This is an article that shows the impact that the Olympiads of Mathematics is having in Paraguay at High School Level, and the way it encourages teenagers to learn Math, and to like Math.

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The impactof Mathematical OlympiadinParaguayan Schools
GabrielaGómezPasquali
Key words
Impact, Mathematical, Olympiad, Paraguay, schools, education.
Abstract
This article aims to present an analysis of the impact of Mathematical Olympiad organized by
OMAPA1in Paraguayan schools. First, the article develops the context of education in Paraguay.
Then,itpresentsboththe MultidisciplinaryOrganization of SupportforTeachersandStudents and
the Program “Paraguay Solves,” which was implemented in between 2011 and 2014. Finally, it
analyzes the results of the evaluation of the impact made by the Institute Development,
Participation and Citizenship on the educational institutions that participated in the National
Mathematical Olympiad.
Contextof Education in Paraguay
The Educación EscolarBásica (EEB) or ElementaryBasicSchool inParaguayincludesninelevelsand
it ismandatory. While in the last 25 years the educational reform improved the coverage of EEB,
and the access andpermanence of studentsinthe educationalsystem, suchreformdid not assure
the trainingof competitive andupdatedteachers.Thus,itcontributedtoworsening the quality of
learning and the development of academic and pedagogical skills.
The quality of the Institutes of Teacher Education (Institutos de Formación Docente - IFD) is low
(World Bank, 2003). Most trainers lack the academic knowledge in the area of concentration, as
well as the properpedagogical skills;the IFD’s libraries are obsolete and underused. Information
Technologies have not been introduced in most institutions. The evaluation of IFD’s in the year
2001 revealed that the future teachers from 73 IFD’s only passed Language and Guaraní, and had
their lowest performance in Mathematics. Additionally, 103 IFD students had a performance
below 45% in Mathematics.
There are several national and international studies that reflect the alarming situation facing
Paraguay in education. According to the Global Competitiveness Index of the World Economic
Forum(2013-2014), the qualityof the Paraguayaneducational systemisranked138 ina rankingof
148 evaluated countries. When it comes to quality of teaching in science and mathematics,
Paraguayis ranked142; and whenthe countryis evaluated onavailabilityof trainingandresearch,
it is ranked 134.
In the Second Regional Comparative and Explanatory Study (SERCE) of 2006, that included 16
countries, Paraguay was one of five countries that scored below average scores in all subjects
tested.Inrelationtothe performance inmathematics,more than half of 3rd grade students were
classifiedinthe lowestlevels.So did 27% of 6th grade students, who could not solve problems in
multiplication,division, andaddition infractionsor did not recognize common geometric shapes.
The EvaluationSystemof Educational Process(SNEPE) made in2010, showedlow levelsof student
performance. In mathematics, more than 50% of students were at the lowest levels of
1
Multidisciplinary Organization of support for teachers and students.

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performance.An IDB study (2012) on mathematics and science education revealed that teachers
had gaps in content. From a total of 100 science classrooms in Paraguay, teachers made at least
one mistake in 59 of them. In more than 90% of the cases, students and teachers did not notice
the mistake. When a student tried to correct the mistake, the teachers usually insisted on their
claim and lost the opportunity to explore the topic with students. It is also of great concern the
observation that in 48% of cases in which students made mistakes, teachers omitted to correct
them or failed to guide students in discovering their mistakes.
Institutional PresentationofOMAPA
OMAPA’s main objective is to assist with improving the quality of education across the country
and therebycontribute toraisingthe qualityof life of men and women of Paraguay, promoted by
improvingtheirintellectual,respect, anddignity,organicandintegral development.Ourstrategies
are to create awarenessandinfluence the academic and business community, promoting quality
ineducation,participationinthe trainingof teachersandstudents,and tofosterthe development
of policies, and the legal and academic tools that promote positive transformation of the basic
training model for young people.
OMAPA was foundedin1989 by a groupof teachers,studentsand otherpeople witha passion for
mathematics. In 2002, OMAPA was formalized as a non-profit organization named Paraguayan
Mathematical Olympiad. Beginning in 2007, its initials came to mean Multidisciplinary
Organization of Support for Teachers and Students (Organización Multidisciplinaria de Apoyo a
Profesores y Alumnos) with the purpose of expanding its scope of action.
OMAPA’s mission is to contribute with the improvement of the quality of education throughout
the country. Thus, OMAPA aims to help elevating the quality of life of men and women by
enhancing their intellectual training, respect, dignity and integral development.
OMAPA’s vision is of a country with young leaders capable of making decisions based on logical
reasoning,analysisof contextsandconsiderationof variables.OMAPA believesinthe efficient use
of science, and particularly mathematics, as tools for developing these capabilities, because of
theirplayfulness,theirinterdisciplinary format and permeability in all areas of human activity. In
addition,OMAPA works to provide equal opportunities for its programs to low-income students
across the country,includingstudentsandteachersfrompublicschools in the process of training,
financing and organization of local competitions.
Since 1989, OMAPA has been promoted the organization of Nationals Mathematical Olympiads.
The work thought the first ten years has been focused in the promotion, development and
attention of Young Talents (“Jóvenes Talentos”), as well as most of the Math Olympiads of Latin
America. In around the year 1999 a reorientation of the Olympiads has been made for the
inclusionof mostof the studentsandteachers,notonlythe talentedones. Thatisto say,it passed
froma perspectivecenteredinthe selectionof the best students toanapproach orientedtowards
improving the academic proposal in the classroom and therefore a massive participation of the
students.
This long-haul of OMAPA, has generated a unique experience of the Mathematic Olympiad in
Paraguay,differentfrom the way itis inothercountries of the world. It is considered, first of all, a
strategyfor the improvementof the Mathematical Education with a direct impact in the teaching

