A Proposal from ICSU ROLAC to Educational Authorities in the

Transcription

A PROPOSAL FROM ICSU ROLAC
TO EDUC ATIONAL
AUTHORITIES IN THE REGION
MATHEMATICS EDUC ATION:
A REALITY TO BE TRANSFORMED
IN LATIN AMERIC A AND THE C ARIBBEAN
Lilliam Alvarez • Patricio Felmer
ICSU-ROLAC
SCIENCE FOR A BETTER LIFE
DEVELOPING REGIONAL SCIENTIFIC PROGRAMS
IN PRIORITY AREAS FOR LATIN AMERICA AND THE CARIBBEAN
INTRODUCCIÓN
1
This book was printed in collaboration with:
Publishing coordination: Camilo Garcia
Design: Juan Carlos Burgoa
Copyright © 2015, Academia Mexicana de Ciencias
Calle Cipreses s/n, km 23.5 de la carretera federal Mexico – Cuernavaca,
San Andres Totoltepec, Tlalpan, C.P. 14400, México, D.F.
www.amc.unam.mx
ISBN: 978-607-8379-14-9
Total or partial reproduction of this publication for commercial purposes
is prohibited.
Printed in Mexico by Offset Rebosan
CONTENTS
FOREWORD
5
INTRODUCTION
7
A PROPOSAL FROM ICSU-ROLAC TO EDUCATIONAL
AUTHORITIES IN THE REGION 9
I. INTRODUCTION
13
II. WHY MATHEMATICS? 15
19
III. REGIONAL CONTEXT
IV. GIRLS AND BOYS LEARNING MATHEMATICS
V. KEY REGIONAL ACTIONS
27
VI. STRATEGIC PROPOSALS FOR ICSU-ROLAC
VII. IN CONCLUSION
53
VIII. BIBLIOGRAPHIC REFERENCES
ACKNOWLEDGEMENTS
57
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55
49
FOREWORD
Within the framework of its mandate, UNESCO promotes education as a fundamental human right
and leads the international educational agenda, playing a political and technical role to bridge the gaps
preventing its fulfillment. In this context, UNESCO contributes knowledge, reliable empirical evidence
and technical assistance to all its Member States.
The fulfillment of the Right to Education is an ongoing process that requires continuous monitoring at all levels. Among the essential tools for this task are learning assessments, which help to determine
the curricular effectiveness and scope of education systems.
To this end, the UNESCO Regional Education Office for Latin America and the Caribbean (OREALC/UNESCO Santiago) is hosting the Latin American Laboratory for Assessment of the Quality of Edu-
cation (LLECE), a network of national assessment units across 16 countries. The LLECE has undertaken
comparative and explanatory learning assessments since 1997.
The assessments carried out by UNESCO Santiago provide solid evidence of progress in assessed
learning, for making decisions in the classroom, at school or in public policy. Through these measurements, we are able to determine the factors that explain success or falling behind, for example, those
variables that impact on learning.
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On December 4, 2014, UNESCO delivered the first results for the TERCE (Third Regional Comparative and Explanatory Study), which focused on comparing the results of the TERCE with those of
the previous study, the SERCE, in the same series.
The results of both studies show that performance at elementary school level (third and sixth
grades) in language, mathematics and sciences improved between 2006 and 2013. The average learning
achievement score improved across all the grades and areas assessed. However, while these developments are encouraging, the results also reveal certain challenges in basic learning acquisition and gender
differences, particularly in mathematics. Both studies show significant differences at sixth grade in favor
of boys in most countries.
UNESCO welcomes the work of the Regional Office of the ICSU for Latin American and the Ca-
ribbean in its efforts to strengthen mathematics education. This publication provides evidence of good
practice in the training of students and teachers in the discipline, coinciding with the primary objective
of UNESCO in the area of assessment: reliable information for decision making in educational policy and
practice that contributes to improving the quality of education in the region.
Jorge Sequeira
Director
OREALC/UNESCO Santiago de Chile
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MATHEMATICS EDUC ATION: A REALITY TO BE TRANSFORMED IN LATIN AMERIC A AND THE C ARIBBEAN
INTRODUCTION
The Regional Office of the ICSU for Latin America and the Caribbean has visibly increased actions to
strengthen mathematics education as a priority area for the region, distinguishing and making it unique
among its peers in the world.
We now present a book that compiles, without being exhaustive, examples of good practice to
contribute to the better training of students and teachers in this important discipline, and in the hope
that it might also be enjoyable, a pleasurable diversion. In general terms, the book presents the experiences of several countries in undertaking novel activities outside school, beyond the primary and secondary school mathematics curriculum.
The idea has been to target decision makers, those who design public policy in the area of mathematics education, and, on the other hand, to offer teachers, professionals and mathematical scientists,
members of national societies as well as regional bodies, a series of actions to be undertaken that are
low cost but have a direct impact on the teaching-learning process in mathematics.
We publish this text in good faith to contribute to and promote a transformation in our current
regional reality, in which, in general, mathematics education is deficient, and because, as stated in the
ICSU vision, we seek to contribute to the transfer of excellence from scientific results to decision mak7
ers and thereby contribute to economic and social sustainable development and to the prosperity to
which our countries in Latin America and the Caribbean aspire.
We invite you to look over the following pages that offer a regional overview of what the community of teachers and scientists from several countries are achieving, and the importance of mathematics
for learning other sciences, development, technological advancement and competitiveness.
Dr. Manuel Limonta
Director ICSU-ROLAC, 2015. 8
A PROPOSAL
FROM ICSU ROLAC
TO EDUCATIONAL
AUTHORITIES IN THE REGION
MATHEMATICS EDUCATION: A REALITY
TO BE TRANSFORMED IN LATIN AMERICA AND THE CARIBBEAN
The ICSU Regional Office for Latin American and the Caribbean is of the belief that mathematics is
a fundamental tool for the development of our countries, the basis of all scientific and technological
disciplines, and that it also constitutes a necessary cultural component of full citizen participation in a
democratic society. In fulfillment of its commitment, ICSU-ROLAC presents this book to the region with
the aim of contributing to the definition and orientation of national policies on mathematics education
and to university policies on the training of Mathematics teachers.
Problems in mathematics education are common to all countries in the region, a situation discussed in international documents(1),(2), and known to those who have had the opportunity to visit institutions and meet students and teachers linked to mathematics education at different levels. This shared
reality, in which the main difficulties are repeated from country to country, contrasts with the numerous
initiatives that successfully tackle parts of the problem in several countries in the region. We have been
able to hear about these initiatives through the organization of three international meetings sponsored
by ICSU-ROLAC, at which mathematicians working on the problem of mathematics education in the
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various countries have discussed in depth these initiatives, their genesis, the difficulties of implementation and the goals achieved.
Through this document, ICSU-ROLAC submits a proposal to the region through a series of recommendations, with the aim of contributing to the transformation of our reality. This proposal is based
on the identification of the main difficulties and on successful experiences in the region. ICSU-ROLAC
presents this text including a sample of reflections, analysis and initiatives for dissemination so that they
can be replicated, adapted and implemented as models elsewhere.
The proposal is aimed at national authorities, intermediate decision makers in government ministries and at government institutions, who are responsible for the definition of public policies that can
transform our education. It is also aimed at the deans and directors of universities, faculties, departments and institutes responsible for the training of mathematics teachers across different attainment
levels. National Mathematics Societies and Associations and Science Academies, the regional bodies for
the advancement of this discipline, must also be key players in promoting and encouraging improvements in school level mathematics.
In the following pages, ICSU-ROLAC invites participation in the design and proposal of new actions,
the strengthening of existing ones, the generalization of best practice and its dissemination throughout
the region, and, crucially, attracting the attention of governments, ministries, universities, academic institutions and scientific societies to raise awareness, allocate funds and collaborate in this key component
in development.
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A PROPOSAL FROM ICSU-ROLAC
TO EDUCATIONAL AUTHORITIES IN THE REGION
1. To establish, as part of public policy, a minimum level of mathematical skills among graduates of
initial teacher training courses who will be in charge of mathematics education at various levels.
2. To involve professional mathematicians in technical teams and in decision making on the national
curriculum, in the definition and implementation of continuing professional development strategies, in
the design of textbooks and in all instances in which school mathematics is involved.
