEL, F.M.M.

Sr. Coronel inished the degrees

BSE Major in Mathematics as magna
cum laude in the University of Sto.
Tomas in 1952 and MS in Mathematics
in Ateneo in 1974. She has received a
Plaque of Recognition for School and
Saturday Programs of Excellence in
Mathematics and other MTAP-DECSNCR Programs for Teachers and
Students from the Division of Quezon City and the National
Capital Region. She was awarded by MATHTED as one the
four Best Mathematics Teachers.
She started her career in 1952 in Sta. Rita Academy,
Pampanga. In 1957-1968, she taught at St. Rose of Limas
School, Hongkong. In 1968-1971 she taught at Colegio
de Santa Rosa de Lima in Macau. She became a college
instructor in Far Eastern University in 1973. She taught at
Ateneo de Manila University in 1974 and took her retirement
in 1991. Since 1982, she has been teaching Mathematics for
the MTAP-DECS-NCR Graduate Programs at the NTC leading
to an MA in Education, Major in Elementary and Secondary
Mathematics.
Since 1977, she has served as the president of MTAPNational. She has been active in Mathematical Society of the
Philippines and Philippine Science and Mathematics Council
as well. She is the co-founder of Matimyas Matematika, and
editor, co-author, or consultant of various publications.
She is the initiator of the MTAP-DECS-NCR Mathematics
Competitions for 1st year to 4th year since 1983-1985 and
for Grade 1 to 4th year from 1985 to the present. Since 1998,
Metrobank became a partner in the competition. In 2001,
the First National MTAP-DECS-NCR became the MetrobankMTAP-DECS Math Challenge for elementary students for
which 114 DECS Divisions participated. Since 2004, the
competition has been national in scope with about 200
participating divisions.
Oozing with energy, enthusiasm, and intellect, Sr.
Coronel is indeed a force to reckon behind the success of
MTAP. /

The Ininity would like to thank Dr. Harold F. Cartagena and

Prof. Jonathan C. Glorial for the biographies of the speakers in the
regional conference.

WHO'S WHO IN THE MATH WORLD

Yout
h at t
he helm
2

Volume IV, Issue 1 | November 2012-September 2013

Work together in selling math to students

THE PARTICIPANTS crack their brains in writing

conjectures and proofs./The Ininity ile photo

"WE NEED to work together in selling

and promoting math to our students."
Thus said Adonis Mosquera, Regional
Education Program Supervisor for
Mathematics in the Department of
Education Region VI, during the closing
rites of the three-day 3rd Regional
Math Investigation Seminar-Workshop
held April 27 at the Center for Teaching
Excellence Building in WVSU, La Paz, Iloilo
City.
Before the newly-sworn oficers of
the Mathematics Teachers Association
of the Philippines Iloilo Chapter and 84
other math mentors from all over Western
Visayas, Mosquera stressed that initiatives
and trainings like this (Math Investigation)
is one of the best evidences of teachers
commitment to further their crafts.
Participants to the three-day event
included teachers from ive provinces
and 12 divisions of DepEd, representing
about 40 schools, universities, and colleges
in Western Visayas. It was sponsored
by MTAP-IC, Inc. and endorsed by the
Department of Education Region VI and the
Commission on Higher Education (CHEd).
Themed
Enriching
classroom
instruction
through
Mathematical
Investigation and Modeling in the K-12
Curriculum, the three-day math workout
was facilitated by four main resource
speakers who were trained by the
University of the Philippines National
Institute for Science and Mathematics
Education (UPNISMED).
All former scholars of the Department
of Science and Technology (DOST), the
four speakers are Dr. Emellie Palomo,
Director of the Integrated Laboratory
School of WVSU, Dr. Myrna Libutaque,
math teacher of Philippine Science High
School-Western Visayas Campus, Dr. Alona
Belarga, Director of Instruction and Quality
Assurance of WVSU, and Dr. Elvira Arellano,
Associate dean of the College of Education
and director of the Center for Research

in Science and Mathematics Education of

WVSU. They are assisted by about 10 more
math doctors, professors, and experts of
the ield coming from the MTAP-IC, Inc.
headed by president Dr. Herman Lagon
and MI Seminar-Workshop committee
head Mr. Kim Jay Encio. The speakers gave
inputs in the irst day of the training, April
20. Dr. Belarga and Dr. Palomo took turns
to discuss the Nature and Purposes of MI,
Types of MI, and Stages in the Conduct of MI.
In the afternoon, Dr. Libutaque shared her
own dissertation on MI and also covered
Conducting MI, Writing Proof in MI, and
Introduction to Mathematical Modeling. Dr.
Arellano, followed after with her lecturediscussion on Mathematical Habits, Using
Investigation in the Classroom, Assessing
and Formulating Rubrics, and the Format
in Writing MI.
Thereafter, the participants were
grouped according to their preference
and were asked to formulate their own
MI topics as a prelude to the hands-on
activitiesthat was facilitated in by the
speakers themselves and the MTAP-IC,
Inc. oficersfor the next day, April 21.
On April 27, participants presented
their inal MI output to the board of
experts for critiquing, assessment, and
evaluation
The winners of the best MI paper
were from Negros Occidental namely
Norben Bendejo (Julio Ledesma National
High School), Joy Cobarrubias (Bagonbon
National High School), Gualberto Genete
(Buluangan National High School), Elenita
Mahinay (Julio Ledesma National High
School), April Love Panoncillo (Julio
Ledesma National High School), Ma.
Salvacion Timoteo (Quezon National High
School), Jeneth Villalor (Julio Ledesma
National High School) all from the Division
of San Carlos City. Joining them on the
same spot are Lilibeth Langrio (Escalante
National High School) from the Division
of Escalante City and Edmundo Pagunsan
(Alangilan National High School) from the
Division of Bacolod City.
Math Investigation is an exploration
of an open-ended mathematical situation
where the student is free to choose what
aspects of the situation he or she would like
to do. Whatever claims or conjectures and
justiications of the same are made as results
of the investigation, and are conveyed in
written or oral form for further evaluation.
This years 3rd Regional MI SeminarWorkshop is sponsored by Panorama
Printing, Inc./

NEWS BLITZ
DepEd-MTAP monitors Saturday classes
DIVISION OF Iloilo supervisor and MTAP-IC
adviser Dr. Kim A. Arcea visited schools in
the Division of Iloilo this September 2013 to
monitor the Saturday classes conducted by
the Mathematics Teachers Association of the
Philippines and Department of Education.
Dr. Arcea together with Prof. Jonathan
C. Glorial, Dr. Harold F. Cartagena, and Dr.
Herman Lagon visited major central schools
in both the southern and the northern
portions of the province. The monitoring
team made sure that the review classes
used the appropriate materials designed
by MTAP-National. Certiicates were also
given to the participants and trainers. The
Saturday classes have ended on September
14, 2013./
Reviewer to be published
PACKED WITH K-12 competency-based
questions and detailed solutions, the
mathematics reviewer is one of the key
publication projects of MTAP-IC in 2013.
With the concerted expertise of the
members of the board of directors for year
2012 and 2013, hundreds of multiple-choice
questions were written, critiqued, answered,
and explained for the irst ever MTAP-IC
Math Reviewer. The idea of publishing the
book started in December 2011 during a
writeshop in Capiz initiated by the former
president Dr. Alona Belarga. As of this
writing, the reviewer is undergoing its inal
stages of editing at Panorama for its release
in the last quarter of 2013 or irst quarter of
2014./
Books donated in Guimaras school
WITH THE contributions of MTAP-IC board
members of 2012 and 2013, more than ive
boxes of books were donated to Sta. Teresa
Elementary School (STES) in July 2013. The
books were turned over to the STES principal
Mrs. Suzette Tomines and head teacher Mrs.
Nenita Gellego through the help of Rosevelle
Galvez and Salvacion Galvez. A bookshelf
was also donated. The books and shelf were
highly welcomed since the historic Gabaldon
Building that housed the STES library was
destroyed by ire in 2012./
CHEd awards Montao in regl convo
THE 4TH Regional Convention of MTAP-IC
was lifted a notch higher with the presence
of Metrobank Foundation Outstanding
Teacher Dr. Hilda Montao. During this
event, Dr. Virginia Resurreccion of Comission
on Higher Education Region VI awarded Dr.
Montao a plaque of appreciation for her
remarkable achievement in the Metrobank
search./
Research journal on the way
DR. WILHELM P. Cerbo, former board
member of MTAP-IC, now serves as the
editor-in-chief of the MTAP-IC Journal which
is targeted to be released this year. Various

Volume IV, Issue 1 | November 2012-September 2013

mathematics teachers and researchers of
the region submitted their papers for the
maiden issue of this peer-reviewed journal.
Dr. Cerbo reported that the reviewer is
undergoing editing and lay-outing./
MTAP leads regional convention, quiz bee
MTAP-IC Inc., held its 4th Regional
Convention and Quiz Bee on October 19,
20 and 21, 2012 at Amigo Terrace Hotel,
Iznart Street, Iloilo City. The convention was
designed for elementary, secondary, and
tertiary mathematics teachers, educators,
and enthusiasts in the region. Centered on
the Theme, Coping with the Demands of
the K-12 Math Curriculum, the convention
included plenary sessions, workshops,
research presentations, general convention,
and inter-tertiary math quiz bee./
MTAP congratulates WVSU
MTAP-IC CONGRATULATED West Visayas
State University, one of its partner
institutions in the yearly conduct of
Mathematical
Investigation
SeminarWorkshop, in its 111th anniversary.
Through the help of Prof. Jonathan Glorial, a
congratulatory streamer was hanged in the
entrance of WVSU. MTAP-IC was organized
by WVSU Director of Instruction and Quality
Assurance Dr. Alona M. Belarga in 2008.
Since its inception, MTAP-IC has members of
board of directors who are students, alumni,
or faculty members of WVSU./
MTAP-WV takes form
AS PART of the campaign of MTAP-IC to form
MTAP-Western Visayas, Mr. Mario E. Baavo
visited several divisions to invite mathematics
teachers to join the Regional Trainers'
Training and Conference on September 2729, 2013. The conference aims to gather
representatives of different divisions of the
region to form the MTAP regional chapter in
Western Visayas. Baavo visited the division
ofices of Roxas, Capiz, Aklan, Bacolod, Bago,
Kabankalan, Escalante, Cadiz, Sagay, Silay, La
Carlota, Passi, Guimaras, and Antique./
MTAP ofcers judge in science fair
OFFICERS OF MTAP-IC, Inc. acted as
judges in the Division of Iloilo Science
Fair last August 22, 2013 at Santa Barbara
Comprehensive National High School. They
were secretary Dr. Rosemarie G. Galvez,
board member Mr. Mario E. Baavo, and
member Dr. Elvira L. Arellano. The event
covered competitions in math investigations
and science investigatory projects./
Math camp blueprint up
AMID THE intensive preparations for
Mathematical
Investigation
SeminarWorkshop and Trainers' Training in
2013, the MTAP-IC Board of Directors is
also pinning its sight on the Math Camp
2014. This activity will highlight teaching
strategies and activities that make math fun
and interactive. Mr. Mario E. Baavo will act
as the chair of this activity./

DepEd, CHEd support MTAP

NO LESS than the Department of
Education and the Commission of
Higher Education have oficially
endorsed the holding of the training
in mathematics of math teachers in
Western Visayas set September 2729, 2013 at Iloilo Grand Hotel, Iznart
Street, Iloilo City.
Initiated by the Mathematics Teachers
Association of the Philippines-Iloilo
Chapter (MTAP-IC), Inc., the MTAP Regional
Seminar-Workshop and Conference is
set to be participated in by hundreds of
mathematics teachers in the region. They
will be trained by math instruction experts
headed by Prof. Rechilda Villame, vice
president of the MTAP-National and the
Mathematics Trainers Guild (MTG) of the
Philippines, and Dr. Ian June Garces, math
professor of Ateneo de Manila University
and former chairperson of the K-12
Technical Panel for Mathematics.
The three-day event is to be held
in partnership with the Department of
Education (DepEd) through DepEd Order
No. 84 series of 2013 which requires
every school division to bring oficial
representatives to the event On Oficial
Business, meaning usual expenses are
chargeable to local funds. Signed by
Regional Director John Arnold Siena, the
order strongly enjoins private and public
basic education (grade school and high
school) teachers to participate and be
given due skills how to eventually train
their co-teachers the fundamentals of
teaching math when they go back to their
respective ields.
CHEd Order 114 series of 2013
also invites college teachers, post-grad
professors, and education students
to join the said seminar-workshop.
Penned by Regional Director Dr. Virginia
Resurreccion, the commission deems
that many tertiary educators will join in
order for them to be equipped with the
necessary skills and knowledge cope with
the demands of the ever-evolving K-12
curriculum and acquire effective content

Prexy speaks in Div-Iloilo org meet

MTAP-IC, Inc. president Dr. Herman M.
Lagon was the guest speaker in the Division
of Iloilo Secondary Mathamatics Teachers'
Association Oficers, Math Mix Fever SubCamp Directors, and Facilitators' Conference
last August 16, 2013 at Monfort Hall in

CHEd-Region VI Director Dr. Virginia Resurreccion

(right) with MTAP-IC president Dr. Herman Lagon
(left) during the endorsement of CHEd Region VI of
MTAP-IC Trainers' Training . /The Ininity ile photo

and pedagogical skills to train other

educators in math.
Dr. Resurreccion said, My goal (of
supporting the training) is to invite and
provide teachers with the venue to learn
how to put math to the level of their
students. Every teacher must make it a
point to show to students the relevance
and use of math in daily lives; to prove
that math may be dificult to some but it
is sure worth it, for it does make sense.
Centered on the theme: Trainers
Training: Catching the Fire in the
K-12 Mathematics Curriculum, the
convention includes trainers training,
plenary sessions, workshops, and general
assembly. Aside from Dr. Villame and Dr.
Garces, about 15 other math doctors and
professors will serve as facilitators and
trainers in the three-day training.
After the general sessions, the
participants are to break down in
groups. They will have separate, rigid
trainings with select math experts in the
ield, including Dr. Villame. The tertiary
teachers shall also have their separate
training-lectures with Dr. Garces as
the main trainer. All the set training
sessions will be designed in alignment
with the competencies set by the new
curriculum./

Deped-Iloilo building, Lapaz, Iloilo City.