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in the classroom and the performance of all the students. Such strategy is translated into a
program: Paraguay Solves, with three axes, which are: 1) Improvement of the Mathematical
Education through the National Olympiad of Mathematics, 2) Training of Teachers in the
Methodology of Problem Solving, and 3) Scientific Initiation for Young Talents.
Program Paraguay Solves
Paraguay Solves has been in execution from the year 2011 with the institutional support of the
Ministry of Education and Culture (MEC) and the financial support of Binational ITAIPÚ. In the
year 2011, this program has been declared of scientific and educational interest by the National
Council of Science andTechnology(CONACYT) andof national interest by the Honorable House of
Representatives.
The three axes of Paraguay Solves, articulated strategically, aim at the improvement of the
Mathematical Education in Paraguay.
Axis 1: The National Olympiad of Mathematics
The National Olympiadof Mathematics isthe strategywithwhichOMAPA is makingtheirway into
the Paraguayan classrooms, with an innovating proposal of a high quality in mathematics that
encourages the logical thought and reasoning, to apply math as a tool of problem solving of all
type. Teachers and students workingtogetherduringthe whole school year, with the purpose of
training for this competition, that consists of five rounds and includes all the school period. By
doingthis, the intention is to improve the performance rates in Mathematics of all the students.
The school with an interest to participate may just register for the contest and immediately, the
teachers of such Institution attendaworkshopof IntroductiontoMathematical ProblemSolvingin
the classroom. Starting from the third month of the beginning of the school year, the first and
second round of the competition is carried out, in which 100% of the students coming from the
newlyregistered school mayparticipate. These school rounds consist in tests of multiple-choice
givenbythe teachers inthe participatinginstitutions. Whatitis achieved isthat,duringhalf of the
first school year, 100 % of the students are participating. Up to 20 students for each one of the
three levels representingone school maypass tothe thirdround,since the ideais to have as much
participation, enthusiasm and celebration around Mathematics as possible.
In the third round, of a zonal type, a school may host students from up to 10 neighboring
educational institutions that participate in the Olympiad with their teams of students
accompaniedby theirteachers. A juryof teachersis selected, and they are the ones who receive
the tests sent by OMAPA in closed envelopes, and then they distribute, control, correct and
elaborate the result sheets. It is an activity out of the ordinary with respect to the daily
educational practice,since itisatime for communicationbetween colleagues,for team work, and
for strengthening a network of teachers working in the same field.
The fourth round, called departmental has the characteristics of a more competitive type, is
carried out in 10 out of the 17 Departments of Paraguay. In the same day the test is carried out,
followingimmediately by the correction of the tests and then the prize awarding of the winners.
An event of prize awarding and recognition of academic excellence is carried out, with the
participation of the families of the students and the local authorities.