3. To establish policies and programs with the aim of narrowing the gender gap in mathematics
learning.
4. To incorporate higher mathematical skills, such as problem solving, modeling and mathematical
reasoning in national school curricula and in initial and continuous teacher training.
5. To support the implementation of Olympiads and Championships or National Mathematics Competitions at the school level, involving all school and college students in the basic competition levels.
6. To promote the incorporation of information and communication technologies in mathematics
education at all levels, including teacher training.
7. To stimulate the national production and international exchange of materials to support school
and university level mathematics education, such as books, videos, computer software, applets, etc.
8. To promote the creation and exchange of knowledge in the area of school mathematics education
by establishing lines of support for bilateral and multilateral research projects and the creation of
networks of collaboration.
A PROPOSAL FROM ICSU ROLAC TO EDUC ATIONAL AUTHORITIES IN THE REGION
11
About ICSU: The creation of three Regional ICSU Offices between 2006 and 2007 located in Africa, Asia/Pacific and Latin America and the Caribbean marked a fundamental shift in the structure of
ICSU, with a twofold objective:
• To increase the participation of scientists and regional organizations from developing countries
in the programs and activities of the ICSU community;
• To ensure ICSU participates more actively in the strengthening of science by means of scientific
collaboration, in the context of regional priorities.
The Regional Office for Latin American and the Caribbean, which, since October 2010, has been
based at the Mexican Academy of Sciences with the support of CONACYT, has established, through its
Regional Committee, four priority areas in its Strategic Plan, namely:
1. Mathematics education;
2. Biodiversity: knowledge, conservation and use of biodiversity;
3. Risks and natural disasters: risk prevention and mitigation, with special attention to the necessary
research in social sciences;
4. Sustainable Energy: assessment of existing capacity in the region and the social impact of the use
and development of new energy resources.
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1. INTRODUCTION
In 1908, the great French Mathematician Henri Poincaré asked:
Why is it that there are so many spirits who refuse to understand mathematics? Isn’t there something
paradoxical about this? If mathematics is underpinned by simple principles and logical reasoning that
appeal to common sense, why do most people find it obscure? Might there be a contradiction between
the nature of the mathematical task and the methods used in its teaching?
Many mathematics educators would agree that the answer to this is yes, and that it is necessary
to work to change this situation.
This document seeks to draw attention to the importance of the discipline of mathematics, the
need to strengthen teacher training and the integration of professional mathematicians into the improvement of teaching across all levels. The document also submits a proposal to national authorities,
intermediate decision makers in government ministries and departments, deans and directors of universities, faculties, departments and institutes, to push forward improvements in school Mathematics
education, providing examples of projects and actions that have been successful in countries in the Latin
American and Caribbean region.
13
In 2008 ICSU-ROLAC commissioned a group of mathematicians in the region, the Scientific Planning Group, to undertake an assessment of the state of mathematics education and a proposal of actions based on good practice in the region. In the group’s report, titled Mathematics Education in Latin
America and the Caribbean: a reality to be transformed, published in 2010(1), the authors present a brief
overview of the state of mathematics education, show good practice developed in particular countries
and present a proposal of specific actions to lay the foundations of a broader program with a greater
regional impact. This report concludes firstly that there is a need to incorporate the entire community
of mathematicians and mathematics researchers and teachers into the task at hand, to maintain permanent monitoring of the state of the discipline in the region, to concentrate efforts on practicing teachers
to provide them with greater knowledge and tools for the teaching-learning process. The report calls
for urgent action to transform the current situation.
14
11. WHY
MATHEMATICS?(4,5)
It should be emphasized that of the three regional offices set up by ICSU, the Regional Office for Latin
America and the Caribbean is the only one that has included the improvement of mathematics education as a priority area to contribute to sustainable socio-economic development. This decision was
fostered by the President of the Regional Committee of ICSU at the time, the Mexican mathematician,
José Antonio de la Peña, with the support of the entire committee.
In today’s world, we know that development and international competition are achieved through
the education of citizens and investment in science and technology. But why mathematics? How can we
explain to decision makers, scientists and professionals in other areas the importance of this discipline
for development? Well, without mathematics, there would be no statistics, indices, indicators to measure
development or policy impact. Mathematics is necessary for the development of the common citizen,
for his or her growth, for understanding the multiple facets of the world we live in, from banking transactions and interpreting graphs to the simplest sum in a supermarket purchase.
But it is also the case that without mathematics, there would be no climate studies nor databases
and analysis for biodiversity, nor models to predict hurricane routes nor natural or social phenomena.
The great advances of the 20th century and the beginnings of the 21st century have been made possible due to the development of physics, whose language is mathematics. Furthermore, the method and
15
development of abstract thought, to which the learning of mathematics contributes, is fundamental to
the promotion and development of other sciences and technologies as well as to decision making at
different levels, from high level government decisions to the most straightforward decisions in the family
environment.
In the UNDP’s periodic reports on the “Technology Achievement of Nations”, an indicator called
Specialist Skills is used, which seeks to explain that in a country it is essential to have a critical mass of
citizens with expertise to guarantee technological dynamism. Both the creators and the users of new
technologies need these specialist skills. Current technology requires skills in order to master the constant flow of innovations. This capacity is part of the basic education required to develop cognitive skills
and aptitudes in science and mathematics.Two indicators are used to reflect the specialist skills required
to create and absorb innovations: the average number years of schooling and the Gross Enrollment
Ratio of tertiary students enrolled in science, mathematics and engineering. That is, if a country aspires
to “technology achievement” it must necessarily strengthen mathematics education.
Mathematics is also a crucial link in studies of perceptions, predictions, the optimization of processes and actions under the Future Earth program promoted by ICSU.
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111. REGIONAL CONTEXT
The fundamental problems we face and the unsatisfactory results obtained by children and young
people in our region have many causes, from poor teacher training to the lack of priority afforded to this
discipline in education policy. Another problem is the lack of integration between scientists researching
the different areas of mathematics and mathematics teachers.
Several studies have been undertaken in Latin America and the Caribbean to diagnose the current state of the teaching-learning process in Mathematics, to throw specific problems into relief and to
suggest solutions to correct policy and strategy.
The UNESCO Regional Office for Education OREAL/UNESCO based in Santiago, Chile, has been
undertaking studies on third and sixth grade primary school students’ performance in the areas
of language, mathematics and recently science. These studies are accompanied by an inquiry into
the factors explaining students’ progress or falling behind. In December 2014 the first results of
the TERCE(3) Third Regional Comparative and Explanatory Study were published, showing significant
progress in the learning achievements of the region’s students, meaning that performance at primary
school level improved between 2006 and 2013. In mathematics, the mean difference in scores in
the SERCE and TERCE is greater in third grade than in sixth grade. At a national level, none of the
17
countries assessed fell behind in third grade and only three countries fell behind in sixth grade. These
TERCE results will be complemented with the study of factors that explain them and that will be
crucial to understanding them, as borne out by the study conducted by UNESCO(3): the contribution
of these studies consists in showing countries’ progress as well as the factors behind their success or
falling behind. The key point is not “who is winning the race” but to understand the reasons behind
their success and to generate mutual learning between education systems. ICSU-ROLAC is interested
PAÍS
Promedio
SERCE
Promedio
TERCE
Diferencia
SERCE-TERCE
Argentina 505.36533.2627.9*
Brazil505.03539.5434.51*
Chile529.46582.4452.98*
Colombia499.35518.8819.53*
Costa Rica538.32557.5219.2*
Cuba 647.93
Ecuador473.07524.1751.1*
Guatemala457.1500.6943.59*
Honduras507.52
Mexico532.1549.2617.16*
Nicaragua472.78484.711.92*
Panama463.04494.1531.11*
Paraguay485.6487.84 2.24
Peru473.94532.7458.8*
Dom. Republic 395.65
448.03
52.38*
Uruguay538.53550.5512.02
Country average 501.15
520.75
31.03*
Nuevo León562.8561.08 -1.72
* Note All differences are presented with a confidence interval of 95%. The country average was
calculated considering that all countries have the same weight (using the senate weight). Honduras is
excluded from this calculation as it is not part of the sample of SERCE-TERCE comparability analysis,
since it did no participated in the second study.