He spoke about the importance of math
in nation building vis-a-vis the challenge
to teachers in making math relevant and
engaging to students.The full-day meeting
was attended by about 60 math teachers all
over Iloilo./

News Correspondents: Dr. Herman M. Lagon, Mr. Kim Jay C. Encio, Dr. Rosemarie G. Galvez

NEWS

NEWS

Volume IV, Issue 1 | November 2012-September 2013

Dr. Harold F. Cartagena

HE DYNAMISM of Tourism is so vast that its impact can be seen in the economic, socio-cultural and environmental aspect of the society.
Generally, tourism plays a vital role in the development of a territory by uplifting quality of life of the host community and implementing
programs for the development of infrastructure and superstructure that are appropriate with the locals socio-cultural structures,
environmental concerns, economic status, philosophy, and needs. Thus, it is necessary to integrate tourism principles in our mathematics class
to allow our students to develop an appreciation of their own culture, encourage preservation of the environment, and realize the signiicance
of tourism in the economy.

Can you imagine the effect if we, math teachers, will facilitate
the marriage of tourism and mathematics in our lessons?
Evidently, some elements of tourism can be integrated with
mathematics. The four As of tourism (Attractions, Accessibility,
Amenities and Accommodations) can be matched with math
concepts such as distance, time, angles, mass, area, rate, business,
and a lot more. This approach can attract students attention since
most of tourist attractions are just around for students to see, touch,
and make use of. Teachers may present pictures to supplement the
presentation.
Let us take for instance the Arroyo fountain. Peppered with a
little creativity, a math teacher can make distance, time, age, geometry
and number problems by using Arroyo fountain. This strengthens
students understanding of math topics and historical value of this
site that may result to students retention of the math concept and
skills and great sense of integrity, ownership and appreciation as an
Ilonggo.
Arroyo fountain is one of the most
captivating man-made spots in
Iloilo City. It is visited by many
tourists because of its symbolic
value. It was built as a way of
recognizing the commitment of
Honorable Jose Maria Arroyo
former senator of the Philippines,
to the establishment of Metro
Iloilo Water Works. Arroyo,
fountain is a classy and stylish
fountain which depicts the neo
classical design (a sculpture style
of the 18th and 19th centuries).
One will see alluring structures
of four women holding basins
above their heads facing different
directions (North, South, East and
West). It also serves as the point
of reference or "kilometer zero"
for Panay Island.

Meanwhile, the economic impact of

tourism is undeniable. It includes increase
in contribution to foreign exchange,
investment, employment generation, taxes,
and other forms of government revenues.
Also, tourism may result to inlation,
inancial leakages, and trade dependence.
These data are very suitable for topics
in statistics such as graphs, measure of
central tendency, and dispersion. They
are even more applicable for basic math
operations that may require analysis and
comprehension.

Certainly, any math teacher can generate as many leading

questions and relective inputs out of the given graph. Aside from
the mathematical concepts or skills one wishes to impart, the
recognition of what tourism and travel can do to the community
will be given much attention so that relevant issues on employment,
inlation, projections, and production.
Now let us go to the socio-cultural world. Tourism includes the
preservation and restoration of cultural and cross cultural exchange.
In the same manner, it may result to commercialization, and conlict
between cultures.
Ilonggos are famous for the warm and passionate melody
of their language. Iloilo, with rich heritage and culture, can offer
delicious cuisine, cultural traditions, historical building, and popular
festivals. One of the remarkable tourism destinations is the Molo
Church or Church of St. Anne.
The Molo Church was
constructed in 1831
and is considered
as one of the most
beautiful in Western
Visayas with its lofty,
neo-Gothic spires and
neo-classical faade.
It was declared as a
national landmark by
the National Historical
Institute in 1992. It
is also known as the
Women Church" for
it housed 16 life-sized
images
of
female
saints. The church
made of white coral
rocks afixed with a
mortar made from egg

whites and mixed with sand. This feminine church stands among the rest,
its strength and beauty is a testament to Ilonggos unrivaled craft and skills
in masonry and arts.

Philippines: Direct Contribution of Travel & Tourism to Employment

Travel & Tourism generated

762,000
jobs
directly
in 2012 (2.0% of total
employment) and this is
forecast to grow by 5.5% in
2013 to 804,500 (2.1% of
total employment) and rise
by 3.5% pa to 1,133,000 jobs
(2.3% of total employment)
in 2023.

Source:
http://www.wttc.org/
site_media/uploads/downloads/
philippines2013_2.pdf

Aside
from
its
historical value, the Molo
Church, can serve as a
good model that may aid
discussion in teaching
geometric concepts such
as parallel lines, polygons,
perpendicular
lines,
geometrical
patterns,
symmetry, and many
more. Presenting the Molo
Church in a geometry
class can touch students

Volume IV, Issue 1 | November 2012-September 2013

spiritual awareness, and learning mathematical concepts becomes
more meaningful.
Lastly, tourism can make signiicant effect in the environment.
Conservation of resources both natural and man-made,
improvement of infrastructure, and increasing environmental
awareness are just few of the positive impacts. In the same manner,
tourism may also lead to pollution, congestion, and exploitation if
problems will not be addressed accordingly.
Iloilo River Esplanade
is a park at the Iloilo
river that serves as a
recreation and attraction
for both locals and
visitors. It stretches 1.2
km from Sen. Benigno
Aquino to Carpenters
Bridge. It was designed
by Arch. Paolo Alcazaren,
who also designed the
Singapore quay and river
esplanade. This project
is part of the efforts to
rehabilitate and bring
back the Iloilo Rivers
beauty.

The Iloilo River Esplanade is one of the best ield trip

destinations for math. Mathematical igures are almost everywhere.
It will be ideal to let the students explore the patterns and shapes
found in this site. Bringing camera with them to take a shot of
whatever they have discovered will add more excitement and fun.
Furthermore, this will awaken students consciousness about the
environment. They will realize that Iloilo River is indeed a gift to the
city and to its people.
I understand that the points above are just few of the million
possibilities of integrating mathematics and tourism. Now the
steering wheel is in your hands, let us then continue to travel with
mathematics./

Dr. Cartagena inished degrees that should have led him to mathematics
teaching, but he ended up as the College Department Head of Bachelor
of Science in Travel Management in Iloilo City Community College.
Nevertheless, he relishes the fact that there is still math in tourism.

Math supervisors call for "more"

NO LESS than the mathematics supervisors of the province
and city of Iloilo who happen to be MTAP-IC, Inc. advisers, in
unison invited all math teachers to take math in the classroom a
notch higher in terms of dedication, innovation, and hard work.
"Our teachers are doing relatively good in the discipline but we
must not rest from this, instead this must push ourselves to the
limits," Dr. Kim Arcea, math supervisor of Division of Iloilo
for elementary schools said. Agreeing to him, math supervisor
of Division of Iloilo for secondary schools Mrs. Hermosisima
Altillero further said that, "teachers must continue to do
research and look for better practices in the classroom." For
Mrs. Ligaya Montelijao, math supervisor of Iloilo City, "for us
to stay on top, Ilonggo teachers must invest in training and
continuous reading of updated materials."/

Mathematics in finance

Prof. Maria Cecelia P. Amparado

ATHEMATICS IS very important in almost all

aspects of our lives. As mathematics educators,
we have great responsibility to bring mathematics
closer to the lives of our students.
The topic Mathematics in Finance really interests me because
of my past experience in the general operation of teachers'
cooperative. I was emerging myself in the world of audit and
inventory tasks as in-charge of the supervisory committee before I
became the treasurer. It was a very rewarding experience, where I
appreciate the actual application of mathematics.
The two basic simple operations, addition and subtraction,
are very important in the following tasks: making entries in the
balance sheets, making the debit and the credit columns, updating
and checking the members individual ledger and passbook, and
preparing the entries in the assets and liabilities in the inancial
statement. The objective is by pooling together members' money
in the form of monthly capital build up (how amazing it reaches
millions), in order to help individual members in their inancial
needs. Knowing how this amount grows over a period of time,
computing the members individual dues, preparing of the
budget, and noting all the expenses incurred over time all require
mathematics. If the inances are not properly accounted for, then
the organization will collapse. Financial statement needs to be
presented for the members to keep track of the organizations
inancial operations. Records should be checked as to its accuracy
so that at the end of the year, the dividend and the patronage
refunds will be allocated among members.
A housewife also needs to monitor the familys inances as
well. Familys income and expenses need to be accounted for so
that the familys basic and other needs can be properly addressed
and managed to avoid opting for loan sharks. Simple mathematical
equations such as income minus expenses equals savings greatly
helps a lot just like in the bigger organizations where the equation
assets minus liabilities equals proit applies. Of course the
concept of integers cannot be underestimated; negative values are
very alarming for it means loss instead of proit!
Nowadays, inancial institutions such as banks and insurance
companies encourage us to invest and save for future use. But
we need also to exercise caution in choosing an institution that
is already well established to safeguard our hard earned money.
Banks offer interest for the use of our money as we deposit it to
them. The rate of interest differs in different institutions and the
kind of product we choose to invest also determines the rate.
For risk takers, they can also try other forms of investment.
For a minimal amount they can participate or buy shares using the
Unit Investment Trust Fund (UITF) where resources from different
participants are pooled together in order to buy shares of stocks of
the different companies, government securities bond, and money
market. This is where values up to 6 decimal places mean a lot.
One could monitor the net asset value per unit (NAVPU) per day.
An increase or decrease even up to the tenths place already has
an impact on the investors, especially for those owning greater
shares or units of participation.
Whether we let inancial experts or managers of inancial
institutions manage our resources or we manage our assets
ourselves, we should know the mathematics of inance. /

MATH CONNECTIONS

MATH CONNECTIONS

Volume IV, Issue 1 | November 2012-September 2013

Volume IV, Issue 1 | November 2012-September 2013

Mathematics in the school for the arts

MATH CONNECTIONS

MATH CONNECTIONS

Mr. Roberto G. Sagge, Jr.

HE HAVEN of the gifted and exceptional students, Iloilo National High School (INHS), houses several special
programs and one of which is named School for the Arts. This program embraces students with innate gift of talents
in different elds of arts. Students here are honed and molded to become more passionate and excellent in their chosen
art eld and at the same time to become globally competitive citizens of the country.

With vast curriculum content, students sometimes ind it dificult to balance their major and their academic subjects especially in
math. There is even this notion that no ordinary people would ever be good at math. Math has a bad reputation in our society, and to
make matters worse, alarmingly, many school teachers even those whose job is to teach mathematics communicate that attitude to
their students directly or indirectly (Coping with Math Anxiety, 1997, pp.2-3).
Joe Ayala, in our National conference for SPA Implementers at Subic Bay said, use the strength of your students to motivate them in
your class." With this idea inculcated in my mind, I started innovate to math-art integrations.
MEDIA ARTS. Students at this area exhibit keen interest in photography, computer art, print media,
broadcasting, video, and ilmmaking. They always have their camera and laptop at their side because these
are the requirements for their major. They are taught how to take pictures properly and to enhance these
pictures using Photoshop or other software available. So I took advantage of their skill in my geometry
class. I grouped my students such that in each group there is one Media Arts major and told them to take
pictures of man-made geometric igures around the campus as their project.
CREATIVE WRITING. Students here have a mastery of English, Filipino, and Hiligaynon in written from.
They must have the passion to write literary pieces as a requirement for their major. So I asked my class
to make haiku, a Japanese poem of seventeen syllables, in three lines of ive, seven, and ive. Most of my
students enjoyed writing haiku on mathematics.

DANCE. Students in this area are honed to become good performers in the ield of ballet, modern dance,
and folkdance. They must have lexible, strong, and well-coordinated body. Angular measurements using
body parts would be more interesting if the one demonstrating are dance majors. My students can easily
lex their body to show different angles without dislocating any bones or swelling muscles.

" Bilog sa Geometry

Kadamo sang iya nga parte
May chord nga kung
mag agi sa center
Isa na ka diameter."

THEATER ARTS. Students in this ield has high level of self-discipline, conidence, and creativity for most of
the time they do stage performance such as declamation, monologue, and improvisation. As they go higher,
they also learn how to direct and manage stage productions. Binalaybay for Math was also a competition
in Division Math Mix Fever of the Division of Iloilo. A theater arts major wrote a Binalaybay and delivered
it in our class before she went to the school level competition. Other students are also encouraged to write
and deliver it.

MUSIC. There are two sub majors in this ield, music-voice and music-instrument. For the voice major, a
student can sing well and read musical notes while a student must know how to play at least one musical
instrument and knows how to read notes in order to be qualiied for music-instrument. Rap-the-math was
one of the competitions in the Division Math Mix Fever, Division of Iloilo. This paved the way for music
enthusiasts in our program to join. In my class, I asked my students to compose music using math as a
subject.
VISUAL ARTS. Students who are interested and gifted in sketching, drawing, painting or sculptural works
enroll in this area. I saw a connect-the-dot game in a magazine, which gave me an idea to ask my students
to plot points on the Cartesian coordinate plane and connect these points to form a igure. I also asked them
to identify the coordinates.