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The fifth round consists in a three-day camping, where the best 450 students of the country may
participate. All the young people who arrive at this instance are invited to participate in the
Program of AttentiontoYoungTalents. This final round and the above mentioned program have
similar characteristics to the programs and competitions in all Latin American countries.
In the year2013, more than 2,500 schools participatedinthe National Olympiad of Mathematics,
out of approximately 6,000 that the country has, from 6th
Grade to the last year of High School.
The participation of students from public and subsidized schools was of 300,277 students out of
the 499,071 studentinthe whole country atthose levels. As far as students from private schools,
there were 10,480 participants from 60 institutions, out of a total of little more than 64,000
students of 500 existing private schools in the country.
Axis 2: Educational Training in the Methodology of Problem Solving.
Once a school is registered in the National Olympiad of Mathematics, the teachers from that
school attend a workshop of "Methodology of Problem Solving." This methodology has a strong
impactin the educational-learningprocess,itis aboutto change the educational practice to make
math exercises repetitive, and to stimulate and to give educational didactic resources to the
teachers sothat they may developwiththe studentschallenging unusual problems that may help
them to develop a logical reasoning and a mathematical thought. The teachers are taught to use
the Mathematical Olympiadsasamotivational strategyand itis explained to them that this is the
true purpose of this national activity: to achieve that all the kids learn to solve complex math
problems.
In thisworkshop,the teachers receive the Manual forTeachers elaborated by OMAPA every year,
with a collection of problems classified for the different levels of education and the items
contained in the curricula, -established by the Ministry of Education and Culture-, that can be
worked during the school year. They are challenging problems designed especially according to
the culture and the Paraguayan context. One of the most valuable instruments that the Program
Paraguay Solvesofferstothe Paraguayan educational community is to achieve the incorporation
of problem solving in the classroom.
Within the framework of the Program Paraguay Solves, in the year 2013, a number of 3,334
teachers from all over the country participated in the workshops of Introduction to the
Methodology of Problem Solving. The number of participants has been growing progressively
during the years of execution of the Program Paraguay Solves, through which 5,159 teachers
received training in Methodology of Problem solving, from the year 2011 to the year 2013.
Axis 3: Scientific Initiation for Young Talents
The most significantcontributionof OMAPA tothe evolution of Mathematics in Paraguay is given
through the Program of "Scientific Initiation, with Emphasis in Mathematics, for Young Talents,"
carriedout at the beginningsof the school year.Throughthisprogram, outstandingstudents from
the National Olympiads of Mathematics are invited to participate in intensive Math courses to
continue cultivatingtheirabilities in the Centers of Attention for Young Talents. In these Centers
are carriedout IntensiveSummerWorkshopsandAnnual Courses, onSaturdays during the school

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year. It is developed Theory of Numbers, Algebra, Geometry and Combinations. It has 5 annual
levels.
In addition,the participantsof this program are those that can be registered to participate in the
classification to represent the country in International Olympiads such as the South Cone, River
plate, Ibero-American and International Olympiads.
This program, thanks to the financial support given by ITAIPÚ BINACIONAL, also increased
significantlyitscoverage fromapproximately40participants inthe beginnings, almost all of them
comingfrom the capital city area, in the beginnings, to more than 500 students from 13 of the 17
Departments and the capital of the country in between the years 2011 and 2013 have already
passed through the workshops for Young Talents. About 20 graduates of this program are
currently enrolled in undergraduate studies and graduate studies related to mathematics in
prestigiousuniversitiesof the UnitedStates(suchasthe MIT, Columbia,StanfordandCornell), and
Spain, Italy, Brazil, Argentina, India and in other foreign countries. Almost all of them are under
scholarships that obtained thanks to their academic merits and, mainly, to their outstanding
performance at the International Olympiads.
Evaluation of Impact of the Mathematics Olympiads
The Evaluationof Impact, carried out in between October 2012 and June 2014, was developed by
the Institute of Development1
, and in charge of Coordination was Rodolfo Elías2
and under the
advice of Daniel Bogoya3
.
The general purpose of the study has been to evaluate through quantitative and qualitative
methods, the effects and scope produced in public and private schools that have a minimum of
three years of experience in the Mathematics Olympiads, as well as the conditions that favor
obtaining better results.
Quantitative evaluationof the Impact ofthe Mathematic Olympiads
The quantitative evaluation was aimed at considering the influence of the National Mathematic
Olympiads in the average performance of students of sixth and ninth grade from the participant
schools, through the achievement that the students showed in tests of abilities in solving
mathematical problems. For that, it was compared the level of achievement in the abilities of
problemsolvingof the students frominstitutions with three or more years of participation in the
Math Olympiadswiththe resultsobtainedbystudentswho belong to institutions that have been
recently participating in the Math Olympiad.
The construction of the sample was carried out considering the universe of educational
institutionsthatparticipate inthe ChildrenandTeenage MathematicOlympiad. The same one is a
randomstratifiedsample,originatedfromtwo frameworksof samples of educational institutions
that participate in the Mathematic Olympiads from 2009 to 2013, in all the territory of Paraguay.
1www.desarrollo.edu.py
2B.A. in Psychology at theCatholicUniversity“Nuestra Señora de la Asunción, Magisterin SocialApplied Psychology,Universityof
Guelph, Ontario,Canada. Coordinatorand Researcher in thefield ofEducation at theInstituteofDevelopment.
3ChemicalEngineer andMagisterin System Engineering. General Directorofthe Colombian Institute for the Development ofHigher
Education(ICFES) andmember ofTechnicalCoordinationofLLECE. Professorofthe Universidad Nacional deColombia.Consultant in
evaluation of thequality ofeducation and factors related toacademic achievement.