Figure I. Difference between mean SERCE and TERCE Mathematics scores in third grade primary school
18
in disseminating good practice in the region, allowing the design of policies and programs to support
progress in school mathematics.
Figure 1. shows the comparative results of SERCE-TERCE in the third grade of elementary school,
in which important progress made by Chile, Guatemala and the Dominican Republic can be observed.
Countries not participating in SERCE or TERCE do not have this comparative data, as in the case of
Honduras and Cuba. Figure 2. shows the comparative regional results of SERCE-TERCE in sixth grade
PAÍS
Promedio
SERCE
Promedio
TERCE
Diferencia
SERCE-TERCE
Argentina 513.03530.2317.2*
Brazil499.42519.6320.21*
Chile517.31580.5163.2*
Colombia492.71514.6921.98*
Costa Rica
549.33
535.19
-14.14*
Cuba 637.47
Ecuador459.5513.1253.62*
Guatemala455.81487.9832.17*
Honduras479.79
Mexico541.61565.7724.16*
Nicaragua457.93462.31 4.38
Panama
451.6
461.48
9.88*
Paraguay
468.31
455.55
-12.76*
Peru489.98527.2537.27*
Dom. Republic
415.64
436.85
21.21*
Uruguay
578.42
566.57
-11.85
Country average 501.87
509.13
19.04*
Nuevo León553.95586.6832.73
* Note: All differences are presented with a confidence interval of 95%. The country average was
calculated considering that all countries have the same weight (using the senate weight). Honduras is
excluded from this calculation as it is not part of the sample of SERCE-TERCE comparability analysis,
since it did not participate in the second study.
Figure 2. Difference between mean SERCE and TERCE Mathematics scores in third grade primary school.
REGIONAL CONTEXT
19
primary school mathematics.The significant progress of Chile, Ecuador and Guatemala can be observed,
as well as the decline in some other countries.
The encouraging TERCE results should be viewed with caution in this first comparative series,
which does not yet allow us to speak of a trend, and because the starting point is very low as indicated
by worldwide studies.The implementation of more effective policies and the incorporation of new policies and programs that facilitate the strengthening and consolidation of this progress will be crucial in
the coming years.
On the other hand, there are reports of tests conducted every three years under the OECD countries’ program for assessing students––Program for International Student Assessment (PISA), ––that not
only examine what students know about mathematics but about reading and science and what they are
able to do with their knowledge. The difficulty is that only seven countries in the Latin American region
participate in these tests, since, among other reasons, you must pay to participate.
According to the published results for PISA 2012(6), corresponding to the fifth round of these
triennial tests, as shown in Figure 3, the best results in mathematical problem solving are shared among
several Asian countries, together with Canada, Australia and Finland. Germany and the United States
are to be found among the average results and countries in our region only occupy the last places
(Chile, Brazil and Colombia)––results from the other four are not included due to their extremely low
performance.
The case of Finland is significant as it is located among the top positions and is an object of study
every time the PISA report is published. Finland appears to have found a model of education that is
free from start to finish, in which private schools are practically non-existent, and in which teachers
and students alike are content. An article published by BBC World in 2013(8) explains that growth in
the quality of teaching in a country is not due to growth in the percentage of GDP devoted to educa20
Figure 3. Results in Mathematics, according to the 2012 PISA Report.
REGIONAL CONTEXT
21
tion. There are many factors that make education in Finland among the best in the world, but one of
the key issues is the quality of teachers. “The teaching faculty has an extraordinary level of training, with
a selection process so demanding it cannot be compared with any other in the world”, explains Xavier
Melgarejo, a Spanish educational psychologist who began studying the Finnish education system more
than a decade ago. “Only people with results above nine, nine and a half out of ten, get into the education
faculties. They’re very demanding. They are tested in reading, artistic sensitivity, proficiency with a musical
instrument, communication”... “As a result, universities only recruit 10% of the students that apply”.
In order teach in Finland, teachers need a master’s degree. The upside of this requirement is their
recognition, not necessarily in economic but in social terms. “Teachers are considered academic professionals and have the responsibility to develop their work, hence they are not excessively controlled.” “The
profession attracts a lot of people because being a teacher is an honor in Finland. It might even be the most
highly valued profession”. Another reason the Finnish system works is, for the most part, because school
is not just another cog in the education process. The other variables are family and society–in the Lutheran tradition–in which there is a high sense of responsibility and where people are valued “for their
education and not for their socioeconomic status”, Melgarejo says. To give us an idea, “in Lutheran culture
you save yourself by reading the Bible, you get close to God through the written word”. And although today
the churches are not very full, the value of learning to read and write is deeply embedded in Finnish
culture, Melgarejo adds.
But the Finns are also committed to education because they know that as a small country surrounded by powerful neighbors and without significant natural resources at their disposal, culture–its
domain in the field of knowledge–is what gives them the opportunity to compete in a global economy.
And at home, excellence in education translates “into a significant degree of social cohesion, which allows
the Finns to feel they are part of society, even in times of crisis”.
22
But what chance have Latin American and Caribbean countries–where public education is far
from a source of pride, where teachers’ salaries are not on a par with their responsibilities and where
there is no welfare state–of implementing an educational system like that of Finland? A useful lesson for
Latin America might be to learn how Finland deals with changes in the field of education. “Everything is
based on mutual trust and consensus building. When we propose major education reforms, for example, we
always involve teachers and students; it’s not about government orders that educators have to follow, these
are reforms we have prepared together.”
After this description, one might imagine a class in Finland to be an idyllic situation: a group of
obedient children listening intently to a lecture and interrupting from time to time with an intelligent
question. Nothing could be further from the truth. The children are as mischievous as anywhere in the
world. Also, sometimes, “when they measure education it’s a paradox because while the children are doing
very well, when you ask them if they like school they always say no. Perhaps this is due to the independent
spirit of our children”.
For Latin American and the Caribbean, while we may have scattered and occasional measurements of learning, this points toward a rather bleak conclusion: education is of low quality. Proficiency in
the written language and mathematical reasoning are a basic requirement for learning and a minimum
objective at primary school level; however, in a significant sample of countries, only 50% of children leaving school are able to understand a text and perform basic numerical calculations (UNDP, 1997(6)). This
means that at the gates of a global society based on knowledge, half–or more–of Latin Americans and
Caribbeans are functionally illiterate.
International comparisons widely disadvantage our region, despite the fact that for several years
experts have produced reports and recommendations to promote what has been called a quality basic
education. These reports have emphasized that learning depends on various factors, many of which can
REGIONAL CONTEXT
23
be controlled from within the education system itself, such as: (a) Motivated, well-trained teachers; (b)
Materials and support that facilitate and enrich the process; (c) A more regular, extensive and intense school
day, and (d) An effective school: that is to say, creative and independent, where inputs and processes are
deliberately subordinated to learning.
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1V. GIRLS AND BOYS
LEARNING MATHEMATICS
The PISA report(7) notes that regarding achievements in mathematical problem solving, there are no
significant differences as a global average between girls and boys; in some tests males outperform females–the countries where you see boys ahead are Colombia, Shanghai in China and Brazil–yet on the
other hand, in countries such as the United Arab Emirates, Bulgaria and Finland, girls outperform boys.
Once again in the gender-based approach to mathematics education, there are various cultural factors–
hierarchical organization, traditions–that tend to keep girls away from “the world of numbers”, from the
“rational world”, and orient them toward careers with a social profile, vocations in the service of others.
Fortunately, in Latin America and the Caribbean this situation has gradually changed in recent decades, due to the considerable efforts of the National Mathematics Societies and campaigns aimed at promoting enjoyment of the discipline and attracting girls to become teachers, lecturers and researchers in
the mathematical sciences.The fact that the scientific community, by consensus in the region, includes these issues on the agenda of the ICSU-ROLAC, and that in education policy and the promotion of science
a perspective on gender is explicit, shows progress and an awareness of the importance of these issues.
Encouraging girls and young women to pursue the dream of being teachers or researchers in this
discipline is a way of incorporating that 50% of human talent to increase the necessary critical mass,
precisely in order to influence the reality we seek to transform.