The activities I did is a response to Sir Joe Ayalas advocacy of using my students' strength. As a result, my students were interested
to attend their math class since they know that their talents and skills are not only intended for their major subjects.
There are also studies that show how arts curriculum can help improve scores in math. For example, in the study of Gardiner et al.
(1996), it was found out that the percentage of students at or above grade level in second-grade math was the highest for those students
who participated in the arts curriculum for two years, less for those students who participated for only one year, and lowest for those
students who did not participate in the arts curriculum.
The activities I did might not be applicable to other math classes since they are intended for students with special skills. But you
can also try and improvise some of them. /

Learning math through

Cabalfins ceramic art

Dr. Rosemarie G. Galvez

After undergoing the lengthy process of sifting out

ONE OF the local artists who could
Department, an alternative class
easily conjure up magic with clay
was organized. About 50 students
pebbles, a lump of clay was mashed by hand. Then, it
is Mr. Alan Cabalin, a multi-media
enrolled in diverse courses illed
was placed on a potters wheel. As the wheel turned,
artist who maintains an art studio
up the Josefa Castro Audio-visual
the clay twirled and gradually took form. The artists
in Leon, Iloilo. His versatility is
Hall of the University of San Agustin
shown in pottery, watercolor, ilm,
for the alternative class on math
hand made a small hole in the middle. As the wheel kept
mixed media, theater, architecture,
in ceramic art. Julie and Lordelyn
turning, the hole became larger and the sides thinner.
and acrylic. His artistry is not
showed a presentation of their
only limited in museums, but
immersion and discussed the basic
The upper portion of the clay rises from the rest of the
also in educational contexts as
mathematical properties of cylinder,
lump. The artist guided the medium and slowly shaped
well. Having had several years of
pyramid, sphere, and prism.
it to a beautiful vase. As the vase gradually rose from
teaching experience in Philippine
Two more preservice teachers,
Science High School, he easily
Jenezeil and Rose, also joined the
the rest of the lump, the artist slowed down the wheels
adapts with the school system.
discussion. The highlight of the
rotation. By using a piece of string, the artist cut the
With his divergent artistic thinking,
show centered on Alan Cabalins
vase from the rest of the lump. Voila, a vase was made!
he collaborated with me and
talk and demonstration on ceramic
mathematics preservice teachers
art. He discussed the different kinds
Magical indeed."
in organizing an alternative
of clay and the possible geometric
From: Galvez, R. (2012). Quantifying artworks: An analysis of the mathematics principles used by local artists. pp-133-134.
class that involved both art and
shapes and mathematical concepts
mathematics.
igures by pounding, rolling, and pressing, and that could be introduced with ceramics. After
With the several art techniques that Alan by knowing the right amount of pressure was which, the students made their own artwork
has mastered, he chose ceramics as his prime enjoyable and fun.
based on the geometric solid that they are
interest in bringing art to school.
assigned in. They also wrote their relections
Lesson Planning
Immersion
Initial possible mathematical concepts and discussed the mathematics concepts that
Bringing the preservice teachers and were discussed in Leon. Parabola, ellipse, they have learned.
the artist together brought to surface the spheres, volumes, and solid igures were
An afternoon with Cabalin may not
underlying mathematical concepts that some of the topics that Lordelyn, Julie, and Mr. be enough to inish an obra maestra. An
could be integrated with ceramics. Two Cabalin mentioned during the immersion. afternoon with clay may not assure students
Augustinian preservice teachers, Lordelyn After some brainstorming, we decided to mastery of geometric concepts. But, the
Santias and Julie Ann Analista, joined the focus on the topics tackled in solid geometry. connection of mathematics and art could
trip to Leon, Iloilo to immerse themselves in Indeed, various solids such as cylinder, cube, spark students interest in learning numerical
Cabalin's Art Studio. Sir Alan was generous rectangular prism, sphere, and cone may be concepts through artistic activities. As
enough to share his experiences in using the discussed through the use of clay. Julie and Cabalin transforms a lump of clay to art,
electronically operated potters wheel and Lordelyn wrote a lesson plan and I made some mathematics teachers should explore how to
transform cultural and artistic experiences to
the one machinery he obtained that produced suggestions and corrections.
mathematical learning. /
tube-like structures of clay. It was an afternoon The Alternative Class

With
the
support
of
the
University
of
delight of folk music and ceramic overload
Dr. Galvez conducts research that centers on
topped with Mr. Cabalins prepared snacks of San Agustin Association of Math and Physics
mathematics in art. E-mail reactions to rggalvez316@
local tubers. The experience of learning to form Society and the Mathematics and Physics
yahoo.com.

Mathdayaw

Volume IV, Issue 1 | November 2012-September 2013

Volume IV, Issue 1 | November 2012-September 2013

Mathematics
prayer
Prof. Jonathan C. Glorial and Ms. Nina Isabelle Juan Loa

Mario E. Baavo, M.S.

Bag- o ako mag umpisa sa akon pagdayaw sining

matahum naton nga Hara,
Ang akon bug -os nga pagtamyaw sa inyo nga tanan nga
may kalipay kag hara-hara;
Ang matunog nga pagpamalakpak sa inyo nga tanan
ang gusto ko nga madunggan,
Nagasigabong nga magpamalakpak sang tanan.

Nian pagpangayo ko sang katahuran sa aton mga

halangdon nga mga dumuluong,
Sa sampaton nga manogdumala sang bulothoan naton;
Mga ginikanan, manunudlo kag mga kabataan
matambok man ukon maniwang,
Putot, lagwayan, laon man ukon binayaan,
May ti-ayon, malipayon ukon nalisdan ang akon pag-abi-abi kag
pagtamyaw maayong gab-i sa inyo nga tanan.
Ang inyo matunog nga pagpamalakpak tanda
sang matuod-tuod nga gugma,
Akon gid ginakalipay kag hugot sa akon tagipusoon
nga dayawon ta ining matahum nga hara;
Katugnaw sang panahon, gatagiti nga init
sang adlaw ang akon ginbatas,
Suba, sapa, kabukiran ang akon ginlat-as;
Mabangis nga kasapatan sa katalunan ang akon gin- away,
Lamang ko makita O Mahal nga Hara ang imo nga Dagway.
Akon mga kamot sa subong O Mahal nga Hara ginatan-ay,
Palihog dawata ining akon pag-alongay;
Lamang mapala ang kapiot sang dughan,
Matambalan ang kauhaw, malipayon nga yari
ako subong sa imo ginhari-an.
Ang imo katahum O Reyna daw kabugwason sang aga,
Nagaigpat-igpat ang imong mga mata bagay gid sa
Oval mo nga guya;
Kotis mo nga daw porcelana daw ginpahiran sang lana,
Kon ikaw magyuhum daw parabola, bagay gid sa
mga circle mo nga mga mata.
Napanaputan ka sang almasiga daw
mga rhombus kag square ang hitsura,
Lainlain nga kortisaba may triangle, rectangle, pentagon, heptagon,
octagon, hexagon, ano ina nagakasari-sari nga polygon?
Mga lantuwelas nagalinya may parallel lines, perpendicular lines
y- intercept, negative ang slope nila.

Heavenly Father

Kon akon gid ikaw himutaran gikan sa origin kag pakadto sa wala,
Daw mga graphs sang polynomial functions kag
exponential and logarithmic functions ang katulad nila;
Subong man ang symmetry nga daw graphs sang
quadratic functions nga napihak sa tuo kag wala.

Ano kamo inyo man saligbat ni Fermat,

Geometry bala siling ni Ceva ang gina-istoryahan?
Theorem, postulates, denition ukon Herons Formula;
Grabe ka Mahal nga Reyna kay pati ang mga,
Great Mathematicians nagakagubot sa imong hitsura.

Ang slope sang imo nga ilong nagagantaw gid sa sining kagab-ihon,
Ang kilay mo nga kinudlit daw mga minor curve nga ginkurit;
Kon ikaw magyuhum Mahal nga Reyna
ang imo katulad daw tapulanga,
Nagapalang-init ako sang 40 degrees centigrade kon ako
manganinawsang maalikaya mong guya;
Dughan ko galinagumba daw ako ang ginataranta.

Apang husto sila indi gid man matungkad ang imong kaanyag,
Wala sang formula nga magamit agud malaragway
ang guya mo nga gapangluspad;
Ginbatiti, gintipigan ka nga prinsesa agud nga mangin Reyna
Subong ikaw ginahingadlan nga Reyna sang Matematika.

Nian akon sipad siparon ang imo nga kagayon,

Ang dughan mo nga gabungyod daw
graphs sang sine kag cosine nga gabawod;
Ang circumference sang imo hawak nga daw botelya sang coke,
Katahum gid sa imo maglikday-likday daw galingkod ka sa trapezoid.
Balikawang mo bagay gid daw family of circles,
Kon ikaw maglingkod daw equilateral triangles;
Congruent gid walay lisa ang imo mga measures,
Vital statistics 26- 6 -26 proportion gid ang imo mga angles.
Lagwayan mo nga mga batiis daw parallel lines,
Wala gid gasantik kasubong sang parpendicular lines;
Daw duha ka mahagwis nga line segment kon ikaw ang magtindog,
Kon ikaw akon gid himutaran daw ako ang mapalangurog.
Wala gid sing tupong ang imo kaanyag daw ugsad ka nga gadilag,
Olitawo sa imo indi gid magligad nga sa imo magpasiplat;
Makagalanyak ang imo tindog ikaw gid makabibihag,
Makailila mo nga bayhon indi gid ako malipat.
Perfect gid ang area sang tanan mo nga pamusod,
Bisan pa ang imo perimeter kon ikaw maga- atubang , magatalikod;
Kaina ko pa nga compute e -extract ko man square root,
Exact gid ang value sang imo 1 and nga foot.
Nangayo ko tabang gintext ko pa gid si Euclid nga ako iya buligan,
Apang si Pythagoras ang nagsabat nga ina lang imo yana masarangan;
Subong man siling ni Rene Descartes, Cartesian Plane lang ang katulad,
May apat lang ina ka quadrants daw pizza pie bala kon magkihad.

11

Kon wala lang inang King sa kilid mo ayon akon gid ikaw nga singiton,
Kay bahandi ka nga diamond wala sing tupong ang imo kagayon;
Apang batunon ko ang tanan nga hasta lang ako sa panalambiton,
Tungod na prove na nga may Hari sa tupad mo nayon.
Mahal nga Hari sang Matematika ako na gid lang ang managubilin,
Mahal nga Reyna Sang Matematika sang Points, Lines and Planes;
Imo siya nga pangapinan kay basi kon may ray sa iya nga magasungkit,
Handa na nga daan si X and Y sa iya magsabnit.
Apang gasalig gid ako sa imo Mahal nga Hari sang Matematika,
Nga ikaw handa gid sa tanan nga oras sa Mahal nga Reyna mag-ambaga;
Makilas mo nga mga alima daw ordinate kag abscissa ka taliwis,
Yara sa imo Domain that x is greater than or equal to zero but not less.
Busa malipayon ako nga magataliwan kay na prove na ang tanan,
Ang Mahal nga Hari kag Reyna sang Matematika
malipayon na sa ila ginharian;
Kon ako lamang tagaan sang kahigayunan
nga makatigbaliw sa isa ka buyog,
Ako na lamang ang maga singhot sining mga magayon nga bulak
Sang Ginharian sang Matematika kag masinalibhog.
Ang akon pagdayaw duna akon na nga tapuson,
Sa sining bulahan nga Hari kag Reyna sang Matematika
sa sining kagab-ihon;
Kon ako man nakapukaw sang inyo balatyagon,
Tungod kay ako isa lang ka nilalang nga
mamalaybay nga buot unta maghapon.
Sang masingkal ko nga mga pulong nga nabuhian ako inyo patawaron,
Kay isa lang ang akon tuyo nga kamo ang lipayon;
Busa indi paghatagan duag ang tinipik lag lantip ko nga pulong,
Agud ako ikaw, kamo kita tanan magmahidaeton.

Our knowledge of appreciating mathematics

multiplied exponentially.
Even though what we learned
might be directly proportional to our attention span,
we learned a lot with every second deducted from our time.
God, we apologize for whatever sins we committed.
We stand here as survivors of challenges.
We may fail to reach the apex
but with You, we have honed our skills to the tenth power
As our carelessness gets multiplied by zero
careful analysis shows that whatever happens
your love still remains equal to tangent 90 degrees
Lord, our love for you is equal to secant 90 degrees
Almighty Father, all our triumphs
are for Your greater glory
All these we pray through Christ our Lord
Amen

An ode to math

Dr. Rosemarie G. Galvez

Your sheer splendor entices me

to immortalize your beauty
My brushstrokes capture your grace
as your sweet lips says
you are an epitome
of practicality
Alas!
Your wavy tresses, so lovely
turned to strands of intricacies and difficulties
You shattered my soul
with complexity of signs and symbols
But my canvas shows your purity
for you are a true beauty

LITERARY

LITERARY

10

FEATURE

Volume IV, Issue 1 | November 2012-September 2013

Volume IV, Issue 1 | November 2012-September 2013

TUDENTS BURYING their heads in a pile of worksheets and scribbles of endless

formulas might not be an ideal picture for todays generation of learners. Alternate
activities that allow students to explore and discover mathematical properties while
having fun may be introduced. Here is a smorgasbord of innovative alternative mathematics
classes.

odels of inite
geometry need
not be lat. At West
Visayas State University,
the BSEd-Math majors
had a fun exhibit of
models made of recycled
materials. Desargues
geometry, anyone?

M
M

ath students could be outdoorsy, too. As part

of the celebration of the Mathematics Week,
Ateneo students explored the premises of their
school campus during the Math Trail.

Photo credits: WVSU BSEd 2-Math students, Mr. Stephen Raymund Jinon, and Mr. Keith Lester Mallorca

MTAP-IC members are encouraged to share their best practices. E-mail photos or articles to mtapiloilo@yahoo.com.

13
13

Volume IV, Issue 1 | November 2012-September 2013

Volume IV, Issue 1 | November 2012-September 2013

ath is fun at
Westbridge. Math
Trail = Proving +
Construction + Tangrams
+ Logic Questions +
Rewards and Consequence
+ Assessment through
rubrics = Exciting math
class.