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For the elaborationof cognitivetests,ithasbeen takenquestionsfree fromthe international tests
TIMSSA4
(Trends in International Mathematics and Science Study) and PISA5
(Program for
International Student Assessment), besides questions of tests of OMAPA and the Project of
Evaluation of Basic Competences of Bogotá. In total, for both tests, it has been selected and
elaborated 120 items: 60 in the Sixth Grade, and 60 in the Ninth Grade.
It was carriedoutan analysisof statistical validity with the model of Rasch4
of the Item Response
Theory(IRT) witha parameter,the one of the difficulty,intwoconsecutive stages: the first one of
pre-calibrationand the second one of calibration The scores of thistheorycannotbe construed in
termsof numberof questionscorrectly answered,butof the probabilityof the students to answer
correctly to questions of different degrees of difficulty. The same as in the case of the Classical
TestTheory(CTT),the averagesof IRT are usedmainlytoestablish acomparisonsand to value the
learninglevel of the students evaluated. Inthe case of the IRT the averagesdonot vary between0
and 100, as the percentagesof correctanswers(orbetween0and the maximum score of the test)
but that the point of reference shall be the media of the population evaluated, that usually is
located in the 500 points by a matter of convenience in the communication of the data (Ravela
2008).
Each studentanswered twoblocksof items,with30problems altogether. 3,765 students of Sixth
Grade from 105 educational institutions and 3,388 students of Ninth Grade from 108 educational
institutions participated in the evaluation. In addition to the cognitive tests there were taken
questionnaires of context to students, teachers and school principals, in order to value certain
related factors or social-educational aspects that influenced in the results obtained.
Main resultsof the Quantitative Evaluation
The general analysis of the results, grouped per years of participation in the Mathematic
Olympiadsforthe SixthandNinth Grades, indicates that the schools that have participated more
years (three or more years) have a higher performance in mathematics as much as in Sixth as in
Ninth Grade in comparison with those who have participated less years (one or two years).
4 http://timssandpirls.bc.edu/timss2011/international-released-items.html
5 http://www.oecd.org/pisa/pisaproducts/Take%20the%20test%20e%20book.pdf
6 Relevant informationabout documents of the modelof Raschandacademic events on their use, are available in the
site of the Institute for Objective Measurements, Inc.:http:/www.rasch.org
7Bogoya, D. (2008). Technical Report of the admissiontest. Case Study:Test ofthe first semester of 2008. Colombia,
UniversidadNacionalde Colombia.
http://sites.google.com/a/unal.edu.co/danielbogoya/3-documentos-de-trabajo

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Chart 3: Chart of average performance of studentspergroups(yearsof participationinthe
MathematicOlympiads) andsectors(PublicandPrivate) for6th
Grade and 9th
Grade.
The teachers are the main allies of the students with respect to the preparation for the
competitions, as we can see in the following chart.
Chart 7: Who help you training for the Mathematic Olympiads? 6th
Grade/9th
Grade
School Particular Classmates Family Books and Other
Teacher Teacher Tests from
OMAPA

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In the followinggraphwe can see how OMAPA developstheir inclusive strategy in the first round
of the Math Olympiads, in which all the students of the institution are summoned.
Chart 9: To whom are applied the First Round of the Mathematic Olympiads in your Institution?
-To all the students -Only to volunteers -To selected students
6th Grade / 9th Grade
In general,the opinionof the studentsof SixthandNinthGrade about the Mathematic Olympiads
are very similar.They have shown ahighdegree of satisfaction regardingtheirparticipation,as we
can appreciate in the following chart.
Chart 5: How do you feel with the participation of your school in the Mathematic Olympiads?
-Very satisfied -Satisfied -Unsatisfied -No opinion
6th Grade / 9th Grade