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V. KEY REGIONAL ACTIONS
In this section, we present some regional experiences that show interesting progress in the development of school mathematics at different levels, and involve the work and leadership of professional mathematicians. The experiences described have been chosen because of the depth of their
success and the novelty they bring with them, although it is not the purpose of this document to
make a complete list of notable experiences. Its purpose is to disseminate examples that show that
the proposals to education authorities in the region made at the beginning of this book are viable and
that they illustrate effective actions. It is wor th pointing out, however, that while the progress we
present points in the right direction, it alone will not address the problem in its entirety, and great
challenges are still ahead.
The number of professional mathematicians who have become involved in educational tasks in
mathematics has grown, incorporating actions from many different actors, including scientific societies,
National Science Academies and regional organizations. This community of professional mathematicians
works in several areas, which is why university professors, researchers, specialists working in institutions
and companies have become increasingly involved in various tasks. Moreover, in some countries, they
have taken steps to influence and recommend actions at various levels of government ministries and
Departments of Education, in the heterogeneous context of the region..
27
Strengthening this tendency to involve professional mathematicians in education was one of the
objectives proposed at the ICSU-ROLAC members’ meeting, in conjunction with representatives from
Mexico and Brazil, which took place at the Institute of Pure and Applied Mathematics in Rio de Janeiro
in 2013. Six objectives for the Mathematics Education Program in the region were defined there:
1. Strengthen links between professional mathematicians and teachers in schools;
2. Develop workable data for the assessment of student achievements and analysis of how
the region progresses;
3. Define a set of minimum standards that the region’s elementary and secondary school
teachers must achieve;
4. Promote the use of information and communications technologies and make them more
accessible to teachers and students;
5. Define strategies to simultaneously improve literacy in language and mathematics;
6. Continue to involve mathematicians in faculties where specialists in mathematics education are trained, helping to convey the most relevant aspects of mathematics education to
schoolteachers.
ICSU-ROLAC: The experiences of mathematicians in school mathematics
and Central American meetings on the teaching and learning of mathematics.
As has been mentioned, for years the growing involvement of mathematicians in mathematics education has been observed, specifically in school mathematics. Seeking to disseminate the experiences of
mathematicians in the region and to encourage collaboration between them, ICSU-ROLAC decided to
28
convene a meeting in Santiago in January 2012 entitled “Mathematicians in School Mathematics Education: in search of an impact on our educational reality”.
In local news media, the meeting was reviewed in an article called, “Latin American Mathematicians
Pose Challenges to Improve Education in the Discipline”, stating amongst other things that, “The first Mathematicians in School Mathematics Education Congress, from January 11 to 13 in Santiago, concluded successfully. A meeting that brought together a select group of mathematicians, representatives of Latin America
and the Caribbean who conduct research in mathematics, but who also share an interest in and concern for
education, many of them being managers of different initiatives launched in their countries with the aim of
improving education in the discipline”.
How could public policy in the training of teachers be effectively influenced ? This was the question that marked the discussion and final goal of the meeting, which took place thanks to the support of
ICSU-ROLAC, the Mathematical Modeling Center (CMM), the Center for Advanced Education Research
(CIAE), and the Chilean Academy of Sciences. For Patricio Felmer, one of the organizers, the goal of
this meeting was to share experiences and achieve a synergy that would enable them to look ahead.
“Mathematicians have a responsibility in all that is mathematics education and expressing that responsibility
isn’t easy. The ultimate objective is the students, the boys and girls who are learning mathematics in schools.
They are our guiding light”, he said.
The conclusions of the meeting in Santiago were summarized in the following four lines of development that guide the work of ICSU-ROLAC. These lines of development represent actions to be
undertaken:
• Conduct massive Olympiads. Mathematics Olympiads are restricted to students who have
already shown special ability in mathematics. These Olympiads appear not to have a significant
KEY REGIONAL ACTIONS
29
impact on mathematics education. Brazil has excellent experience in conducting highly successful
Olympiads involving the majority of students from public schools from sixth to twelfth grade and
teachers, family members and young people who are not in school which have proved to have a
positive social impact.
• Initial training for teachers. A common problem in Latin American and the Caribbean is
the poor training of mathematics teachers. ICSU-ROLAC and regional networks of scientists and
educators may be able to influence national policy in the initial training of teachers. Chile and some
Central American countries such as Costa Rica have already implemented initiatives to solve this
problem.
• Continuous teacher development. Following a governmental decision, the Brazilian
Mathematical Society coordinates a National Master’s Degree in Mathematics Program designed for mathematics teachers. It now has close to 3,000 par ticipants and 400 teachers have
already graduated. This Master’s Program improves the quality of secondary school teachers;
this continuous improvement experience has yet to be extended to primary school teacher
training. A long-term project to improve mathematics education must include similar initiatives to these.
• Create a stock of teaching materials. The Brazilian Mathematics Society and the National
Autonomous University of Mexico have digital libraries and provide links to teaching resources.
With the idea of continuing these efforts and the discussion, the second version of these meetings
was held at the Convention Center at BIRS, Banff International Research Station for Mathematical Innovation and Discovery, in Canada in January 2014. Members of the organizing committee of this meeting
included the North American mathematicians Solomon Friedberg of Boston College and William Mc30
Callum of the University of Arizona. This meeting included the active participation of mathematicians
from the United States and Canada who, together with mathematicians from the Latin American and
Caribbean region, discussed the progress of and obstacles to mathematics education and learning in
the region.
According to José Antonio de la Peña, “the idea is to arrive at conclusions that can be brought
together to promote lines of action that are political, so that governments will take action to prioritize
mathematics.”
ICSU-ROLAC has begun a second line of work with the aim of exchanging successful experiences
of mathematicians in school mathematics and disseminating progress. Thus the first meeting of this
nature was held on June 5 and 6 2014 in El Salvador, with the active collaboration of the Vice-Ministry
of Science and Technology; the National Science, Technology and Innovation Bureau and the Office of
Education for Science, Technology and Innovation. It also had the support of the recently appointed
Minister for Education of El Salvador, Carlos Canjura, a mathematician known for his contributions to
the work with talented young people in the Olympiad in El Salvador.
The El Salvador Workshop included representatives from eight countries in the region: Chile,
Cuba, Honduras, Mexico, Nicaragua, Panama, Paraguay and the Dominican Republic. The program for
the meeting was spread over two days, with the first devoted to a discussion of experiences in mathematics education in each participating country, particularly with the participation of representatives
from El Salvador.
These included decision makers from public and private higher education institutions directly
involved in teacher training activities in the field of Mathematics, as well as officials from units of the
Ministry of Education; Office of Education for Science, Technology and Innovation; the National Bureau
of Higher Education, Curriculum, Office of Gifted Education and Assessment Office among others. The
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second day was devoted to practicing teachers, nearly to 120 of whom gathered at the University of
El Salvador. In the morning they were invited to three presentations: the experience of the Olympiad in
Paraguay, the Science at Your School program in Mexico and Standards for Mathematics Teacher Preparation,
the Chilean experience. In the afternoon the teachers conducted problem-solving workshops with the
international speakers.
Among the main goals of this meeting, which ICSU-ROLAC plans to replicate in other countries,
is the promotion of inter-institutional relations both locally and internationally through interaction between researchers, professors, students and other professionals from different organizations and institutions, disseminating experiences, processes and the development of innovative educational projects,
showing the results of training in the area of basic mathematics in the country and the region, with the
aim of strengthening mathematics education in the region.
Brazil: the Brazilian Public Schools Mathematics Olympiad
and the PROFMAT Program.
The massive public movement generated in this country by the Brazilian Public Schools Mathematics
Olympiad, OBMEP, founded by President Luiz Inacio Lula da Silva, is impressive, and the project was
designed to promote the study of mathematics among students and teachers from all over Brazil. It is
promoted by the Ministries of Science and Technology and of Education, and is organized and developed by the National Institute of Pure and Applied Mathematics, IMPA, with the support and active
participation of the Brazilian Society of Mathematics, SBM.
It is one of the best examples of a combination of the government’s political will, a teachers’ union
and the mathematics professionals in a country. There have been nine editions of this Olympiad and
32
participation figures across the Brazilian nation are impressive, from remote and inaccessible schools
to prisons where young people are serving their sentences. It is not only about the participation of
millions of young people but the prestige they have acquired and the movement generated within Brazilian society, which has managed to involve the whole family alongside teachers and school principals.