FEATURE

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Volume IV, Issue 1 | November 2012-September 2013

Volume IV, Issue 1 | November 2012-September 2013

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Volume IV, Issue 1 | November 2012-September 2013

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Volume IV, Issue 1 | November 2012-September 2013

Dr. Herman M. Lagon

Tips for neophytes

HE REAL deal is always

in the classroom. This is
the dreaded reality that
all new teachers must embrace
regardless of their teaching
pedigree, academic medals,
or extra-curricular experience.

Most of the time, the greenhorns

ind it rocky to trek through the calvary of
school work. Minus the demand in terms
of pedagogy and content, the nastiest
stumbling block is the students themselves.
It is as if every day is a puzzle to crack; every
student is a riddle to solve.
I chanced upon an article from The
Jesuit Post authored by Jesuit priest Ryan
Duns where he offered some bag of
tricks for new teachers. Blending it with
my own experience as a teacher for 13
years, I am presenting some hodgepodge
points to relect upon. Some points may
be sensible to some. Others may ind
these tips strange. Nonetheless, I am
presenting them to you, dear fellow
teachers, hoping that these will end up
helpful to those who will make use of
them, tantum quantum.
Let me start by this one touchy point:
Teenagers are not shallow.
Yes, these young ones may be clueless of
this but they do think deep. This is precisely
the reason why we, teachers, must extend
conscious help to uncover latent gifts and
hidden depths of these learners.
One way is to ask in-depth, HOTS,
leading questions. We may also develop
strategies to talk about sensitive issues
giving these young thinkers the leeway to
engage with each other. Beyond content, we
are teaching a style of thinking and a way of
processing evidence, a way of being human.
Students also appreciate teachers who
listen to and discourse with them. Hence,
it wont hurt if we take time to read, and
comment, on any written work of students.
A lone check mark or just a score grade in
a kids essay or solution is a downer. The
best things to do, among others, are to take
a few seconds and write a comment, or ask
a question. It is in this way that we learn a
great deal about our students and give an
opening for further conversations.

Consequently, we must pain ourselves

to anchor our lessons to students world. In
short, consciously convince them in the most
spontaneous way that what we are talking
or covering about has signiicance to their
way of life. It is ultimately relevant to the
present reality. What is this for? students
always ask us, usually innocently. We must
personify our answer to this question in the
classroom to convince our students that our
lesson makes sense and class chore is never
a waste of time.
Next point: Students are social beings
The smallest unit in the classroom is not
the student. It is the sub-group of students.
We must watch how our students arrange
themselves into various cliques. Tread this
reality carefully for one student hurt or
insulted may mean hurting or insulting the
whole herd. This may also work in a positive
way. Knowing the dynamics of these small
groups gives us better options and clearer

Mr. Stephen Raymund T. Jinon

means to be an adult. Instead of pandering

to them, we can help elevate them.
One way is to be real. Students have a
sixth sense for detecting silliness and we
dont need to force ourselves to be relevant
to be liked. We need to be ourselves, our
adult self, and give them an example of the
type of adult they can aspire to be.
Students deplore hypocrisy and
demand for consistency. For instance, we
must never let students see us texting if is
prohibited in school. We should not demand
to be always on time or to produce better
outputs if we ourselves are always late or do
mediocre things. As soon as they know we
do not walk our talk, they will just walk
out from our class or shut down from our
rants.
Besides, we must not make our
students the center of our life because
we are not the center of their lives. I have
seen new teachers treat their students as
if it is the end-all-and-be-all of things. Do
not get me wrong, our students are vitally
important to us (it is your job, after all)
but we have to remember who is at the
heart of our life God.
Another controversial point: Kids cheat.
Dont take it personally. It is just that if
a warm body is pushed against the wall, and
there is this easy way out, human nature will
tell us to take it for survival purposes. That
is why we must be ultra conscious in giving
assessments. Pro-activeness is the key. We
must never give our students the venue or
even the chance to consider cheating their
way out of the test. It is in this way that
they catch and appreciate the values of selfconidence, authenticity, and intellectual
honesty.
Do not get me wrong. I am not overly
pessimistic or seemingly Machiavellian here.
This is simply a recognition of the reality of
original sin in the world. As a wise Jesuit
teacher once quipped, See nothing, but
observe everything. Hence, be alert and
vigilant!
Nonetheless, we can always tell the
students not to do this or that. But then
again, the best teacher is our person. As

As soon as they know we do not

walk our talk, they will just
walk out from our class or shut
down from our rants.
perspectives how to deal with them. We can
make use of these social dynamics to our end,
ensuring maximized learning environment,
saturating critical mass, and eventually
enhancing classroom management.
However, as cliques are given focus,
we must also keep an eye on those in the
margins and frontiers. Its easy to want to
be the popular teacher and get in with the
popular kids. But we must never forget the
learners on the edges and corners. Note that
many successful people, loner in their early
age, have cited particular teachers who went
out of their way and pushed them enough to
do better in school, and eventually in life.
Hence, the next point: Students deserve
our respect.
Believe me. They are human, after all,
even if they dont always act or smell like it.
We can laugh with them. To be truthful,
they can be brutally funny. But we must not,
however, scapegoat a student or fall prey
to a mob mentality. We must not abuse our
power over them. We are modeling what it

INIONS ARE the scene stealers in the movie Despicable Me. They
are cute creatures loved by many kids for their child-like attitudes.
They were created to make the life of Gru more exciting. They were
taught to follow orders and they respected the one who created them.

to page 23

Watching this movie many times made

me realize its good sides and the importance
of minions and Gru in education. Gru, just like
guro, is an educator that made an impact
to the kids and the minions. Through his
ideas, he taught the minions how to develop
their skills and serve others. He might be the
reason why some of the minions are doing
evil things through his modeling, but at the
end he had taught the minions how to love
and care.
The minions are just like primary
kids and elementary pupils who just enjoy
the carefree stage of their life. They follow

KNOW a person who, in

his young years, seemed
to be a math illiterate.
When he was in Grade 1, his
teacher asked him a very
challenging question.
Maam X: What number is between 1 and 3?
Student Y: Hmmm, 4?
Maam X: (In an irritated and angry voice)
What? Again, what number is between
1 and 3?
Student Y: (sobbing) Hmmm 0?
His teacher was in rage! And he spent
the next few minutes crawling under three
long tables. Every time he reminisces the
old days, he would laugh recalling how
stupid he is. That young lad who does not
know the middle number between 1 and
3 is ironically teaching pupils and students
do basic and advanced darithmetic up to
solving equations and do some shortcut
techniques.
Amidst those bad experiences, it
has been a learning experience for him
to study harder and more intelligently, to
listen more attentively and be obedient to
the teacher. Hence, though that experience
may have proved unpleasant (and a bit
funny) but still he is very thankful for he
developed virtues in the course of studying

instructions, but they sometimes fail to be

consistent because of their age. They know
how to understand and they are fun to be
with. They differ from each other, but they
deserve a lot of respect from any Gru in the
world.
For the Gru who teaches mathematics,
we should start training the students as
early as possible. This would mean hard
work. Elementary Gru is the one who could
make these minions love math. This is the
stage where these kids/children will explore
how important math is in their lives.
Each Gru has different strategies in

teaching mathematics. The following are

some strategies that can be used in making
mathematics exciting and interesting.
Story telling. Elementary teachers are
considered good storytellers. Story telling
is not only used in English and Filipino but
also in mathematics. I am not referring to
using any story books and big books. Rather,
storytelling involves teachers who make
stories that integrate topics in mathematics.
This sounds hard, but storytelling could
really help for greater retention. Primary
kids like adventure stories such as dinosaurs,

to page 19

Joining forces of math and virtue

Mr. Kim Jay C. Encio

mathematics.
Based on his personal experience, the
teaching of Mathematics has been dedicated
to the learning of cognitive concepts. More
often than not, the inclusion of the affective
side of mathematics has not been given
much attention- paving more emphasis on
the cognitive (and psychomotor domain)
aspects of mastering the skill through drills,
repetition, reinforcement, and assessment
and evaluation.
A teachers role is not solely to sharpen
the mind but also touch the heart. A teacher
showed form men of integrity who later
on will not serve as intellectual monsters,
but men of character who will better forge
society by their good will and example.
Some of us are concerned that a
ifty-minute or one-hour time frame for
the subject matter is not enough. Is there
any place for values integration in the
curriculum? Yes. values be integrated in
usual math classes and topics.
Decimals and the Decimal Point
Say, there are PhP12, 345, 678.00 and
PhP1.234567800 bank checks. For the
irst number, with the value of the money,
you may consider yourself rich (or may
be in the upper middle class) but with the

latter, maybe you wont bother dragging

your friend with you to the bank to
encash a check much lower than an
Emilio Aguinaldo coin. The positioning
of a small decimal point tremendously
affects the value of a particular number.
Hence, the students should realize the
proper placement of the decimal point
in any of the four operations (+, , x, ),
reinforcing in them the virtue of accuracy.
Furthermore, giving value even to small
things is emphasized.
Like us, we may not know the effects
of these small things inside and outside
the classroom to our students. A simple
smile may brighten someone elses day,
a small bond may be a big deal for them,
a simple tap on the shoulder may signal
how we truly appreciate and care for
them, a not-so-harsh correction may
signal how we care and value them as a
person.
Venn Diagram
Venn Diagram encompasses math and
logic. Aside from knowing relationships of
sets, union, and intersectio, the students
may be made to realize that we are like

to page 19

FEATURE

FEATURE

16

MATHEMATICAL INVESTIGATION

Volume IV, Issue 1 | November 2012-September 2013

The difference of the

terms of a series generated
by a polynomial function
Mr. Matthew T. Lasap

STATEMENT OF THE PROBLEM

This paper aims to ind a generalization
of the common difference of a series
generated by a polynomial. Speciically, it
seeks to pursue the following problems:
1. What is the 1st difference of series
generated by a polynomial function of
degree 1?
2. What is the 2nd difference of a series
generated by a polynomial function of
degree 2?
3. What is the 3rd difference of a series
generated by a polynomial function of
degree 3?
4. What is the nth difference of a series
generated by a polynomial function of
degree n?
INVESTIGATION
A. Series of numbers generated by a
polynomial function of degree 1 (=1)
Consider a series deined by, = +2.

B. Series deined by a polynomial function of

degree 2 ( = 2).
Consider = 2.

C. Series deined by a polynomial function of

degree 3 ( = 3).
Consider = .

More examples and explorations would

show that there is a common difference in
the series generated by a polynomial.
CONJECTURES
As a product of the investigation, the
following conjectures are proposed:

1. If 1, , , ,... is a series of numbers

deined by a linear function = +,
where N, then the irst difference of the
consecutive terms in the series is equal to
.
2. If 1, , , ,... is a series of
numbers deined by a quadratic function
=++,
where N, then the
second difference of the consecutive terms
in the series is equal to 2a.
3. If , , , ,... is a series of
numbers deined by a cubic function =a
+ a + a + a , where N, then the third
difference of the consecutive terms in the
series is equal to 6a .
4. To generalize, if , , , ,... is a
series of numbers deined by a polynomial
function =a+a-1+a-3+...+an+an+1,
where N, then the difference of the
consecutive terms in the series is equal to
!a .
JUSTIFICATION
Conjecture 1. If , , , ,... is a series
of numbers deined by a linear function
=a+a where N, then the irst
difference of the consecutive terms in the
series is equal to a .
Proof:
=a+a is a linear function whose
graph is a line. The slope of a line (m) is

2-1

deined to be
or - . If we let =1
x
2
1
where , N(since in this MI, the focus is
on the difference of the consecutive terms
of a series, or equivalently the values of
the function for some given consecutive
-

values), 2-1 = 2 1 = . Hence, m=

1
2
1
.
But when =1 where , N
(meaning
values are taken to be
consecutive) , refers to the irst
difference of the consecutive values. This
implies that the slope m is equivalent to the
irst difference of the consecutive terms of
the series.
dy
The slope of the line =a+a is
dx
=a. Therefore, the irst difference of the
consecutive terms in the series equals a.
The following lemma will be used to
prove the succeeding conjectures.

Lemma 1. If a polynomial curve deined by a

polynomial function is cut by a secant l at
, and , such that l does
not intersect the curve in the interval 1,
, then there exist , such that
the slope of l equals the slope of the tangent
to the curve at , or in symbols

= '.

Proof:
Let l be a secant through ,
and , , where > and is a
polynomial function. Suppose, further that l
does not intersect the curve in the interval

,. The slope of the secant is .

Suppose we take R where >>
such that , and construct
altitude m to l through , . From
altitude m, we construct a perpendicular l
at , . Since l m and m l , this
implies that l || l. Since l || l and that is a
polynomial function R, where >>
and , such that l intersects
the curve at , . From , ,
altitude can be drawn perpendicular to l.
This implies that l.
Let the length of the segment l joining
, and , be . It must
be evident that as decreases, the points
, and , becomes closer
and closer to each other, so that when =0,
, =, . Consequently, l
becomes a tangent to the curve at ,
with slope '. But l || l, and this implies
that their slopes are equal, hence,
='.

Therefore, , where
, such that ='.

