Experiences of mathematicians
in School Mathematics in Chile
Patricio Felmer
BIRS, 30 January 2014
Overview of Chilean context
Population: !7 millions
Surface: 750.000 km2
Capital: Santiago
Main cities: Concepción, Valparaíso,
Antofagasta, La Serena, Temuco
Neighbors: Argentina, Bolivia and Perú
The name of our country has nothing
to do with hot pepper!
Overview of Chilean context
Results in international tests
 TIMMS 2011
31 among 42 with 416 points, 84 below the center of the
scale. About 200 points below the highest scores: South
Korea, Singapore and Taipei obtained 613, 611 and 609,
respectively.
 PISA 2012
Chile got position 51 in Mathematics with 423 points.
71 points below 494, the OECD average.
50% of our students are below level 1 in
PISA…
Overview of Chilean context
Results in national tests
SIMCE System of Assessment of Quality of Education (absolute
scale). Various levels (4th, 8th and others), without
consequences for students, but high consequences for schools.
4th grade
10th grade
89
92
91
94
Overview of Chilean context
SIMCE (assesses students in schools)
PSU (university entrance exam)
The scores in these tests are highly correlated with
socio-economic variables. The Chilean educational
system is highly segregated by these variables and no
major change in this situation has been seen the last
years.
… what about other indices?
How does Chile do on them?
Chile reaches position 34 among 148
countries !
On the 4th of September of 2014, the Chilean
Minister of Finance proudly announced in CNN
our results in the annual competitiveness index
by the World Economic Forum
4 de septiembre 2014
Let us see…
Haelth and Primary Education
Higher Education and Training
Overview of Chilean context
• Chilean national curriculum in transition:
1º
2º
3º
4º
5º
6º
1º
2º
3º
4º
5º
6º
• Most teachers graduate from universities (but many
universities are quite bad)
• Profile of Pre-service teacher programs:
General Primary teacher program
Specialized Primary teacher program
Bachelor degree in Mathematics + Pedagogy (4+1 year)
Mathematics Pedagogy (4,5 to 5 years)
Mathematicians in Chile
Mathematicians in Chile
• In 2005 we were about 170 active
mathematicians, today we should be more
than 200.
• Chilean mathematicians have published 1,468
research papers with a citation average 3.93
per paper (place 17th in the world)
Mathematicians interested in
mathematics education
• Hard to count…
• Say 10? 20? 50?
• With very different level of comitments…
SOMACHI Chilean Mathematical
Society
• The society runs the National Olympiad and
organizes Chilean participation in
International Olympiads (national network)
• It published the ‘teacher magazine’ (with huge
gaps). Mathematicians write articles about
something they think is interesting to teachers
• Some members have participated sporadically
in national curriculum discussions
… in Concepción, in the south of Chile
• Two mathematicians have got together with
other scholars and run research and
development projects.
• They have a program called Mathematical
Enrichment Unity inside the mathematics
department in the University of Concepción.
• Their main work is to provide enrichment
activities, math contests and math discussions
with teachers.
The work of mathematicians in
mathematical contests
• There are local contests leaded by
mathematicians and with math university
students volunteers (math., math engineers
and pre-service teachers)
• There are online constest, involving thousands
of students playing mathematically based
games. It even involves international students
Mathematicians and the
National Curriculum
Involvement of mathematicians in
national curriculum
• That mathematicians are members of the
committee for the curriculum is not always
good…
• During the definition of the current national
curriculum three mathematicians participated,
while many of us strongly disagreed with the
outcome.
• Still the curriculum got something good…
New Chilean curriculum
• The curriculum is defined in three areas:
-abilities
-contents
-attitudes
While the attitudes where not well settled, our
main disagreement was with the contents, but
something was good about the abilities…
New Chilean Curriculum
The abilities:
•
•
•
•
Problem solving
Argumentation and communication
Modeling
Representation
These abilities make sense to mathematicians
New Chilean Curriculum
The abilities open the way to
- Encourage teachers to develop these abilities
in their students since it is in the curriculum
- Encourage universities to develop these
abilities in prospective teachers since it is in the
curriculum
- Encourage National Assesment Office to design
tests to measure abitilities, since it is in the
curriculum…
abilities vs. contents
• The abilities are essential for the development
of the individual, far beyond mathematics,
they give meaning to mathematics for all
children who will not use mathematics
significantly in their professional lives, beyond
the content
The Center for Mathematical
Modeling
Let us move to CMM
The Center for Mathematical Modeling is a state
funded research center in Applied Mathematics
Mission
The mission of the CMM is to create new
mathematics and use it to solve problems
coming from other sciences, the industry and
public policies. Its aim is to develop science with
the highest standards, which also guides its
endeavors in industrial research and education.
The Fondef projects…
The state funds Research an Developments
projects that ends up in some product for the
market… after some years of running these
projects, the state decided to open a line in
‘education’, yes Fondef in education, ending up
with a ‘product for the market’…
At CMM there were three mathematicians that
lead the first project called IDEA+, the first
Fondef in education at CMM
The Fondef projects…
• Teaching Innovations in teaching and learning higher
mathematics
• Standards for Science Formation of High School Teachers
• Interactive Tutoring in Math and Sciences
• Tools for the formations of mathematics high school teachers
• Scenarios for significant learning via video games
• Teaching resources for the implementation of the standards
for initial training of primary school teachers in mathematics
• Tools to strengthen elementary teacher training based on
teaching experiences in mathematics classrooms
• and more…
Fondef Project:
Tools for the formations of
mathematics high school
teachers
A Fondef project…
The project: Tools for the formations of
mathematics high school teachers.