They are raising awareness of the importance of mathematics for the future of young people and the
development of Brazil.
The OBMEP is specifically aimed at sixth to ninth grade students in public primary and secondary,
state and federal schools, who compete for prizes depending on their ranking in the tests. The movement also generates competition between teachers, schools and departments for their students to win
prizes. On the website of the Brazilian Olympiad http://www.obmep.org.br/ this is outlined (published
on 8/5/2014 and left in Portuguese):
Na premiação da 9ª Olimpíada Brasileira de Matemática das Escolas Públicas (OBMEP), nesta quartafeira no Rio de Janeiro, a presidenta Dilma Rousseff afirmou que sem professores valorizados, bem capacitados, bem formados e valorizados socialmente, não é possível ter educação de qualidade. Para isso, ela
lembrou a importância da lei sancionada em 2013 que destina 75% dos royalties do petróleo e 50% do
fundo social do Pré-Sal para obter os recursos necessários na área da educação. Saiba mais no Blog do
Planalto: http://goo.gl/bZAqxG
To give some idea of the magnitude and scope of this 9th edition, suffice it to say that there were
500 gold medalists, 900 silver medalists and 4,600 bronze medalists from sixth grade of elementary
school to ninth grade of secondary school. A total of 18.7 million students from more than 47 thousand schools participated, and 99,35% of institutions from all Brazilian municipalities were represented.
33
This effort, yielding concrete results and impacts, is one of the recommendations that ICSU-ROLAC
proposes to disseminate and replicate throughout our region.
In addition to the successful experiences of the Olympiad, training courses are offered at universities and mathematical research institutes to thousands of schoolteachers from all over Brazil. This is the
PROFMAT Program, which offers a Professional Master’s in Mathematics in the form of distance learning
courses conducted by a network of higher education institutions within the context of the Open University of Brazil, and coordinated by the Mathematical Society of Brazil.
This program targets in-service mathematics teachers, particularly at public schools, and seeks to
improve their preparation with an emphasis on full command of the mathematical content relevant to
their teaching performance. The program operates on a large scale, with the medium-term aim of having a substantial impact on mathematics teacher training throughout the country.
The objectives of the PROFMAT program are consistent with the mission of the Mathematical Society of Brazil: “To encourage the improvement of mathematics education at all levels”, and comply with
Law N° 13.005 of 25 June 2014 of the National Education Plan, which lists among its aims the training
of fifty percent of secondary school teachers to Master’s level and a guarantee to meet the continuing
educational needs of all school teachers.
CHILE: Standards for the preparation of Mathematics teachers
and the REFIP project.
In 2008, the Ministry of Education commissioned a group of mathematicians from the Center for
Mathematical Modeling at the University of Chile to form a team of mathematicians and mathematics
educators to define the standards for mathematics teacher training at primary and secondary level.
34
The development of these standards should be understood in a context in which the initial training of
teachers in Chile has been damaged by the lack of regulation.
The Ministry of Education justified this decision by the need to improve teaching as an activity
and a profession, a central aim of national education policy being to raise the status of teaching as a
profession in order to attract and retain the best candidates as teachers. This requires a discussion
of the knowledge and skills base for teaching and to systematize standards as clearly as possible, in
which terms the training and performance of future teachers must be judged. This is taking place
at a moment in which a sharp increase in the supply of teacher training programs has been seen,
generating a genuine explosion in enrollment. These programs are extraordinarily heterogeneous
and some are not able to guarantee the quality of their graduates’ training. This situation is compounded by the low results obtained by the country in international tests (TIMSS y PISA) and the
profound differences in the levels of learning shown by national instruments of student and teacher
assessment.
In this context the purpose of setting standards was: to determine and describe the knowledge and abilities specific to the task of teaching Mathematics at primary and secondary level, as
demanded by the school curriculum. To achieve this goal, the University of Chile through the Center
for Mathematical Modeling formed a multidisciplinary team that embarked on the task of setting
standards for mathematics. The setting of these standards was enriched by conducting a broad technical consultation with experts from other universities in the country, professionals and directors of
educational foundations, in-service teachers and trainee teachers. This consultation was extended
to two teams of international experts from universities with extensive and successful experience of
teacher training.
The standards developed currently form part of public policy in education and can be found at
35
http://www.cpeip.cl/usuarios/cpeip/File/2012/librobasicaokdos.pdf
http://www.cpeip.cl/usuarios/cpeip/File/librosestandaresvale/libromediafinal.pdf
The Standards for Initial Training of Primary and Secondary Level Teachers are tools to ensure
the quality of mathematics education. Their incorporation into other countries in Latin America and the
Caribbean, after being localized, could be very useful. For the English-speaking Caribbean and for wider
dissemination throughout the world, the World Press has published a version in English. This book can
also be seen as a resource for in-service teachers and educators.(9)
Of particular relevance to Chile has been the development of the project Resources for the Initial
Training of Teachers at the primary school level, the memorandum(10) of which was published in March
2014. It is a collection of four texts: Numbers, Geometry, Algebra and Data, and Chance focused on mathematics for teaching, the basic knowledge required by primary education teachers. This collection was
compiled by a team of experts in the discipline and in education, from different universities, led by the
mathematician Salome Martínez, director of the Education Laboratory at the Centre for Mathematical
Modeling at the University of Chile.
The process of compiling these texts was undertaken over three years and preliminary versions of
the texts were piloted in teaching degree courses in Primary Education at 16 universities. Around 5,000
student teachers from around the country participated in this pilot phase, making these texts extremely
useful tools for teacher training.
The texts promote the relationship between school mathematics and its teaching, just as they
contribute to the integration of disciplinary and teaching skills. They address school mathematics as
set out in each axis of the national curriculum, in a way that is deep and specific to the teaching
profession. Each point of content is analyzed and developed, setting out mathematical skills alongside
aspects of their teaching at elementary school level, including possible student mistakes, the analysis
36
of school activities and the use of concrete material. The texts also promote reflection on mathematics and its teaching.
COLOMBIA: In-service teachers in the Antioch Province and mathematicians
in action, including the governor.
Antioch the Most Educated and Envigado the City of Mathematics are the mottos of the State of Antioch and the municipality of Envigado, and this is no coincidence. Education has become one of the
pillars of the governor of Antioch’s political commitment and the learning of mathematics a priority for
the children of this important region of Colombia–and its governor certainly knows about mathematics. Sergio Fajardo holds a doctorate in Mathematics from the University of Wisconsin, and his thesis in
the field of Logic led him to teach mathematics at the University of the Andes in Bogotá, from whence
he went into politics as Mayor of Medellín and now Governor of Antioch. This mathematician sought
out Colombian mathematicians grouped together in the Colombian Mathematical Society (SCM) and
in 2012 he signed a partnership agreement between them and the Government of Antioch with the
aim of carrying out the Plan to Improve the Teaching and Apropiación of Mathematics in Schools in the
Province of Antioch.
In turn, for support in the undertaking and launch of the plan, the SCM signed a cooperation
agreement with the Faculty of Science at the National University of Colombia at Medellin, through its
department, the School of Mathematics.
This ambitious plan has as a general objective: to promote the improvement of the quality of mathematics learning and teaching in the Province of Antioch, using available technology and impacting directly
upon teachers in training, in-service teachers, students and the community at large. This plan is structured
37
into four programs currently underway, which we describe below, along with their objectives and
activities:
Program 1. Training and Qualification of Trainee Teachers. The aim of this program is to
improve the level of mathematics teachers at educational institutions in Antioch, as well as trainee
teachers at Antioch’s teacher training schools. In this program a collection of texts were written which
are now used to train teachers and students in the various municipalities of the Province of Antioch:
Notions of Calculus, Notions of Algebra, Notions of Euclidean Geometry, Notions of Arithmetic and
Notions of Trigonometry and Analytic Geometry.