Conjecture 2. If , , , ,... is a series

of numbers deined by a quadratic function
=a+a+a, where N, then the second
difference of the consecutive terms in the
series is equal to 2a .
The derivative of a function gives the
slope of the tangent line at a point on the
curve deined by the function. Hence, taking
the irst derivative of the quadratic function
will yield slopes of tangents to the parabola
deined by the function. But the difference
of the terms (established to be or ,
when and are consecutive integers, in
the preceding proof), refers to the slope of
a secant joining , and , . This
seemingly implies that the irst derivative
cannot describe the difference of the terms
or the .
However, it should be noted from the
exploration that the irst differences of
this series is not anyway a constant. The
irst derivative can be an equation that

19

Volume IV, Issue 1 | November 2012-September 2013

contains the said differences. It would then
be suficient to show that if R where
>> or , such that the slope
2-1

of the secant 2-1 (which is equivalent to )

is equal to the slope ' of the tangent line
at , then the irst derivative can preserve
and describe or the difference of the
terms. Lemma 1 justiies this. Moreover, the
case, which is not covered by the lemma,
where the secant intersects the curve at
some number of points can be shown to have
at least one tangent by dividing the curve
into intervals enclosed by the intersection of
the secant with the curve and use the lemma
to show that a tangent can be found on this
interval parallel with the secant.
Hence, the irst difference () can
be described and preserved by the irst
derivative.
So, the irst difference of the series
is '=2a+a. This equation justiies
that the irst differences of consecutive
terms will not a constant as the they will be
dependent on the value under consideration.
(Disclaimer: This MI does not provide a way
to compute the irst difference between two
speciic terms.)
But ' is itself a linear equation that
can deine a series of numbers (a series of

irst differences that is). Using the reasoning

in the proof of Conjecture 1, the derivative
of ' should describe the differences
between the terms of the series it deines.
Hence, "=2a. Therefore, the second
differences is a constant equal to 2a.
Conjecture 3. If , , , ,... is a series
of numbers deined by a cubic function
=a+a+a+a, where N, then the
third difference of the consecutive terms in
the series is equal to 6a.
The
irst
derivative
'=3a+2a+a describes the irst
differences of the consecutive terms in the
series, R. ' is not a constant value.
The second derivative "=6a+2a
describes the second differences of the
consecutive terms in the series, R. "
is not a constant value.
The third derivative "'=6a is the
third differences of the consecutive terms in
the series R. "' is a constant.
Therefore, the third differences is 6a.

Conjecture 4. If , , , ,... is a series of

numbers deined by a polynomial function
=a + a-1 + ... + a + a+1, where N,

Teaching... from page 17

aliens, dragons, and other ictional

characters. Thus, a teacher may introduce
learners to the world of imagination and
fantasies while immersing himself or herself
in the universe of stories that children love.
On the other hand, intermediate children
may be immersed in real life stories since
they are expected to master solving real
life problems. It is also recommended that
teachers should watch more movies, read
more books, and observe the environment
more.
Manipulatives.
Popsicle
sticks,
fraction bars and pies, strips are some of the
manipulatives that work for the kids. Telling
directly that + 1/3 is 5/6 because of LCD
is a big no no. Students should discover
through these manipulatives the value of
LCD before knowing what LCD is.
Block Model. For students who want
to love problem solving and algebra, the
block model approach is one of the best
ways. As early as grade 1, the block model
could help these students understand the
problem more because of its visual aspects.
If it is consistently used, this could help the
students appreciate algebra more. This can
also be a great help in teaching fractions and
the like most especially for the mastery of
solving problems using the basic operations

Investigation and teaching through

patterns. Students will have meaningful
learning experience through these strategies
because they enjoy more if they discover
something. Teaching through patterns and
investigation is a gateway for discovering
shortcuts and formulas.
Using whiteboard and games.
Students love games. It is a good motivation
for the students if you allot 5 to 10
minutes every day for games. Games using
whiteboard (for each student) can make the
teacher assess if the student is studying or
learning something in the class. Students
love competition. Using whiteboard + group
competition + previous lesson = interesting
math class and meaningful learning.
Without the whiteboard, papers can be a
good replacement.
Worksheets. The role of the teachers
are more on facilitating. Thus through the
exploration stage of the K-12 Curriculum,
worksheets are of great help. These are used
before instruction. The worksheets contain
deinition or examples and more exercises.
There are more strategies that can be
used to ensure that the minions are learning.
We should not focus on one strategy alone.
We should learn more, since we are dealing
with the 21st century learners. /

then the nth difference of the consecutive

terms in the series is equal to !a .
It was shown in the preceding proofs
that the differentiation can preserve the
differences of consecutive terms in the
series. The derivative of is -1. For
every differentiation, decreases by 1. This
implies that =0 after the nth differentiation
(=0). Since 0 = 1, the nth difference will
yield a constant.
A theorem in calculus provides that
the nth derivative of g=a is g=a!.
The leading term in the polynomial is only
considered in this proof since the other
terms will have an kth derivative which
is 0, where kR.
Therefore, the nth difference of the
series is !a.

EXTENSION
The following extensions are proposed:
1. How many tangents within the
interval , are there if the secant
intersect the curve n times?
2. How can a polynomial function be
derived from a series of numbers where the
nth differences are equal./

Joining... from page 17

joint sets. That
is, we are all
different from
one another (as
represented
by the white
portions at the
interior of two circles) yet we have common
characteristics (as represented by the
shaded region). This should remind us that
we are all distinct from one another and we
are all special, yet we are united.
These are just a few ways of integrating
virtue in our lessons. In the long run, our
students may fail to remember how to ind
the GCF and LCM of two or more numbers.
They might forget how to use the quadratic
formula to ind the value of x. But, what
matters most is the development of good
habits, attitude, and values. The goal of
our education is not deformation (forming
intellectual monsters), but formation.
We need to be reminded that we have to
produce individuals who are persons of
conscience and of integrity who are positive
trailblazers in their ields.
So, be considerate to "math illiterate"
students because they could transform, too.
Case in point: the one who did not know the
number between 1 and 3 is now the writer
of this article. /

MATHEMATICAL INVESTIGATION

T
18

Volume IV, Issue 1 | November 2012-September 2013

Rectangles in a pile of congruent rectangles

A Mathematical Investigation Paper Presented during the 3 Mathematical Investigation Congress, Center for Teaching Excellence (CTE) Building
West Visayas State University, La Paz, Iloilo City, April 20, 2013
rd

Proponents: NORBEN BENDEJO, Julio Ledesma National High School (San Carlos City); JOY COBARRUBIAS, Bagonbon National High School (San Carlos
City); GUALBERTO GENETE, Buluangan National High School (San Carlos City); LILIBETH LANGRIO, Escalante National High School (Escalante City);
ELENITA MAHINAY, Julio Ledesma National High School (San Carlos City); EDMUNDO PAGUNSAN, Alangilan National High School (Bacolod City); APRIL
LOVE PANONCILLO, Julio Ledesma National High School (San Carlos City); MA. SALVACION TIMOTEO, Quezon National High School (San Carlos City); JENETH
VILLAFLOR, Julio Ledesma National High School (San Carlos City); KIM JAY C. ENCIO, Editor/Reviser

SITUATION
Construct a pile of n congruent rectangles. Investigate.

STATEMENT OF THE PROBLEM

The investigators would like to
determine the total number of rectangles
formed from a given pile of n congruent
rectangles.
Speciically, this study sought to ind an
answer to the question:
What function can describe the total
number of rectangles R that can be formed
from a given pile of n congruent rectangles?
DERIVING CONJECTURE
From the given situations, the total
number of rectangles R was noted vis--vis
the pile of n congruent rectangles.
The results and patterns observed are
noted on the following table:

Based on the given table, the conjecture

can
was formulated. The formula, R =+1
2
be used to determine the total number of
possible rectangles R formed from a given
pile of n congruent rectangles.
Based on the gathered data, the
following table summarizes the total
number of rectangles R with respect to the
number of congruent rectangles n in a pile.
Taking the differences in ns and Rs we
have

It can be noted that equal irst

differences in ns produced equal second
differences in Rs. Thus, the function/
equation that possibly describes the total
number of rectangles R with respect to the
n piles of rectangles is an equation of the
second degree (quadratic function) which
takes the form

Substituting A = , B = and C = 0 to the

form An2+Bn+C = N, we have
n2 + n = R.
Or in complete factored form, we arrive to
R = +1 , where n N.
2
This leads us to the following conjecture
below:

An +Bn+C = N, where A,B and C R .

2

Since there are three arbitrary constants in the said form (i.e. A, B and C) in this
case we will arbitrarily pick (1, 1), (2, 3) and
(3, 6). Substituting each of these points to
the aforementioned form and solving for A,
B and C by elimination, we have
A(1)2 + B(1) + C = 1
or
A+B+C=1
(Equation 1)
A(2)2 + B(2) + C = 3
or
4A + 2B + C = 3 (Equation 2)
A(3)2 + B(3) + C = 6
or
9A + 3B + C = 6 (Equation 3)
Taking equations 1 & 2
4A + 2B + C = 3
A + B + C = 1__
3A + B = 2
(Equation 4)
Taking equations 2 & 3
9A + 3B + C = 6
4A + 2B + C = 3
5A + B = 3
(Equation 5)
Taking equations 4 & 5
5A + B = 3
3A + B = 2
2A
=1
A=
Substituting A = in equation 4, we have
3A + B = 2
3() + B = 2
(/) + B = 2
B=
Substituting A = and B = to equation 1,
we have
A+B+C=1
++C=1
1+C=1
C=0

JUSTIFICATION
Veriication. Test if the formula holds for
n = 1,2.
A. If n = 1
+1
R= 2

B. If n = 2
+1
R= 2

R=1

R=3

R = 11+1
2

R = 22+1
2

Assumption. Assume that the formula is

true for n = k, i.e.
R = 1 + 2 + 3 + + (k 1) + k = ki=1 = i =
kk+1
2 , where k N.

Proof by Induction. Prove true for the next

integer n = k + 1. We will add 1 rectangle to a
pile of k congruent rectangles. Our goal is to
arrive at k+1 k+2 .

Ups and downs: series of negative integers

Jesus P. Pormento Jr.
Pavia National High School-Special Science Class

SITUATION

-1=-1
-1+-2+-1=-2+-2
-1+-2+-3+-2+-1=-3+-3+-3
-1+-2+-3+-4+-3+-2+-1=-4+-4+-4+-4
.
.
.
.
.
.
Investigate . . .

STATEMENT OF THE PROBLEM

This investigation sought to answer the
following question:
What is the formula in inding the sum
(dn) of the sequence of consecutive negative
integers described by
-1 + -2 + -3 + + -n + + -3 + -2 + -1?
CONJECTURE
Systematic Listing of Data by Using Table

Using the methods of differences

between each term in a sequence, the
general function of this pattern is a 2nd

The added rectangle in a pile is counted

as one. The added rectangle then could be
associated with k other rectangles, thus
giving us k+1 rectangles every time a new
rectangle in the pile is added. We need to
show that k k+2 + (k + 1) = k+1 k+2 .
2

21

Volume IV, Issue 1 | November 2012-September 2013

Conclusion. Since the proposition was

veriied true for n = 1,2 and was prove true
for n = k + 1, thus the formula holds true,
N./

This mathematical investigation is an edited

excerpt of the paper that was awarded 1st in the
2013 MTAP MI Seminar-Workshop.

degree polynomial.
Consider the general function of
quadratic equation
an + bn + c = d
We have points: (1, -1), (2,-4), and (3,-9)

Point: (1, -1)

an + bn + c = d
a(1) + b(1) + c = -1
a + b + c = -1
Point: (2, -4)
an + bn + c = d
a(2) + b(2) + c = -4
4a + 2b + c = -4
Point: (3, -9)
an + bn + c = d
a(3) + b(3) + c = -9
9a + 3b + c = -9

equation 1
equation 2
equation 3

Eliminate c:
Equation 2 minus equation 1
4a + 2b + c = -4
-(a + b + c =-1)
3a + b = -3
equation 4
Equation 3 minus equation 2
9a + 3b + c = -9
-(4a + 2b + c = -4)
5 a + b = -5
equation 5
Eliminate b and ind a:
Equation 5 minus Equation 4
5a + b = -5
-(3a + b =-3)
2a=-2
a=-1
solving for b:
3a + b = -3
3(-1) + b = -3
-3 + b = -3
-3 + 3 = b
b=0
solving for c:
a + b + c = -1
(-1) + (0) + c = -1
-1 + 1 = c
c = 1+1
c= 0
The values of its coeficients are
a = -1, b = 0, & c = 0.
Substitute a, b and c in the quadratic
equation: an + bn + c = dn
-n + 0 + 0 =dn
Hence, the formula is:
-n = dn

Conjecture
The sum (dn ) of the sequence deined
by -1 + -2 + -3 + + -n ++ -3 + -2 + -1
is n2, N.

JUSTIFICATION
Veriication. Verify that the statement is
true for = 1
-1= -(1)2 = -2

Assumption.
Assume
that
the
proposition is true for some positive
integers n = k
If n = k
-1+-2+-3+... +(-k+2)+(-k+1)+(-k) + (-k+1)+(-k+2)+ + -3 +-2 + -1 = -k2

Proof by Induction. Prove that the

proposition is true for n = k + 1.
Since
-1+-2+-3+... +(-k+1)+(-k) + (-k+1)+ + -3 +-2 + -1 = -k2
then,
-1+-2+-3+... +(-k+1) +(-k) +[-(k+1)] +(-k) + (-k+1)+ + -3 +-2 + -1
=-1+-2+-3+... +(-k+1) +(-k) + (-k+1)+ + -3 +-2 + -1 +[-(k+1)] +(-k)
by commutative property of addition.
By using the assumption and by
substitution, we obtain
-k2+[-(k+1)] +(-k)
Simplifying, we obtain
-k2 k 1 k = -k2 2k 1
= -(k2 + k +1 )
= - (k + 1)2
which is what we want.
Hence, the conjecture was proven to be
true. /

This mathematical investigation is an edited

excerpt of the entry to the National Science Fair
2013 (Division Level) in the Individual Category
(Cluster 2). The advisers are Ms. Julie Janagap and
Mrs. Marlyn Perocho.

