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Experiences of mathematicians in School Mathematics in Chile. Patricio Felmer BIRS, 30 January 2014. Overview of Chilean context. Population : ! 7 millions Surface: 750.000 km 2 Capital: Santiago Main cities: Concepción, Valparaíso, Antofagasta, La Serena, Temuco

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Overview of chilean context
Overview of Chileancontext

Population: !7millions

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 context1
Overview of Chileancontext

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
50% of ourstudents are belowlevel 1 in PISA…

Overview of chilean context2
Overview of Chileancontext

89 92 91 94

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

Overview of chilean context3
Overview of Chileancontext

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.

Experiences of mathematicians in school mathematics in chile


Howdoes Chile do onthem?

Experiences of mathematicians in school mathematics in chile

Chile reaches position 34 among 148 countries !On the 4th of September of 2014, the ChileanMinisterof Financeproudlyannounced in CNN ourresults in the annualcompetitivenessindexby the WorldEconomicForum4 de septiembre 2014

Let us see

Haelth and primary education
Haelth and PrimaryEducation

Higher education and training
HigherEducation and Training

Experiences of mathematicians in school mathematics in chile

Overview of Chileancontext

Chilean national curriculum in transition:

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
Mathematicians interested in mathematics education

  • Hard to count…

  • Say 10? 20? 50?

  • With very different level of comitments…

Somachi chilean mathematical society
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 concepci n in the south of chile
… 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
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

Involvement of mathematicians in 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
New Chilean curriculum

  • The curriculum is defined in three areas:




    While the attitudes where not well settled, our main disagreement was with the contents, but something was good about the abilities…

New chilean curriculum1
New Chilean Curriculum


  • Problem solving

  • Argumentation and communication

  • Modeling

  • Representation


New chilean curriculum2
New Chilean Curriculum

Theabilitiesopen thewayto

- Encourage teachers todeveloptheseabilities in theirstudents since itis in thecurriculum

- Encourageuniversitiestodeveloptheseabilities in prospective teachers since itis in thecurriculum

- EncourageNationalAssesment Office todesignteststomeasureabitilities, since itis in thecurriculum…

Abilities vs contents
abilities vs. contents

  • Theabilitiesare essentialforthedevelopment of the individual, farbeyondmathematics, theygivemeaningtomathematicsforallchildrenwhowillnot use mathematicssignificantly in theirprofessionallives, beyondthecontent

Let us move to cmm
Let us move to CMM

The Center for Mathematical Modeling is a state funded research center in Applied Mathematics


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 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 projects1
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…

Experiences of mathematicians in school mathematics in chile

Fondef Project:

Tools for the formations of mathematics high school teachers

A fondef project
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.

Experiences of mathematicians in school mathematics in chile

Case Studies for the Formation

of Mathematics Teachers:

Integrating Mathematics and


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
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

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 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

How did we get there
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 there1
How did we get there?

  • 2007 Intent of a projectwiththeInter-American DevelopmentBank todevelopstandardsforelementary teachers

  • March 2008 wewereinvitedbytheministry of educationtodevelopstandardsfortheformation of elementary teachers toteachmathematics

  • March 2010 thestandardswereready, but…

The standards for initial formation of elementary teachers
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


  • 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

Experiences of mathematicians in school mathematics in chile

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
The book…

  • In 2011 we got the invitation to publish the standards in World Scientific

  • 3 years of bureaucracyand lack of will in the ministry…

  • In 2014 the book is about to see light…

Experiences of mathematicians in school mathematics in chile

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 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
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 program1
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
To support INITIA program…

  • Books for pre-service elementary teachers

  • Material for mathematics educators and teachers

  • Mid career monitoring tests

Some challenges at cmm
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 cmm1
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
…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 collaboration1
…and increase international collaboration

And this great opportunity…

Mathematicians and School Mathematics education.

Guanajuato 2014
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?


  • Format: in depth discussion and workshops