The aim of these training courses is to improve the knowledge of mathematics teachers at primary and secondary levels, and to complement students’ training at teacher education schools or in
the final years of secondary schools. In this respect, the texts submitted show the solution in detail in
terms of examples and exercises, as well as the theoretical side. Since 2012, using these texts, 36-hour
courses and 6-hour short courses have been set up, training around 500 teachers and students in the
following municipalities of Antioch: Copacabana, Santa Rosa de Osos, Jerico, Andes, Amaga, Marinilla,
Envigado,Yarumal, Sonson, Carepa, Santa Rosa de Osos, Frontino, Urrao, Abejorral, San Jerónimo,Titiribi,
Santuario and Puerto Berrio.
Program 2. Training and Qualification of Mathematics Teachers in the Province and
Mathematics Outreach in the Community. The aim of this program is to promote mathematics
among teachers, students, and the wider community in the different regions of Antioch. The program is
implemented through two main activities: Encounter with Numbers and Festival of Numbers.
In Meeting with Numbers, lectures on informative topics of a pedagogical or mathematical nature
38
are offered. Short courses are also available to encourage teachers to improve their skills in different
key areas of Mathematics. These meetings are accompanied by the Festivals of Numbers. These Festivals
are open to the whole community and take place in the parks of selected municipalities. The Festivals
are also held in municipalities where the 6-hour short courses mentioned in Program I.
Since 2012, Meetings with Numbers have been organized in the cities of Envigado and Apartado
in the region of Uraba, with the participation of more than 2,000 teachers and students with a talent
for mathematics.
Program 3. Modernization of Programs in the Area of Mathematics, Revision of Texts
Used, and Creation of Class Guides and Student Assessment Systems. The aim of this program
is to propose new area plans and to compile guides for teaching mathematics classes in primary and secondary education. Minimum area plans have been written for grades 6 to 11.
As a complement to these plans, the aforementioned books have been written, which are
class guides in the field of mathematical content for the various area plans. The texts are designed
for teachers and each is accompanied by 90 lesson plans. It is hoped that these guidelines will be
helpful for teachers as they teach their classes, as they are written in simple language; the examples
and exercises provided are fully detailed. Teachers are expected to complement their classes with
additional activities.
Program 4. Use of Information Technologies and Television in Mathematics Education.
The objective of this program is to use Information and Communication Technologies–ICTs–with the
aim of achieving a massive impact through the mathematics programs that will be developed.
This program has seen the making of multiple videos and accompanied the Antioch Mathematical
39
Network in the mathematical component of the Knowledge Olympiad, a regional contest between
students in grades 10 and 11 which has taken place since 2012, and in the creation of a website. More
than 100 videos in various series have been created: From Pythagoras to Cantor Series, Mathematics with
the Governor Series and Introduction to GeoGebra, which can be found at
http://www.youtube.com/playlist?list=PLvTcv97ZWEgx9DwK7HKz047S0AC1pnYfV
The Think About It Series has also been produced, alongside a mathematics course, which was
broadcast on the regional channel Teleantioquia and can be found on youtube. Two of them can be
seen at:
http://www.youtube.com/watch?v=PIsy5aatmT0
https://es-es.facebook.com/MiClaseTV/posts/309145825888796
This program also includes an accompaniment to the Knowledge Olympiad in the mathematics
component. These Olympiads are a regional contest between students in grades 10 and 11 which has
taken place since 2012. See information about the Olympiad at:
http://www.antioquiadigital.edu.co/index.php?option=com_community&view=groups&task=view
group&groupid=1013&Itemid=622
CUBA: The Mathematics and Computing Society of Cuba and the Encouragement
of Women Mathematicians.
Once a month the Mathematics and Computing Society of Cuba holds the Seminar on Mathematical
Culture, inviting mainly teachers, professors and professional mathematicians. In 2013 in particular, it
being the International Year of Statistics, various activities were held. The Society designated October
31 as Cuban Mathematicians’ Day and it has become a tradition to present the winners of the “For
40
Mathematical Culture” contest and the National University Mathematics Olympiad with their prizes on
that day.
The Mathematics and Computing Society of Cuba, together with the Faculty of Mathematics and
Computing at the University of Havana invited participants to compete in the 14th National University
Mathematics Olympiad “Raimundo Reguera” (ONUM), held on April 26 2014. Its participants are undergraduate students, studying regular daily courses on any university degree, who have a particular interest
in mathematics.To compete they are organized into three groups: I (mathematics, physics and computer
science students), II (teacher trainees) and III (the rest).
Under the auspices of the Mathematics and Computing Society of Cuba, three editions of the
“Luis J. Davidson” National Competition for Mathematics Teachers have been held. Teachers working
in general and polytechnic schools participate in the competition, as well as freelance mathematics
coaches. The content of courses includes logical reasoning, geometry, algebraic work, functions and
trigonometry.
In 2012 the Delta project was launched by the Faculty of Mathematics at the University of Havana,
a project that takes mathematical culture to theaters through humor. On March 14 every year, World
Pi Day is celebrated. For this reason, the Delta project invites the public to a Havana theater where
this humorous show is performed: “Mathematics: Pi’s the Limit”, on Mathematics, the number Pi and other
incredible but true issues.” It is an interactive show, with audience participation and guest artists.
For its part, the Ministry of Education is working on the continuous improvement of the curricula
of Mathematics teachers (because to be a primary, secondary and pre-university teacher in Cuba, you
must have a bachelor’s degree in Education). It has established student scientific societies, it organizes
groups for high performers in Mathematics in pre-university institutions, prepares students for mathematics courses at school, municipal, regional and national levels as well as students entering the various
41
Latin American and international Olympiad, where Cuban students obtain satisfactory results and occasionally medals in all three categories.
A highlight this year is the publication of the article How to make mathematical discourse appetizing? Experiences with a Cuban flavor (11), by Prof. Carlos Sanchez Fernandez of the University of Havana,
who is also the author of The Endearing Charm of Mathematics (2011).
The Cuban Academy of Sciences works on the promotion and development of science and also
organizes Popularization of Mathematics Conferences, combining efforts to promote a task we consider
paramount: to create in the population a positive mental association with mathematics, to restore the
social image of what mathematical knowledge is and what it is for. It contributed toward the publication of “Numbers and Figures in History”(12), which was the basis for a course in an educational television
series called “University for All”.
An example of the promotion of motivation and vocational training by non-formal means, in
mathematics and exact sciences in general, are the Children’s and Youth Festivals of Science and Technology held in parks and open squares several times a year, in which teachers, together with scientists
and families, participate in interactive experiences, and where the motto is “learn through play”.
In 2013, young mathematicians were also encouraged to participate in the Meeting of Young Scientists organized by ICSU-ROLAC, with the presence of a young Cuban mathematician, Noslen Hernández. The biography of this talented mathematician is being disseminated in the Women of Science
Program of IANAS, the Network of Academies of the Americas. Prizes are awarded every two years by
the Cuban Academy of Science, with the support of the Kovalieveskaia Foundation, to young women
with significant results in the exact sciences.
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MEXICO: Science at your School, including Mathematics
As regards the work of promoting and encouraging the study and appreciation of mathematics, as well
as the work of seeking and channeling the skills of young people with considerable talent for the discipline, it is important to note that the Mexican Mathematics Olympiad was the first national competition
of its kind. It began with the Mexican Mathematical Society more than 15 years ago, strongly supported
by the Mexican Academy of Sciences. For more than 10 years the Academy has also coordinated the
Spring Mathematics Competition and the “Cotorra Mathematics Competition” for children and young
people. Similarly, the important project “Science at your School”, propelled and implemented during José
Antonio de la Peña’s presidency of the Academy, has had a positive impact on the elementary education
sector, within which the generations that will go on to create a critical mass of mathematicians, necessary today and in the future, are surely to be found. These programs offset–within the scope afforded
to the Academy–the considerable shortcomings in the mathematical training of young learners. .
The Funny Mathematics Competition began in 1998 for students under 12 years. The competition
consists of two levels: children under 10 and children under 12. The invitation to participate in both
levels consists of three stages: The first allows the voluntary participation of all children who comply
with the age restrictions. No more than 10% of participants at each level are invited to go on to the
second stage. During this second stage the best at each level are selected, no more than 10% who
are then invited to go on to the third phase, corresponding to the May Olympiad. Out of the top ten
places at each level of the Spring Mathematics Competition and the top ten at the second level of the
Funny Competition, the top 6 are selected to participate in the Rio de la Plata Mathematics Olympiad.