In the Mathematical
Investigation full paper, the
following parts are included:
I. Introduction
II. Statement of the Problem
III. Conjecture
IV. Verifying Conjecture
V. Justication
VI. Summary
VII. Possible Extension

MATHEMATICAL INVESTIGATION

MATHEMATICAL INVESTIGATION

20

Volume IV, Issue 1 | November 2012-September 2013

sa pagtudlo sang ginagikanan sang pulong nga nagalatonlaton

M a t h e m a t i c s , kag ginagamit sang mga kabataan.
Ang mga nasambit sa hitaas, pila sa
mas
labing
maayo
nga mga pananglitan nga bisan sa pulong nga
b i n a g b i n a g o n Hiligaynon may problema mismo sa mga
Mario E. Baavo, M.S.
naton
anay nagagamit sini. Ang masubo sa tanan kay
ang mga gumontang sa likod sang amo ini ang ginagamit nga pulong sa pagtudlo
sang Mathematics. Yara sa Grade 2 subong
pulong nga Hiligaynon kag ang tul-id nga
ang akon anak nga masami nagapalibog
pagpanigbato, pagmitlang kag labaw sa kag indi makahangop sa iya mga lessons sa
UMPISA SANG SY 2012-2013 malapnagon
tanan ang paggamit sini. Pila lamang ang Mathematics nga pilit ginalubad sa pulong nga
nga ginpatuman sang DepEd ang K-12
mga masunod: Hunahuna-a bala, ang tul- Hiligaynon. Halimbawa sang pagsulondan:
Curriculum sa tuyo nga ang 12 ka tuig
id nga paggamit sang kataga nga sang kag Duagan sing asul, dalag, berde ukon pula ang
nga programa
napamatud-an
nga
sing. Ang sang kag sing walay katuladan. mga masunod." Duagan sang granate Sa
matagaan sang tul-id nga panahon ang
Ang ang sa kinaandan ginasundan sang pagmitlang sang mga numbers, isa (1), duha
isa ka bumolotho sa paghibalo sang
pangalan, pangkabilugan nga pangalan, (2), tatlo (3), apat (4), lima (5), anum (6), pito
labing sadsaran sang edukasyon. Dugang
tal-us pangalan, inapidan nga tagidsay kag (7), walo (8), siyam (9), pulo (10), maayo
pa diri, agud nga ang mga bumolotho
likga. Subong man ginagamit ang sang sa kon may igures madumduman nya pero
ukon mga titulado na ang pagakilalahon
pagpanugod sang halambalanon. Ang sing kasubong sang onse, dose, trese..., "Papa
sa luwas sang punsod (i. e., the Bologna
sa kinaandan kon ginasundan sang Tigsari mga ano ina sila?" Inosente nga pagpangutana
sang akon anak nga nagapadayon sa pagtuon
Process for the European Union and
ukon Ubay- Likga, kag ginagamit man kon ang
kay tungod kinahanglan nga mahibaloan.
the Washington Accord for the United
ginasundan sini pang-isip. Pananglit: Sang Makahalangusbo ini nga kamatuoran, mas a
States). Suno sa mga pagpanalawsaw, ang
nagdalugdog sang mabaskog, nagkulorog man lamang sang bata ang mga ini mabatian
Pilipinas na lamang ang katapusan
sa sulod sang panimalay ukon wala gid
nga pungsod sa Asya kag sa tatlo ka
" uno sa mga pagpanalawsaw mas mahapos kag madali gani nila ini mabatian. Ang modern
mga pungsod pangkalibutanon nga
sa subong nga panahon wala
may 10 year pre-university cycle.
nga makahangop ang bumolotho kon ginagamit ang MT family
na nagagamit
sang pulong nga
Ang duha amo ang Angola kag
Hiligaynon kondi siling sang isa ka
sa
pagtudlo.
Amo
ini
ang
isa
sa
mga
kabangdanan
Djibouti.
manogwaragwag sa telibesyon ini
nga mataas ang performance sang mga kabataan sang
Bisan pa sa malapnagon
ang ginatawag nila nga functional
nga problema nga gin-abaga sa
Japan, Korea kag Singapore sa ginhiwat nga Trends of Hiligaynon. Buot silingon indi na
pagpatuman sang K-12 Curriculum
siya Hiligaynon nga matuod kondi
kasubong sang kakulangan sang International Mathematics and Science Survey(TIMSS) mga banyaga nga tinaga nga pilit nga
ginalubad sa pulong nga Hiligaynon.
manunudlo, hulot klasehan kag iban
nga kon sa diin yara sa tabtaban permi ang
Ang impluwensiya sang teknolohiya...
pa, hugot ini nga ginbaton sang mga
tagpumalasakop sang Pilipinas."
kag siyensia... "Ang iya obligasyon amo
katawhan sa DepEd kag subong man
lamang ang pagseparar sang pundo.
sa pribado nga mga bulothoan agud
si Martha sing hinali. Pila bala sa aton ang (Ang iya katungdanan amo lamang ang
masabat ang mga pagpanghangkat sa patag
may ihibalo sini? Ano gid bala? Bisan ukon pagpain sang pundo.)" Kag madamu pa sang
sang edukasyon kag pasalig sang mga utok
biskan, pabalo ukon pahibalo, kinanlan kasubong nga aton mabatian. "Baby you want
sang amo nga curriculum.
ukon kinahanglan, tungod ukon bangod? to eat na ? Anak do you have your baon na
Sa K-12 Curriculum ang bumolotho
Tungod nagakahulogan 1.) Nakatambi- bigay ni Mommy?" "Wis naman me c ni Irmat
makatuon sang maayo sa rason nga
palad na 2.) Natuhoy sa. Samtang ang forget nalang." "Yesterday (Yes) so lispyok ka
magagamit ang bumolotho sang iya namatbangod nagakahulogan sang rason sa likod. nalang Day." "So, whats the problema mo?
an nga pulong [Mother Tongue (MT)], i.
Pananglit : Indi kana magpangaluyag kay You have your ive ( singko) or ten ( diyes)
e., Building Proiciency through Language
Rosa kay may tungod na siya. Bangod pesos na okey na ba? Ang masadya pa gid kon
ala texting ang ginagamit. "OK, c u me sa SM
(Mother
Tongue-Based
Multiligual
sang paglikom niya sa iyang tiayon, tungod
ct. @ 5:30."
Education). May yara nga dose (12) ka
sang ila negosyo gani nagbulagay sila. Ang
Kon amo sini ang sahi sang mga tinaga
MT nga pulong nga ginkilala sang DepEd
makahalam- ot pa gid sa tanan nakabati ka
nga masami mabatian kag namat-an nga
sa SY 2012-2013. Ang mga ini amo ang
na sini?. Ang iya rolyo (role) is to implement
pulong sang bata kutob sa pagpanamkon
Bahasa Sug, Meranao, Tagalog, Waray, Bikol,
the rules and regulations, mas maayo guro
tubtob sa iya amat-amat nga paghamtong,
Cebuano, Iloko, Chabacano, Pangasinense,
kon Ilonggohon. Ilonggohon? ( Ilonggo, tawo
mangin madinuagon ayhan ang pagtudlo
Kapampangan,
Maguindanaoan
kag
nga nagapuyo sa Iloilo, gani nga tawohon?
sang Mathematics sa pulong nga Hiligaynon?
Hiligaynon. Maluwas sa MT, ang English kag
Rolyo? Ano banig nga lulokoton? Functional
Tag- isa ukon tig-sa? Tig-isa lang ukon tigFilipino igatudlo man nga subjects umpisa
Hiligaynon kuno, buot hambalon ang Ingles
isa lamang? Kon diri ka sa dakbanwa sang
sa Grade 1.
nga tinaga hilway nga isalin sa Ilonggo a
Iloilo, husto ang lang. Apang kon ang bata
Sa mga nasambit nga MT isa ang
este Hiligaynon. Kon amo, ano ang mother
Karay-a (South, Central, North, Antique) ang
Hiligaynon sa mga pulong nga ginakabig nga
tongue (MT)? Hiligaynon gid bala ukon ang
ginagamit puwedi nga lang ukon lamang. Ang
Mother Tongue (MT) sang mga katawhan
una nga mabatian nga pulong sa sulod sang
tul-id nga paggamit sang lang kag lamang
sa Panay kag Negros Occidental. Gani nga
panimalay. Sa binag-o nga pagkabuhi subong,
ang may kinatuhay man. Ang problema pa
ginagamit ini sang mga manunudlo sa
madata na gid ang paggamit sang mga
gid kon ang bata nagbalhin sang bulothoan.
pagtudlo sang nagakalainlain nga subjects
bag-ohan nga mga pagkabutang, kasubong
Ano subong nga pulong ang iya namat-an
nga isa na sini ang Mathematics. Bag-o
sang computer (internet), radio, TV, mga
[MT] Paano si Manunudlo magtul-id tudlo
naton salaysayon ang problema nga
pamantalaan kag kon ano pa nga media nga
sa pulong nga Hiligaynon kay si Manunudlo
nagahigot sa paggamit sang sini nga pulong

Pagtudlo sang mathematics

sa namat- an nga pulong

23

Volume IV, Issue 1 | November 2012-September 2013

mismo may problema gani sa sini nga pulong.
Ayhan ang mga kasubong nga mga
scenario natalupangdan man sang aton
curriculum makers? Yara na available ang
mga modules kag teachers guide kon paano
magtudlo sang mga subjects sa pulong
nga Hiligaynon [MT] ilabi na gid sa patag
sang Mathematics. Busa, himayhimayon
sang mga manunodlo kon ano ang mga
kaungdan
agud nga matalunsay ang
pagtudlo sini sa mga hulot klasehan. Suno
sa mga pagpanalawsaw mas mahapos kag
madali nga makahangop ang bumolotho kon
ginagamit ang MT sa pagtudlo. Amo ini ang
isa sa mga kabangdanan nga mataas ang
performance sang mga kabataan sang Japan,
Korea kag Singapore sa ginhiwat nga Trends of
International Mathematics and Science Survey
(TIMSS) nga kon sa diin yara sa tabtaban

permi ang tagpumalasakop sang Pilipinas.

Apang ang aton MT nga Hiligaynon masiling
bala naton nga kasubong sang Mandarin sang
Singapore? Ang ila nga MT amo kag amo gid,
ang aton iya hybrid na. Masiling bala naton nga
amo ini dapat?
Nian mga butang nga ini nga dapat gid
naton hatagan sang pagtamod. Wala naman
kita sang mahimo pa kay isa na ka kasugoan ang
paggamit sang MT. Bilang katapo sang hublag
sang pagpalapnag sang edukasyon sa aton nga
pungsod ang pagsakdag sini sa kon ano man
nga pamaagi agud sa sina kita makabulig kag
makapasanyog sang aton dunang manggad
ang namat-an nga pulong [MT] amo lamang
ang nagakaigo nga tikang. Gani, bilang katapo
sang Sumakwelan Iloilo, Inc., katilingaban sang
mga manunolat kag mamalaybay sa puod kag
Dakbanwa sang Iloilo sa Pulong nga Hiligaynon,

Can mathematics be
appreciated?

Prof. Alexander J. Balsomo

WHILE I was waiting for my part during
a rehearsal for a theater play, I grabbed
the opportunity to scribble on my notes
in Probability Theory and worked on a
problem set. One of the actors looked at
what I was doing, full of equations with
double or triple integrations involved.
His comment made me laugh, "What a
beautiful drawing." In the same rehearsal
studio, I was reading a book entitled Real
Analysis by H.L. Royden during a break.
He came again to me and asked me a
question that made me laugh again, "Is
there a false analysis?"
In college, I entered UPV as a
history major (with a purpose to shift to

Tips... from page 16

we demand for academic faithfulness from

them, we must also consistently show them
how honesty is done in the way we deliver
our lessons, give evaluations, and deal with
moral issues and dilemmas. This way they
can catch the attitude from us and embrace
it more permanently.
Now, for other random points:
Parents can be our most effective
partners. If there are any problems with
students, let the parents know immediately.
If the teachers and the parents can work
this out well, then the students can be
helped more24/7 this time. The same
is true with our school authorities and inschool partners (principal, subject area
supervisors, guidance councilors, discipline
head, class adviser, co-teachers, etc.). Once
they are aware of the context, they can

Accountancy the
following year).
I had classmates
who confessed
they took history

because they wanted to avoid math. They

metaphorically described math as bleeding
to death. It is also seconded by my students
in College Algebra classes.
What is with mathematics that
makes it hard? Many educational theorists
mentioned that this might be due to the lack
of appreciation. How will one appreciate
it? Well, you can see how mathematics is
applied in daily life, from performing simple
calculations to using computer programs.
Still, it is hard for any ordinary person to
really connect the reality to an abstract
nuance.
With respect to so called "appreciation
of mathematics," it is futile or hypocritical to
say that high school algebra can be used in

always go out of their way and collaborate

with you to help the one that binds you all
your students.
We must judiciously craft appropriate
assignments, projects, or assessment tools to
help students discover things on their own.
Stretching them is a good thing, especially
if we encourage them and help build their
conidence. This is a generation often afraid
of being wrong. We must therefore embolden
them to ask the right questions, even if they
get it wrong sometimes. We must also teach
them how to welcome challenges and accept
criticisms like how a learned adult does it. In
the words of Socrates, the more one knows,
the more he knows less.
Its always better to over-prepare than
to under-prepare. Most students repay good
preparation with good participation. They
know if you are just teaching to teach or just
surviving the day. Hence, make sure that a

kita nagatinguha gid nga mapasanyog kag

maamligan ining aton namat-an nga pulong.
Bisan pa sa pagkamatuod lang nagsaligmato
ini sa pagpatuman sa pagtudlo sang
Mathematics, apang kita nagapanindugan
nga maayo ini nga lihok agud aton man
mapalatonlaton ang nasambit nga pulong kag
sa sina kita makilala nga kita nagikan sa duog
sang Kabisayaan Nakatungdan. May matahum
nga pulong, matam-is kag nagaragumo
kon mitlangon, ang pulong nga namat-an
Hiligaynon kon pagahingadlan./

Si G. Baavo katapo sang Sumakwelan Iloilo,

Inc. (katilingban sang mga manunolat kag
mamalaybay sa puod kag dakbanwa sang Iloilo sa
Pulong nga Hiligaynon) kag champion sa paindisindis sa patag sang Binalaybay (professional
category), Sentro ng Wika ng Pilipinas.

the real world. In the real sense, examples

which we read in books in the application
of algebra are very unreal (except for a few).
If one really has to appreciate mathematics,
one has to learn more about it. Algebra in
high school and college is just a scratch of
what mathematics is.
Mathematics can be beautiful and/or
can be useful. It can be plainly beautiful
but never useful. In fact, the greatest
mathematical problems in the world that
need solutions are abstract ideas that are
not useful in the real world (e. g., Fermat's
Last Theorem and Goldbach conjecture).
Mathematicians pursued answers to these
problems just for the passion of solving
them and not because they are very useful.
Some can be appreciated since they are
very useful. But, such appreciation would
require more mathematical background to
understand them. Mathematics teachers
should face this reality. /

lesson plan or at least a bullet plan for the

day is always ready to be delivered fresh and
furious in class. Visual aids and novel strategies
are proofs of good preparation. Just make sure
that they it in the standard competencies and
objectives of your curriculum.
Lastly, love your students. Long after they
have left our classroom, years after they have
forgotten the content of our course, they will
remember you. You are, whether you like it or
not, assuming a role in their lifes story. Will
you contribute a chapter or a footnote? Will
you allow yourself to be a major character or
will you play a supporting role? Your guess is
as good as mine. /

Dr. Lagon helps several neophytes in teaching as an

assistant principal in Ateno de Iloilo. Reactions and
comments may be sent to hermanlagon1@gmail.
com.