Researchers: Patricio Felmer, Salomé Martínez,
Cristián Reyes and Leonor Varas
The product: 15 books
14 books of mathematics for pre-service teachers
written by mathematicians.
The 15th book is called Case study for the formation
of mathematics teachers.
Herramientas para la formación
de profesores de matemática
Case Studies for the Formation
of Mathematics Teachers:
Integrating Mathematics and
Pedagogy
Written by Cristian Reyes (mathematician)
It contains cases for pre-service teachers
discussion about what happens in a typical
Mathematics classroom.
Case Studies for the Formation
of Mathematics Teachers:
• Collaboration between mathematicians and
mathematics educators (lots of discussions, lots
of fights, lots of agreements)
• Example of international collaboration between
mathematicians.
• Solomon Friedberg supported the application for
the project and once it was granted he visited us
and taught us about Case Studies in mathematics
education
• Catherine Merseth was part of the international
support
The inspiration….
At CMM
• At CMM, the challenge has always been to work in
projects with a national view, aiming for national
impact.
• We early realized that
…we cannot blame students
…we cannot blame teachers
…we cannot blame math educators…
All of them are part of the landscape, we have to
work with them.
And we have to work also with mathematicians….
At CMM, a long way to recognition…
• At the beginning, research projects in education were not
seen with enthusiasm
• There was perseverance in the development of those
projects
• Peer review evaluation made a difference
• We had some succesful projects
• Education became more important in the country
• The research authority appretiates our work in education
• Mathematics Education is one of the 6 consolidated ‘labs’
at CMM
• We have got recognition at CMM
The Standards
The standards for initial formation of
teachers
How did we get there?
• 2003 project for developing standards for
various courses in the University of Chile
• 2004-2006 Standards for Science Formation of
High School Teachers. As a result we wrote 4
books for standards in Biology, Chemistry,
Mathematics and Physics and 1 book on
Didactics of mathematics.
How did we get there?
• 2007 Intent of a project with the InterAmerican Development Bank to develop
standards for elementary teachers
• March 2008 we were invited by the ministry of
education to develop standards for the
formation of elementary teachers to teach
mathematics
• March 2010 the standards were ready, but…
The standards for initial formation of
elementary teachers
• The new government was not ready… it took a
year and a half for them to accept the
standards and they called them, finally…
‘Guiding standards for pre-service elementary
teachers’
…were published in July, 2011
Collaboration
• Team of mathematicians and mathematics
educator (lots of discussions, lots of fights, lots of
agreements)
• Coming from various universities
• With insight from other mathematicians,
mathematics educators, deans of Education
Faculties, experts
• International support: Michigan State University
and National Institute of Education were reviewer
of the standards
•
•
•
•
Four Strands
Numbers (5 standards)
Geometry (5 standards)
Algebra (3 standards)
Data and Chance (3 standards)
Two dimensions
• Knowing the content to teach
• Knowing how to teach the content
The book…
• In 2011 we got the invitation to publish the
standards in World Scientific
• 3 years of bureaucracy and lack of will in the
ministry…
• In 2014 the book is about to see light…
The book…
This book contains a careful description
of the standards that future elementary
mathematics teachers in Chile should
meet after graduation from teacher
training. The contents is the result of the
work of a broad team of mathematicians
and mathematics educators led by the
University of Chile to develop Content
and Pedagogical Standards for Primary
School Teachers Education in
Mathematics commissioned by the
Chilean Ministry of Education.
Readership: Mathematics educators,
pre-service and in-service elementary
teachers, university and national policy
makers, curricular experts.
The standards are part of a
broader policy: INITIA program
• The standards
• The INITIA Test
• Funding for universities to change their
curricula for teacher formation
…towards an abilitation test
The INITIA Test
• Is taken voluntarily
• It includes all areas (Language, Sciences, Social
Sciences and Mathematics)
• At CMM we prepared the mathematics test
2012 Elementary and Secondary test
2013 –
2014 Secondary test
As a consequence of INITIA program
• Some universities are changing their
curriculum
• Some universities may include more
mathematics courses in the future
If they put more mathematics courses
requirements…what a challenge for
mathematicians…
As a consequence of INITIA program
…together with more mathematics courses there is
the need that students learn more mathematics,
enjoy mathematics and learn how to teach
mathematics…How to do it?
Make mathematicians to teach them…
In many high school teacher formation programs in
Chile there are a great number of mathematics
courses taught by mathematicians…
Both, the way of teaching and the contents are like
regular mathematics courses…
To support INITIA program…
• Books for pre-service elementary teachers
• Material for mathematics educators and
teachers
• Mid career monitoring tests
Some challenges at CMM
• Get a deeper influence in initial formation of
teachers in universities in the country
• Develop assesment tools for monitoring the
advance of pre-service teachers in their
careers
• Develop on-line material for teachers
Some challenges at CMM
• Become an actor in in-service teacher
formation
• Atract more mathematicians
• Support recognition in their departments of
mathematician doing work in education
• Research in Mathematics Education
…and increase international
collaboration
Our examples:
The book on Case Studies (Boston College)
The development of Standards (Michigan State
& NIE)
The math books for elementary pre-service
teachers (Michigan State and Texas State
University, UNAM)
Research in Problem Solving (University of
Helsinki)
…and increase international
collaboration
And this great opportunity…
Mathematicians and School Mathematics
education.
Guanajuato 2014
• Mathematicians and School Mathematics
Education
• At CIMAT, Guanajuato, MEXICO
• In October, 20-24
• Work around themes:
Standards for preservice teachers
Pre-service teachers, what and how to do it?
In-service teachers, what and how to do it?
others?
• Format: in depth discussion and workshops
Muchas gracias …