43
The Science at your School program, coordinated by the Academy, is designed to improve primary
school teachers’ attitudes toward science and Mathematics, as well as updating their knowledge in these
disciplines. Scientists, teachers and students doing mandatory social service participate in the program.
www.lacienciaentuescuela.amc.edu.mx contains interesting teaching and study materials, and an online
consultation forum where teachers ask scientists questions.
Another interesting example is the Spring Mathematics Competition, created in 1996 by Dr. Carlos Bosch. This competition is aimed at young people at secondary school, divided into two age groups:
under thirteens and under fifteens. In these competitions, participation takes place on an individual basis,
at a local as well as international level. The aim of the program is to encourage interest in mathematics
among young participants. These competitions have also helped teachers at these levels to reflect on
and exchange experiences of mathematics education.
Mexico is also developing, as part of a great tradition, the Mexican Mathematics Olympiad (OMM),
a Program designed by the Mexican Mathematical Society, the principal objective of which is to encourage
the study of mathematics as a discipline of thought that develops students’ intelligence through methods of
structured, deductive and creative reasoning. The OMM takes place annually in four stages: State Competitions, the National Competition, training and the selection of representatives from Mexico for the
International Olympiad and participation in the International Olympiad. It is striking that these Olympiad
have been held for 27 years. This year’s winners comprised the Mexican delegation to the 55th International Mathematics Olympiad in South Africa in July 2014, and the 24th Latin American Olympiad
in Honduras in September 2014. The OMMs are organized by the Department of Mathematics in the
Faculty of Science at the National Autonomous University of Mexico. The Mexican Mathematics Olympiad’s official webpage is: http://www.omm.unam.mx/
Since 1999, Mexico has been developing the PUEMAC (Computer Assisted Mathematics Educa44
tion Project), created in response to the need to promote mathematics learning at all levels.The mechanism used to reach the public is a website, which makes intensive and extensive use of hypertext, with
straightforward navigation, which increases the speed of access to information. The aim of the program
is to depict mathematics education as a playful activity: by means of activities, interesting issues and
games it presents visitors with an enticing bait that leads to knowledge. Webpages have been developed
that support the entertaining and interactive learning of mathematics, whereby visitors will be able to
choose the activities through which they can learn while playing.
University Computer Assisted Mathematics Education Project
http://puemac.matem.unam.mx
Although it is true much still remains to be done, these programs designed by the AMC, the SMM
and the UNAM are admirable and should be widely disseminated and shared throughout the Latin
American region. Studying, understanding and extending the Mexican experience as regards the improvement of mathematics education is the main focus of ICSU-ROLAC.
PARAGUAY: The Mathematics Olympiad, beyond the search for talent.
What was originally the Paraguay Mathematics Olympiad, OMAPA, has now become the Multidisciplinary Support Organization for Teachers and Students, extending its radius of action beyond the
Mathematics Olympiad.
The mission of OMAPA is to collaborate in the improvement of education quality throughout the
country and thus to contribute to improving the quality of life of the men and women of Paraguay.
The aims and objectives of OMAPA are based on working for a better future, with social equality and
45
sustainable development. OMAPA seeks to raise awareness and influence academic and business communities; promote quality education; participate in the training of teachers and students and encourage
the development of policies and legal and academic tools to promote the positive transformation of
the basic training model for young people.(14)
Although OMAPA has extended its sphere of action, the National Mathematics Olympiad continue
to be OMAPA’s main program, and they fulfill each of the institution’s objectives mentioned above.
Since 1989, OMAPA has promoted the undertaking of national mathematics competitions, where
students participate voluntarily at various levels. It organizes various competitions for public and private
schools: The National Mathematics Olympiad (in its Children’s and Young People’s editions) that seeks
to solve problems by encouraging ingenuity and the ability to use mathematical concepts, and the
Kangaroo Olympiad, based on an international game-contest and geared toward students from third
grade and above, which seeks to promote mathematical culture. The statement of problems improves
the quality of skills and above all the ingenuity and ability to use them in various contexts. Students and
those enrolled in the formal education system in Paraguay participate voluntarily. It is recommended
that all students from each institution participate, to spark interest in and enjoyment of mathematics
through problem solving.
In 2013 the National Mathematics Olympiad reached an historic milestone with 499,071 students,
whose institutions enrolled voluntarily in the competition. The program involves working in classrooms,
throughout the school year, solving challenging mathematical problems using materials specially created
by the academic team at OMAPA, which were delivered to more than 5,000 educators at teachers’
workshops held all over the country.
The Olympiad take place on two levels: the Youth Olympiad (from 6th to 11th grade) and the
Children’s Olympiad (from 3rd to 6th grade). These Olympiad consist of various rounds, encouraging
46
the active participation of a large number of students and teachers in the various participating schools.
For example, the Youth Olympiad consists of five rounds. The first is for training, the second is held at
the school level: both take place in each participating institution. In the third round the best from each
school compete to obtain places in the departmental round and from there to the national round. In
the various rounds, teachers participate actively in assessment and integration activities. Activities end
with the Awards Ceremony, in which medals are award to the winning students and trophies to the
winning schools.
The students with the highest score in the country are invited to the Scientific Initiation Program
with an emphasis on Mathematics for Talented Youth. The principal aim of this program is that young
people with an aptitude for exact sciences find an optimal space in which to develop their capacities; in
this way, interested students are prepared from a young age in the study of science.
In each region, the Regional Medals Festival is held on a normal school day at a school in the
region, where all the students invited receive medals, the color of which is decided after the final test.
In addition to the test, integration activities for the young finalists and their companions are organized.
Awards are given out at the end of the day, with medals handed out to all students who have completed
the test and trophies to the winning schools.
The strategy followed by OMAPA for the undertaking of the Mathematics Olympiad, involving students and teachers in the first levels of the competition, has had a significant impact on the teaching and
learning of Mathematics in the country. This achievement is of the utmost importance because it turns
the Olympiad into a vehicle to improve the mathematics of all children beyond the search for talent.
The achievements of OMAPA have been described in a study examining the influence of the Mathematics Olympiad in participating schools, through the achievements demonstrated by students in tests
of mathematical ability. To this end, the level of achievement of students from institutions with three or
47
more years of participation in the Olympiad were compared with the results obtained by students at
schools that only recently began to participate in the Olympiad (one or two years). Questionnaires on
associated factors were also carried out.
The general analysis of results, grouped by years of participation in the Mathematics Olympiad
for sixth and ninth grades, indicates that schools that have participated for more years (three or more)
show a higher performance in mathematics in both sixth and ninth grade, compared with schools that
have participated for a shorter length of time (one or two years). On the other hand, students that
have participated in the zonal round of the Olympiad obtain the highest results in the mathematics
test, outperforming those who only participated in the school round and those students who did not
participate.(13)
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VI. STRATEGIC PROPOSALS
FOR ICSU-ROLAC
At the ICSU-ROLAC meeting held at the Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro in August 2013, and with the participation of Marcelo Viana, President of the SBM, and representatives
from Mexico and Brazil, it was agreed to strengthen links between ICSU-ROLAC and ICMI, by promoting
initiatives of common interest. It was also agreed to promote special sessions on Mathematics education
with EMALCA schools and include the active participation of mathematicians and mathematics teachers.
UMALCA, ICMI and ICSU-ROLAC must promote continuous training activities for teachers at EMALCA schools. It was emphasized that greater integration and active participation of mathematics so-
cieties in the region is needed, and that positive experiences like those of the SBM are needed. In
countries that do not yet have Mathematics Societies, ICSU-ROLAC’s approach could be through the
organizers of local Mathematics Olympiad.
ICSU-ROLAC must promote the participation of mathematicians in universities and research cen-
ters in the continuous training of teachers. Experiences such as those of Brazil and the University of
Guanajuato in Mexico should serve as examples.
ICSU-ROLAC can contribute to the integration and development of initiatives to create stocks of
resources for Mathematics education, and facilitate the dissemination and exchange of their experiences, teaching materials and literature of interest.