OPINION

OPINION

22

24
On the other hand, plans to hold
the Inter-Tertiary Quiz Competition,
headed by Prof. Lindley Kent Faina, is also
underway as it is set in the irst week of
December 2013. Expected to participate
are scores of math wizards from colleges
and universities all over Western Visayas.
For the past years, we have been holding
this during our convention; this year,
the contest will be done independently
not just in terms of personnel, but also
in terms of logistics. Also in the drawing
board is the holding of the Mr. Mario
Baavo-led Regional Math Camp this
February 2014, that will invite hundreds
of students and teachers to appreciate
math in an overnight, two-day, hands-on,
and highly-interactive affair. Here, it is
planned that an MI competition shall also
be held.
MTAP-IC, Inc. has also maximized the
power of the tri-media. This year, we have
released a number of press news releases,
features, and columns in the local and
national newspapers which cover the
different activities of the organization.
These highlighted our advocacies such as
the enhancement of math skills, exploring
non-traditional math approaches, and
tips in teaching and loving math. As MTAP
president, I was even interviewed by
GMA Iloilo and Bombo Radyo Iloilo to talk
about the situation of math education in
the country.
As part of our outreach drive, boxes
of books and school supplies (plus a book
shelf) from MTAP oficers and members
were also donated to the students of Sta.
Teresa Elementary School in Guimaras
last July 2013. The schools library was
just burned into ashes in an accident in
2012; thus, the donation drive.
MTAP oficers Prof. Glorial, Dr.
Harold Cartagena, Mr. Encio, and myself
also went to elementary schools in Iloilo
in coordination with adviser Dr. Kim
Arcea, math supervisor of DepEd Iloilo,
to supervise for free MTAP Saturday
math classes this September, 2013. The
team covered about 15 schools in both
the southern and the northern portions
of the province. It aimed to observe how
the teachers deliver the training to the
students and provide assistance if need
be in the process. To note, the modules
that they used are designed by the MTAPNational. Similar visitation will be done
this October 2013 for the MTAP Saturday
math classes for advanced students.
Meanwhile, streamlining initiatives
were also made within the organization.
Embracing the policy of accountability,

all regular and emergency meetings so far

were held in quorum and with clear agenda
laid on the table. The BOD members made
it a point to consistently follow the rules
of order starting and ending with a prayer,
and with its minutes of the previous session
always being read and adopted every start
of the meeting. And to minimize cost by half,
the board has been holding its meeting in
Iloilo Smart Alternative Tutorial Center of
Prof. Glorial, MTAP-IC Vice President.
Close link with the advisers (Dr. Arcea,
Mrs. Ligaya Montelijao, Dr. Belarga, and Mrs.
Hermosisima Altillero), DepEd heads (Dir.
John Arnold Siena, Mr. Adonis Mosquera, Dr.
Novelyn Vilches, and Mr. Jerry Oquendo), and
CHEd oficials (Dr. Virginia Resurreccion, Dr.
Mercedes Monsale, and Jean Chan) is also
one key in the continued effort to solidify
the organization. The constant coordination
with and visits to their ofices have mustered
better participation in our recent activities.
Also, they have constantly given the
organization (even through text and email)
information and recommendation on how
to do things to maximize eficiency. Similar
nature of coordination is also maintained
between the chapter and the oficials of the
MTAP-National (Sr. Iluminada Coronel and
Dr. Rechilda Villame).
For
a
non-stock,
non-proit
organization, such as MTAP, to network
with local counterparts is a must. Hence,
our chapter has already initiated contacts to
other MTAP organizations in the region that
will hopefully lead to the future institution
of a Regional Federation of MTAP Chapters.
So far, we have already forged initial talks
with seven counterpart divisions. We plan
to initiate the organization of an Interim
Group for the proposed Federation in a
lunch meeting with chapter representatives
from at least 14 divisions this September
28, 2013 at Iloilo Grand Hotel. In the same
vein, we have also managed to coordinate
and partner with institutions such as the
Department of Education (regional and
division ofices), Commission on Higher
Education, Mathematics Trainers' Guild
(MTG) of the Philippines, Division of Iloilo
Secondary Math Teachers Association,
WDSA (DOST Scholars Association in WVSU
COE GS), printing and publishing houses,
among others. Many MTAP-IC, Inc. oficers
were already asked to act as judge, keynote
or resource speaker, trainer, facilitator,
supervisor, or observer to the different
ofices mentioned.
In the inancial management side, the
organization is currently on a tight budget
(please refer to inancial report). As such,
we have decided to centralize our inances,
including sponsorships and donations.
This also called for asking our cost centers

like seminars, contests, and The Ininity

publication to look for ways to inance itself
without necessarily affecting the general
fund. Although this is still a work in progress,
we hope that this can minimize costs and
will eventually put the organization to a
more liquid condition. Corollary to this is the
reprinting of our oficial receipts consistent
with the demands of the Bureau of Internal
Revenue.
All these necessitate the general review
and reconiguration of our inancial health
and procedures under the leadership of our
treasurer, Prof. Rhodora Cartagena. As such,
we have already improved and updated our
membership list, past accounts, sponsorship
list, and bookkeeping processes. With the
improved system in place and with the
help of every member, we hope we can
increase our working general fund by three
folds this year consistent with the policy of
transparency and accountability.
It is worthy to note that, with the help of
sponsors, we have also printed free oficial
chapter notepads for oficers and members
of the organization. Likewise, we have
initiated pockets of fundraising projects
such as the selling of our old Ininity tabloids,
reproduction of mathematical investigation
materials, printing of synthetic-laminated
Membership ID cards, and embossing of
MTAP t-shirts.
Aside from the usual, the organization
has also made bold steps in the name of
math education, research, and investigation.
One of which is the remodeling of our The
Ininity publication from a tabloid into
a magazine form, making it more userfriendly without losing its substance. With
the highly-competent editor-in-chief Dr.
Rosemarie Galvez at the helm, the annual
ISSN-registered paper shall continue to print
out informative column and feature articles,
math investigations, and news reports
related to mathematics as a discipline and
as a means for nation building.
One work in progress is the MTAP
Research Journal which is currently on its
inalization stage. Here, with Dr. Wilhelm
Cerbo as editor-in-chief, a good number
of math-related research papers shall be
published for members to use or to learn
from.
Lastly, the most anticipated of all is
the release of our K-12 compliant MTAP
Reviewer for Grades 6 and 7 late this year in
partnership with C and E Bookstore. With Dr.
Galvez as the head of the Editorial Board, this
booklet type manuscript is now on its inal
editing and lay-outing stage covering the
following core areas: number and number
sense, geometry, measurement, statistics
and probability, patterns and algebra. Most
of the authors of this reviewer come from

25

Volume IV, Issue 1 | November 2012-September 2013

MTAP BOD batches 2012 and 2013. The
concept was cooked in 2011, but the bulk
of work was done from December 2012 up
to May 2013 through series of meetings of
the authors, leading to the inalization of the
text this June 2013. It mainly covers items
in multiple-choice format and answers with
tailor-made explanations. God willing, the
book will be up in the bookstores before the
end of the year and versions for other grade
levels may be milled by next years set of
oficers and authors.
These we have humbly done and more
we wish to respectfully achieve late this
year. As our simple contribution to nation
building, we wish to inspire others to do
better and to be better; be active in the fold
and set the organization on ire.
In essence, my presidency simply
continued what have been done in the past
with some tweaking and streamlining here
and there. Be that as it may, none has been
and will be easy to do if not for the priceless
sacriices and sometimes thankless
contribution of our oficers, partners,
advisers, and members. Hats off to all of you!
But most of all, whatever the things
we have accomplished, the things we have
planned to carry out, or the things we have
failed to do, we offer everything to Him
The Uncaused Cause, the Unmoved Mover,
the Necessary Being. He is the reason why
MTAP was, is, and will be. Amen./

Are you a high-performing

Ilonggo math teacher?
Dr. Harold F. Cartagena

STANDARDS THAT deine the effectiveness of mathematics teachers is existent in

the international arena. But, are these standards applicable in the local setting?
Factors such as culture, norms, and beliefs could make generalities irrelevant and
futile.
The model from my study entitled Factors Associated with the Attributes and
Practices of High-Performing Secondary Math Teachers attempts to answer this
intriguing issue in the context of Ilonggo teachers. Shown here is the result of the study,
the Cartagena's Model Theory of Factors Associated with the Attributes and Practices of
High-Performing Filipino Secondary Mathematics Teachers. /

Book Review

21st century mathematics

A vision for a better future
Prof. Maria Cecelia P. Amparado

WITH
THE
implementation of
K-12
Curriculum,
authors have been
in the rat race to
provide schools with
K-12 compliant books.
Phoenix
Publishing
House
with
Ma.
Luisa Villano, Lowela
Mupas,
Roberto
Degolacion,
and Dr. Simon Chua as authors, published
a textbook in mathematics intended for
Grade 7. The sequence of the book follows
the spiral curriculum as indicated in the
K-12 program.
Every topic is provided with follow
up practice for oral or written practice
especially for slow learners. The Maintain
your skills part is intended for individual
written practice. Brain Strainers and Brain
Provokers that require a skill in problem
solving can accommodate both the slow
learners as well as the talented ones. The

book also includes the "Math Focus" at the

start of every lesson. This is where main
deinitions and results are highlighted by
boxes. The "Think and Try" part are activities
provided that extends the mathematics skills
in activities that are fun to do. As a summative
assessment, every chapter is provided with
a chapter test, mostly in multiple-choice

format. The Spare a Moment to Know More,"

composed of problems presented at the end
of the chapter, gives contest-bound students
the opportunity to succeed in mathematics
contest.
With the features discussed above,
this book is indeed timely with the current
curricular change. /

FEATURE

Streamlining ... from page 1

Volume IV, Issue 1 | November 2012-September 2013

26

DR. HERMAN M. LAGON,

President, is a graduate
of Bachelor of Science in
Civil Engineering (Most
Outstanding
Engineering
Graduate) in University
of Iloilo. He inished his Master of Arts in
Science Education in the same school in 2008
and his PhD in Science Education Major in
Mathematics in 2011 at West Visayas State
University (WVSU) under the Department of
Science and Technology-Science Education
Institute (DOST-SEI) scholarship. He also
inished the degree Master in Business
Administration at University of Iloilo-Phinma
in 2013. Dr. Lagon acted as the president of
WDSA, an association of graduate DOST-SEI
scholars in WVSU, from 2008-2010. He was
awarded Most Outstanding Teacher in Region
6 (PRISSAAP) and in the Philippines (PERAA),
and Most Outstanding School Paper Adviser in
the region (PIA) and in the country (DepEd).
He worked as a professional journalist
for six years before teaching physics (and
supervising the science program) in Ateneo
de Iloilo High School (2000-March 2013). He
is presently the consultant of MTAP-ICs The
Ininity, the president of MTAP-IC, and the
assistant principal of Ateneo de Iloilo.
PROF.
JONATHAN
C.
GLORIAL, Vice President,
graduated from WVSU with
the degree of Bachelor
in Elementary Education
specializing in Mathematics.
He earned his masters degree in Education
(M.A Ed. Mathematics) and has completed
his academic requirements as Doctor of
Philosophy in Mathematics Education from
the same institution. He is now a member of
its faculty serving the following functions:
Associate Professor II College of Education
(Center of Excellence in Teacher Education);
Faculty Dept. of Mathematics Education;
Core Faculty CRISMed; Adviser- University
Student Council (USC) 2010 to present; and
a Critic Teacher (Math Subjects) in the WVSU
Division of Elementary Teacher Training
(DETT). Prof. Glorial is also the center
coordinator of the Mathematics Trainers
Guild, Philippines (MTG) in the city and
province of Iloilo and has served as the coach
and deputy team leader of the Philippine
delegate in several math contests all over
Asia (Thailand, China, Indonesia, Singapore,
Korea, India, and Hong Kong). He also serves

