Experiences of mathematicians in School Mathematics in Chile

Patricio FelmerBIRS, 30 January 2014

Overview of Chilean context

Population: !7 millionsSurface: 750.000 km2

Capital: SantiagoMain cities: Concepción, Valparaíso, Antofagasta, La Serena, TemucoNeighbors: Argentina, Bolivia and Perú

The name of our country has nothing to do with hot pepper!

Overview of Chilean contextResults in international tests

TIMMS 201131 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 contextResults 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

• 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)

1º 2º 3º 4º 5º 6º 1º 2º 3º 4º 5º 6º

Overview of Chilean context

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 MathematicsMissionThe 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 VarasThe product: 15 books14 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 andPedagogy

Written by Cristian Reyes (mathematician)

It contains cases for pre-service teachersdiscussion about what happens in a typicalMathematics 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 Inter-American 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 teachersPre-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 …