49
An ICSU-ROLAC Agenda for Mathematics Education in the Region was proposed with
the following points:
1. ICSU-ROLAC must explore, in order to subsequently recommend, the proposal of Mathematics
Education Standards in the Region, for the training of primary and secondary school teachers.The
aim will be the preparation of a reference document, prepared with the participation of representatives (mathematicians and mathematics teachers), OREALC/UNESCO, ICMI, ICSU-ROLAC and
other organizations. The experience of Chile, which has already developed these standards, could
serve as a starting point.
2. ICSU-ROLAC should send a letter to the presidents of all countries in the region, presenting a
comparative diagnosis of the state of mathematics education in our countries and how they are
faring relative to the world, emphasizing the importance of mathematics for life, for sustainable
development and for decision-making.The letter might include a series of ideas that can be developed and examples of successful experiences that contribute to the transformation of our reality.
Committee members will contribute to the drafting of these letters, which should be signed by
the President of ICSU and the Director of ICSU-ROLAC.
3. ICSU-ROLAC should help to organize the Mathematics Olympiad on a massive scale in other
countries in the region, as achieved by the OBMEP in Brazil.
4. ICSU-ROLAC should serve as an advocate for mathematics education with decision makers and
establish channels of communication with Ministers of Education, Science and Technology bodies,
National Mathematics Societies, Science Academies and Associations for the Advancement of
Science.
50
5. ICSU-ROLAC should propose a Scientific Planning Group for Mathematics education with the
aim of publishing a second book on Mathematics Education in Latin America and the Caribbean:
A Reality to Be Transformed 2.0, to be disseminated among politicians and decision makers.
ICSU-ROLAC should consider creating a standing committee to be responsible for promoting and
supporting the initiatives of ICSU-ROLAC for Mathematics education.
6. ICSU-ROLAC should establish contacts and closer links with organizations that could support
the initiatives of mathematics education, such as IANAS, OEA, JICA, TWAS, ICTP, BID, etc.
7. ICSU-ROLAC should encourage international collaboration to improve mathematics education
by means of collaboration in the construction and strengthening of regional networks.
8. ICSU-ROLAC should establish and promote partnerships between mathematics education and
other ICSU-ROLAC programs, such as risk management, sustainable energy, biodiversity, emphasizing the need to foster an active interface with initiatives such as the Future Earth program and
others implemented in the region.
9. Support the Meeting at the BIRS International Center in Banff, Canada, in January 2014.
10. Join forces with the International Mathematical Union (IMU), the is IACME (the Inter-American
Committee on Mathematics Education), UNESCO, the International Mathematics Center (CIMAT,
Guanajuato), and with the Ministers and Secretaries of Education of the Latin American and
Caribbean region.
These 10 points on the Agenda for Mathematics Education were followed up and analyzed at
meetings of the ICSU-ROLAC Regional Committee, which held its 14th meeting in Panama in September
2013, and its 15th meeting also in Panama in April, and in Rio de Janeiro in 2014.
STRATEGIC PROPOSALS FOR ICSU-ROLAC
51
VII. IN CONCLUSION
Developing mathematics and mathematical thought is not a matter a choice. It is an obligation of governments to prioritize the strengthening of the teaching of this science and the basic sciences in general
on their agenda. First, because of the implications it has for the development of new technologies and
for solving concrete problems of social and economic development. Second, because of the development of abstract thought encouraged by the method of mathematics learning, and third, because of its
applications and use in the development of citizens’ everyday lives.
Through this document, ICSU-ROLAC proposes concrete actions to promote the teaching and
learning of school mathematics and showcases successful initiatives in which these recommendations
have been implemented. A country that aspires to develop technologies that resolve important problems to improve the lives of its citizens must rely on the promotion and balanced support of basic
science and, as such, pay significant attention to the strengthening of its mathematics. That is, to the
training and development of mathematics professionals and the growth and consolidation of institutions
devoted to it.
Mathematicians, that critical mass we need to form, are now sitting in the classrooms of primary
and secondary schools and it is there that our main focus of attention should be, and it is for this reason
53
that we are focusing on perfecting mathematics education at all levels, attracting talent, forming vocations, apprenticeship training, skills tests, competitions and the Olympiads.
The other priority is the installation of massive campaigns to improve teaching standards and involve professional mathematicians, university professors, scientists and academics in this crusade.
54
VIII. BIBLIOGRAPHICAL
REFERENCES
ICSU-ROLAC Annual Report, Mathematics education in Latin America and the Caribbean: A reality to be transformed,
Volume 4, 2010. www.icsu.org/latin-america-caribbean
(2)
UNESCO: SERCE. Segundo Estudio Regional Comparativo y Explicativo, Aportes para la enseñanza de la Matemática.
Latin American Laboratory for Assessment of the Quality of Education, ISBN 978-956-322-004-9, Printed by Salesianos
Impresores S.A. Santiago, Chile; January, 2009.
(3)
UNESCO: Comparison of Results of the Second and Third Comparative and Explanatory Regional SERCE and
TERCE Study 2006-2013. Santiago, Chile; December, 2014.
(4)
Concepcion Valdes Castro, Paradojas en la problematización del cálculo, Cuadernos de Investigación y Formación en
Educación Matemática. 2013. Year 8. Number 11. pp 265-279. Costa Rica.
(5)
Lilliam Alvarez, ¿Por qué las Matemáticas?, ICSU-ROLAC Newsletter, Number 1, May 2014. www.icsu.org/latinamerica-caribbean
(6)
United Nations Development Program, Educación: la Agenda del Siglo XXI, Hacia un desarrollo humano. Hernando
Gomez Buendia (director), 1997.
(7)
PISA 2012 Results: Creative Problem Solving Students’ Skills in Tackling Real-Life Problems. Volume V, OECD Publishing,
ISBN 978-92-64 20806-3 – 2014-04, 2014. Consult this publication online at: http://dx.doi.org/10.1787/9789264208070(8)
BBC World. No son los que más invierten en educación (menos del 7% del PBI), ni los que imponen la mayor carga
horaria a los niños en las escuelas, More at BBC WORLD http://www.bbc.co.uk/mundo/ Tags: Finlandia, Educacion, BBC,
Educacion en Finlandia.
(9)
Book: Primary Mathematics Standards for Pre-Service Teachers in Chile: A Resource Book for Teachers and Educators
(Series on Mathematics Education), by Patricio Felmer, Renato Lewin, Salome Martinez, Cristina Reyes, Leonor Varas, Eugenio Chandia, Pablo Dartnell, Alejandro Lopez, Claudia Martinez, Arturo Mena, Andres Ortiz, Gloria Schwarze, Pierina
Zanocco, 2014.
(10)
Recursos para la formación inicial de profesores de educación básica. Project FONDEF – CONICYT D09 I1023
(2011 – 2014). Project Director: Salome Martinez, Authors: Francisco Martinez, Salome Martinez, Hector Ramirez, Maria
Leonor Varas. www.ediciones-sm.cl
(11)
Carlos Sanchez, ¿Cómo hacer apetitoso el discurso matemático? Experiencias con sabor cubano, Conference at the
(1)
55
13th CIAEM (Recife, Brasil, 2011), appeared in the official journal of the CIAEM (Interamerican Council on Mathematics
Education) “Cuadernos de Investigación y Formación en Educación Matemática” published in Costa Rica, 2013.
(12)
Carlos Sanchez y Rita Roldan, Números y Figuras en la Historia, ACADEMIA Publishing, Havana, Cuba, 2012.
(13)
Adolfo Sanchez Valenzuela, Reflexiones sobre el curso de la matemática en México a 45 años de la formación de la
Academia Mexicana de Ciencias, Mathematics Section of the AMC, 2004.
(14)
Evaluation of the Impact of Mathematics Olympiad in Paraguay. Final report, July, 2014, OMAPA.
56
ACKNOWLEDGMENTS
To Manuel Limonta, Director of ICSU-ROLAC for his concern for and profound understanding of the importance of
the issue, and to his collaborators Ángela Guzmán, Camilo
García and Angélica Bucio for their efficient support.
To Patrick (Rick) Scott, Vice President of the InterAmerican Committee on Mathematics Education, for the
kind and competent revision of this english version.
57

A Proposal from ICSU ROLAC to Educational Authorities in the

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