Volume IV, Issue 1 | November 2012-September 2013

as a quality trainer and professional lecturer,

not only for MTG Philippines, but for MTAPTL, MTAP-Iloilo (Vice President), MATHTED,
and PAFTE Region VI as well. He has received
numerous awards including Outstanding
Alumnus of INHS for the 21st Century in
2012, University Research Awardee 2010,
Metrobank Outstanding Teacher National
Finalist in 2009 and is one of the authors of
the book, Soaring 21st Century and Integrative
Mathematics which was published by Phoenix
and SIBS Publishing House, respectively. He
has also been invited to speak on several
seminars with regards to the topic Improving
the Mathematics Proiciency of Teachers and
Students.
DR.
ROSEMARIE
G.
GALVEZ, Secretary, inished
the degrees Bachelor of
Secondary
EducationMathematics (Magna Cum
Laude & Rotary Awardee for
Outstanding Graduate) and PhD in Science
Education-Mathematics at WVSU (Best
Dissertation Awardee). She clinched the top
seven spot in the Professional Licensure
Examination for Teachers in 2004 and earned
her Master of Education-Mathematics at the
University of the Philippines Visayas (UPV)
in 2006. She has taught at Sun Yat Sen High
School, Ateneo de Iloilo, and University of San
Agustin (USA). She served as the President of
WDSA, an association of DOST-SEI scholars
from November 2011 to June 2012. Currently,
she is an instructor at WVSU.
MR. KIM JAY C. ENCIO,
Assistant Secretary, inished
the degree Bachelor of
Secondary Education major
in Mathematics at West
Visayas State University
(WVSU) in 2010 as summa cum laude. He
clinched the third spot in the September
2010 Licensure Examination for Teachers.
He is currently teaching at PAREF Westbridge
School, Inc. and he is inishing the degree
Master of Arts in Education-Mathematics at
WVSU.
PROF.
RHODORA
A.
CARTAGENA, Treasurer, is
the chairperson of Math and
Physics Department of the
University of San Agustin
and the in-charge of the USA
Statistical Analysis Center. She is a graduate of
Bachelor of Science in Applied Mathematics

and Master of Education (Mathematics) in

UPV. She is currently inishing the degree PhD
in Science Education (Mathematics) at WVSU.
PROF. MARIA CECELIA
P. AMPARADO, Assistant
Treasurer, inished the
degree
Bachelor
of
Secondary
EducationMathematics at WVSU
as cum laude. She inished her Master in
Education-Mathematics at UPV. She taught
mathematics as a college professor at De Paul
College. Currently, she is connected with the
University of San Agustin and she is pursuing
the degree PhD in Science EducationMathematics at the WVSU as a DOST-SEI
scholar.
PROF. LINDLEY KENT M.
FAINA, Auditor, holds the
rank of Assistant Professor
VII and serves as the
Chairperson of Mathematics
in the Division of Physical
Sciences and Mathematics of the College
of Arts and Sciences in UPV. He inished
the degree Bachelor of Science in Applied
Mathematics at UPV in 2000 as magna cum
laude and the degree Master of Science
in Mathematics at UP-Diliman in 2006.
His thesis on Single-Strain HIV Model has
been presented in local and international
conferences. He has also written research
papers that have been published in refereed
journals. He served as
the Regional
Coordinator of Philippine Mathematical
Olympiad in 2007 to 2010.
PROF.
ALEXANDER
J.
BALSOMO,
Board
Member, is a graduate
of Bachelor of Science
in Applied Mathematics
and Master of Education
(Mathematics) in UPV. His research
engagements are in the ield of Group
Theory and application of mathematics in
Fisheries. He once served as a chairperson of
the Mathematics Department of WVSU. His
interests, other than mathematics, include
music composition, choral conducting and
backpacking. Currently, he is a Straight PhD
Math student in Ateneo de Manila University
as a CHED-FDP II scholar. He also served
as an oficer of the Mathematical Society
of the Philippines Region 6 and Philippine
Statistical Association 6.
MR. MARIO E. BAAVO,
Board Member, is a Model
Public
School
Teacher
of Iloilo City (HALIGI
Foundation). He is presently
a Master Teacher II at Iloilo
City National High School. A poet, orator,
singer, international research presenter, and a

Volume IV, Issue 1 | November 2012-September 2013

multi-awarded teacher, Baavo is a graduate
of Bachelor of Science in Mathematics at
Western Institute of Technology and Master
of Science in Mathematics Education at
Ateneo de Manila University as DepEd/NEAP
scholar. He is inishing his PhD in Science
Education Major in Mathematics course at
WVSU. Baavo is a national Metrobank inalist
for the Search for Outstanding Teacher, and
a Pres. Gloria Macapagal Arroyo Awardee
in Campus Journalism. He was awarded as
the Outstanding Teacher of Western Visayas
in Secondary Mathematics. He is the math
coordinator of Gintong Aral, the President
of the Math Association of Division of Iloilo
City, Chairman of ICNHS Teachers and
Employees Cooperative, Chairman of ICNHS
Senior Council, and Regional Trainer in Math
Investigation and Information Technology in
Secondary Mathematics & the author of the
Handbook in Mathematics Investigation.
DR.
HAROLD
F.
CARTAGENA,
Board
Member, is the department
head and faculty member
of Iloilo City Community
College. He graduated
cum laude in Bachelor of Secondary
Education (Math) at WVSU under the SM
Foundation and COEXSTEP Scholarships.
He is a graduate of Master of Education
(Mathematics) at UPV and PhD in Science
Education (Mathematics) in WVSU under
the DOST-SEI Scholarship.
DR. ALEX B. FACINABAO,
Board Member, is the Dean
of the College of Education
of the University of San
Agustin since 2009. He was
chairperson of Mathematics
and Physics Department in the same
school prior to his present assignment.
He is a graduate of BS in Math Education
at Western Institute of Technology (WIT)
and Master of Arts in Education at WVSU.
Amid his Doctor of Education degree for
Curriculum, Instruction, and Evaluation
taken in WVSU, he now inishes his PhD
in Science Education -Mathematics course
in the same university. He is currently the
Business Manager of Association of Deans
of Teacher Education Institutions, Inc.
Region VI.
ENGR.
RAMON
S.
JARDINIANO,
Board
Member, is a graduate of
WIT with distinction and
became a faculty member
of the Department of
Mathematics of the same school since 1982.
A mechanical engineer by profession, he
also completed his academic requirements
for Master of Engineering in WIT in 2011.

MR. STEPHEN RAYMUND

T. JINON, Board Member, is
a graduate of BSEd major
in Mathematics at WVSU
in 2010.
He graduated
magna cum laude and was a
recipient of the Best Student Teacher Award.
Presently, he is connected with PAREF
Westbridge School, Inc. He is also inishing
the degree Master of Arts in EducationMathematics at WVSU.
MR. MATTHEW T. LASAP,
Board Member, graduated
summa cum laude at WVSU
with the course Bachelor
in Secondary EducationMathematics as a DOST-SEI
scholar on March 2009. He has been a faculty
member of Ateneo de Iloilo since 2009. He
has served as the Subject Area Coordinator
for Mathematics of the same school since June
2013. He is currently inishing the degree
Master of Education-Mathematics at UPV.
MR. ROBERTO G. SAGGE,
JR.,* Board Member, is a
teacher III of Iloilo National
High School in Iloilo City. He
inished the degree Bachelor
of Secondary Education at
WVSU in 2005 as cum laude. He obtained the
degree MA Ed major in Mathematics at WVSU
in 2010. Currently, he is pursuing the degree
PhD in Science Education-Mathematics as
a DOST-SEI scholar also at WVSU. He is a
trainer, lecturer, and research presenter in
seminar-workshop and research conference
held in local, division, regional, national, and
international levels.
DR. KIM S. ARCEA,
Adviser, is the Education
Supervisor (MathematicsElementary) and Research
Coordinator
of
the
Department of Education
in the Divison of Iloilo. He is a graduate
of Bachelor of Elementary Education with
specialization in Mathematics, Master
of Education in Administration and
Supervision, and Doctor of Education major
in Educational Management at WVSU.
Dr. Arcea has attended a JICA Training
Program for Young Leaders (Education
Category) in Kochi, Japan in 2007, the
Regional Training of the TIP Teams on
the Mass Implementation of the Teachers
Induction Program, and the DedpEd-MTAP

27
National Conference on Mathematics
Education in 2008. He is a writer of the
Division and Regional Mathematics Module,
and the Module on Local Taxation in the
Division of Iloilo, and has constructed the
Division Test Reviewer in Mathematics for
the National Achievement Test.
MRS.
LIGAYA
H.
MONTELIJAO,
Adviser,
is an Education Program
Supervisor in Mathematics
in the Division of Iloilo City.
She inished the degree
BSED major in Math at WVSU.
MS.
HERMOSISIMA
L.
ALTILLERO, Adviser, is
an Education Supervisor
(Mathematics-Secondary) of
the Department of Education,
Division of Iloilo. Prior to her
appointment as Education Supervisor, she
once served as Principal of Major Manuel
A. Aaron Memorial National High School in
Janiuay and Head Teacher of Cadagmayan
National High School in Sta. Barbara.
DR. ALONA M. BELARGA,
Adviser, holds the academic
rank of Professor 2 at West
Visayas State University
College of Education. She
inished the degree of
Bachelor of Science in Education major
in Mathematics at WVSU in 1984 (Magna
Cum Laude) as WVSU-Teacher Education
scholar. In 1995, she inished her Master
of Arts in Teaching Mathematics at UPDiliman as Academic Excellence Awardee
under DOST-SEI scholarship. In AY 19961998, she was awarded a MONBUSHO
scholarship by the government of Japan
for her post graduate in teacher training
program at Ehime University, Matsuyama
City, Ehime, Japan. She earned her Doctor
of Philosophy in Mathematics Education
in 2001 at UP-Diliman as DOST-SEI scholar
and as Academic Excellence Awardee. Dr.
Belarga served as Associate Dean of the
WVSU College of Education Graduate School
in June 2007-June 2010, and as chair of
the Mathematics Education Division from
June 2010 to October 2011. She serves
as the Director of Instruction and Quality
Assurance of WVSU from November 2011 to
the present. /
*Mr. Sagge has resigned from his position and Prof. Merle
Junsay of Central Philippine University will take over
effective September 27, 2013.

FROM THE EDITORS DESK

28

Volume IV, Issue 1 | November 2012-September 2013

Dr. Rosemarie G. Galvez

Editor-in-Chief

CHANGE IS INEVITABLE.

I cut my hair short. I transferred school. I became an editor-in-chief. The Ininity

is now a magazine.

But, some changes just have to be delayed. I still remain a

secretary. My family name is still the same, at least for now.
Some things just have to be the same. We remain committed
to MTAP-IC. I still use the chalkboard. Of course, my given name is
still the same.
The same scenario is happening in the MTAP-IC community.
Change is inevitable. Dr. Elnora V. Loriega, dean of the College
of Education at West Visayas State University, will retire this
year. Despite being a non-math teacher, she has been a mentor
of several members and oficers of the MTAP-IC. Her passion in
qualitative research and social studies has inluenced many of us
mathematically-oriented learners to love a non-statistical inquiry.
I, for one, have been under her wing as I took the road less taken, a
research on mathematics in art. Working with her means pushing
myself beyond the limits, bringing out my best, thinking outside
the box, and pursuing excellence. Her intellect, charm, skill to
hand-hold, and sense of humor made us focus on our abilities and
face our limitations. I have learned from her that that an adviser/
teacher is not a sage on the stage, but a guide on the side. Dr.
Loriega, MTAP-IC salutes you for your signiicant contribution in
the ield of education!
But, some changes just have to be delayed but just equally

Keep in touch with MTAP-IC online

As of September 20, 2013, MTAP-Iloilo Chapter, the facebook group
of MTAP-IC, has 461 members. Invite more mathematics teachers in the
region and join us in our online conversation that ranges from problemsolving to seminars.
Angela Perol-Villaruz posted:
MTAP members please help me solve these:
1. A chemist has one solution that is 18% acid and a second solution
that is 45% acid. If she wishes to obtain 12 liters of a 36% acid
solution, how many liters of each should be combined to obtain the
mixture?
2. What quantities of 60% and 80% silver must be mixed together to
give 20 grams that has 75% silver?
3. A part of Php50 000 was invested at 16% simple interest and the
remaining part at 14%. The yearly interest from the 16% investment
was Php800 more than that from the 14% investment. How much
was invested in each rate?

Junmar Gerazol Gentuya replied

Acid Solution Problem
Answer: 4 L of 18% and 8 L of 45%
....................................................
Silver Problem
Answer: 5 g of 60% Ag and 15 g of 80% Ag
....................................................
Investment Problem Answer:
P23,360 to invest in 16% and P26,640 to invest in 14%

Do you have alternative solutions and helpful explanations? Join us online by

being a member of the MTAP-Iloilo Chapter facebook group,
being connected through yahoomail at mtapiloilo@yahoo.com, and
leaving comments in the MTAP-IC blog at www.mtapiloilo.blogspot.com.

inevitable. Dr. Herman Lagon, the courageous president who took

the reins from the hands of Dr. Alona Belarga has led MTAP-IC in
this challenging year of change of leadership. With him, we took
pride in selless service, ind reasons in our sacriices, and enjoy
the small things in being part of the MTAP-IC BOD.
Some things just have to be the same. Dr. Belarga still
remains a signiicant part of MTAP-IC. The prime mover behind
the organization became our adviser after she vacated her
presidency. Her guidance and advice have been truly helpful.
Her patience, love, and kindness have been instrumental in the
empowerment of the new breed of MTAP-IC leaders.
As we try to adapt with the rapid changes in our society
and organization, we try to do away with practices that do not
work and hold on to those that still work. Sometimes, change is
overwhelming that we just simply jump in the bandwagon and
forget to embrace the timeless classics (or at least learn from
them). Well, classics are the ones that survive the test of time. So,
decide wisely whether you decide to change, delay change, or be
the same.
I hope that with 28 substantial pages, this years issue of
The Ininity has given you some bits and pieces in being wise in
adapting with change./