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Qualitative Evaluation of the Impact of the Mathematic Olympiads
The qualitative evaluation had the purpose of analyzing the perceptions of the different
educational playersonthe MathematicOlympiads inParaguay, makinganemphasisinthe process
of change generated at a personal and institutional level starting from the participation in the
Mathematic Olympiads.
The study wasbasedon semi-structuredinterviews and focal groups with 178 people, and among
them are: the students, teachers, school principals, fathers, mothers, former participants and
membersof OMAPA. These educational players belong to the different political Departments of
the country where OMAPA works. It was also taken the opinion and experience of former
participants whowere atthat time inside andoutside the country(byelectronicmail),of members
of the team of OMAPA at a central level, including their directors. It was used this approach
because it was considered appropriate in order to complement the quantitative information, as
well asto collectthe life experiencesof the participants, and to extract information starting from
its subjectivity, processing it by means of an interpretative analysis.
18 educational institutions were selected according to the following criteria: a) years of
participation in the Mathematic Olympiads, b) by context: urban or rural, and c) type of
educational management: public or private. The institutions are located in seven political
Departments of the country: Alto Parana, Caaguazú, Guairá, Boquerón, Paraguarí, Pedro Juan
Caballero, Central and the Capital City.
For the analysisof the interviews, the followingdimensionswereused.a) Pedagogical aspects; b)
educational Inclusion; c) Expectations, attitudes, perceptions, concept of education; d)
Organizationof the Project,and; e) Resultsof the process. In eachsectionthe perspective of the
different players were analyzed, including some segments of the interviews as an example.
Main results from the Qualitative Evaluation
In the pedagogical dimension it is possible to emphasize that the problems and exercises of
OMAPA awaken the interest and the motivation of the students, who find it challenging, useful
and amused,changingthe predominantvisionthat they hadaboutmathematics. The organization
of the time and preparation for the Mathematic Olympiads varies very much, depending on the
institution,havinggreateradvantage the students from institutions that accompany the training.
As much the books as the Web site of OMAPA Web serve as support for the different players,
usingsome more than others. Eventhough there is a degree of transference of the methodology
of the MathematicOlympiads tothe Math classrooms,itstill prevailsatraditional educationof the
mathematicsinthe classroom, outside the activities established for the Mathematic Olympiads.
Regardingthe dimensionof educational inclusion, there is little to say about the participation of
students with special needs. With respect to the gender of the students, teachers, and school
principals most of them have a traditional vision of the roles, prevailing the boys in the
MathematicOlympiads, afactthat, accordingto the people interviewed, is due to the preference
of girls in other areas of interest bound to the roles socially assumed as feminine.

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With respect to the expectations, attitudes, perceptions and concept of education, the
conceptionsthat they hadon mathematicsare related to the thinking, reasoning, interpretation,
payingattention,the logic,and the creativity. The differentplayers have shown positive attitudes
on the Mathematic Olympiads, the expectations are very wide, focused in being beneficial to
highereducation, which facilitates the admission and to study for obtaining a university degree,
and in addition to the learning that facilitates the mathematical approach of OMAPA and the
participation in the Mathematic Olympiads can extend to other aspects of life.
As far as the organization of the Mathematic Olympiads in the institutions, differences in the
appropriationof the project in the institution are identified, since some educational players are
more involved inthe processthanothers. Insome schoolstheyorganize themselves and become
self-managedinordertofacilitate the participationof theirstudents,nevertheless, in other cases
the students demand more support and information about the Mathematic Olympiads. The
training of teachers made by OMAPA are required and considered of great support in order to
improve the education of teachers,anditisnoticedthe need toreachmore teachers, since not all
of them are participating. They realized the difficulties of mobility and participation in the
Mathematic Olympiads of schools from rural area.
Finally,the achievementsresultingfrom the participationinthe MathematicOlympiads are many.
At a personal level,the studentsimprove very much their school performance in mathematics as
well as inothersubjects, andthey alsodeveloptheirability to pay attention, their reasoning, and
theircreativity. Ata social-emotional level,theygain more confidence in themselves, they make
newfriendsandtheylearntoface the challengesof life. At a professional level, it generates new
opportunities, anditmake aninfluence intheirprofessionalselection, it facilitates the admission
into the university and their study at that educational stage. At an institutional level, the
achievements are fewer, since the teachers do not change their pedagogical practices. At a more
general level, it has been managed to increase the interest from the institutions.