Mathematics is an exact science. No matter what direction society takes, two plus two will continue to be four. The same cannot be said about the training of teachers who teach mathematics to children and young people. For it to make sense to people, teachers need to look at the reality in which the subject is learned. This way, students can use the skills it provides to make life simpler. But doing this in a society that is constantly changing is not at all simple and, therefore, the mission of teachers - and those who train them - is even more challenging.
The result of this challenge has not been positive, at least in international assessments. Released this Tuesday (3), the results of the International Student Assessment Program (Pisa) show that more than two thirds of Brazilian students had lower than ideal performance in mathematics. In contrast to the Brazilian reality, Chile was the country with the best performance in Latin America.
But even though they are important indicators, these results are not enough for educational policies to be developed. It is on these subjects that the Unicamp website spoke with Jeannette Galleguillos, Chilean, teacher at Valparaiso University. With a PhD in Mathematics Education from Unesp, she develops research in the area of mathematics teacher training and advocates that new teachers be encouraged to look at the social reality of their students and make mathematics closer to that reality. In her doctorate, she studied the concept of mathematical modeling, which is the way in which everyday situations and problems can be translated into numbers and thus solved. At the end of November, Jeannette was at Unicamp participating in the research group's III International Seminar CIEspMAT and the II Research Seminar of the Professional Master's in School Education, both events at the Faculty of Education (FE).
In the interview, she talks a little about her vision regarding teaching in schools and also comments on the current social situation in Chile, and how much the demands of education are present in the demonstrations.
Why did you choose to work with mathematical modeling in your PhD?
I got involved in mathematical modeling because the point of view used in Brazil is not exactly focused on solving precise, closed problems, here the problems are more open. And the teacher (Marcelo) Borba It has a proposal in which the student chooses the problem they are going to solve, develops this problem in groups and looks at the surroundings, at reality, and thus Mathematics emerges in a more tangible way for the students. I was very engaged and found it difficult, in this context, to think about how the teacher will guide this completely open process, in which the student will build. I saw a difficulty, but I also saw a possibility of working with this topic. So I used activity theory, which foresees a way of learning from the environment, with different tools, and this implies the knowledge that the teacher must have for this development. Here I got to work with the teachers on the concept of specialized knowledge, so that they could think about open-ended problems. Sometimes the teacher focuses on a topic, geometry, for example, and that’s it. In my case then, it was thinking about what qualities, what knowledge a teacher has to have to work with open problems, to manage this situation with students.
And how does technology enter into this process?
The truth is that it didn't come in directly (laughs), it practically fell out of focus because with activity theory the focus is on the activity itself, the learning process. Technologies play a role, but that was not my focus. But since there was an interest in this technology participation, I also looked at it. In this case, I collected data from an online course, where there was also a difficulty in communication between teachers, due to the artifacts they were using. It was a two-month continuing education course for mathematics teachers, and the teachers communicated on Facebook, in a closed group, and I collected data from the discussions and the construction of problems they chose.
What results do you find most interesting from this study?
I think the most interesting thing is that I analyzed the data from an analysis framework based on activity theory, looking at the speeches, the teachers' statements to construct problems. And in activity theory you look at tensions and their solutions, which we call expansions. Generally in literature tensions appeared between one and the other, but not directly in mathematics. I wanted to bring this to mathematics teaching, relating these tensions to mathematics teaching, even though they were not problems, but learning opportunities. So the different perspectives put forward by the teachers, from modeling and from their own backgrounds, that appeared as they discussed, all these differences were striking. One had a closed problem view, the other an open problem. Then by discussing, they were able to move from a very closed problem to an open problem view, which allows students to discuss. They saw all kinds of problems in the course, which ended up including issues such as interdisciplinarity, concrete issues, such as the lack of water, which at that time was a problem in São Paulo. And in this practice, as teachers, they were able to construct and solve very simple mathematical problems, but in which they could put themselves in the students' shoes, who do not know the results and need to look for ways. Teachers like to know the problems to direct the paths, but in this case they had the difficulty of dealing with issues of reality in which mathematics is involved.
What differences exist between teacher training in Brazil and Chile? Is there a big difference?
The focuses are a little different. But now there is a movement for change in Chile, because there I have never heard of project development, for example, in teaching mathematics. In Chile things are more closed, more in line with the country's assessments. Teachers are more focused on preparing students for assessments. Here I found a different world, a more intercultural school, with this issue of projects, of choosing themes, a richness that comes from Paulo Freire. When I returned to Chile, I noticed that some project questions were already appearing, they are already in the curriculum base, so there is already an opening to develop these themes.
And how does this end up reaching the teaching provided in schools? Do you notice changes in the way teachers work in Chile and Brazil?
In fact, I didn't have many experiences in Brazilian classrooms. But, based on some observations, I think there is a great influence of the curriculum base and teacher assessments, and also the cultural issue. Here the teacher has a much more open way of expressing themselves, and the students are better at discussing, getting into a topic. In Chile, students have more of a profile of being ready, with pencil in hand, without discussing issues, more individualistic, so that they perform in assessments, an idea more linked to competence. But this model is leaving the curriculum base, they are trying to implement projects, but it is not as certain as the experiences that exist here. They are even offering courses for teachers focused on this.
This observation is interesting, because here in Brazil there is a common sense that educational issues in Chile are more advanced than in Brazil. Is this aspect that you observe here that there is greater freedom positive then?
Yes, what happens is that Chile participated in international competitions, and many have their problems. But Chile is a little below the international average, but compared to other South American countries, it is ahead. But there is great criticism of these forms of assessment.
That's what I was going to ask, because here in Brazil the criticisms made about learning mathematics are based on these assessments. What do you think of them? Are there other ways to assess learning?
These assessments look at the individual student, but all teaching cannot be focused on this individual side. This makes the student think that, by answering a test, the ability is already in their mind. He performs well in tests, then goes to university and everything goes well. There are also groups of students with difficulties and this more closed form of teaching does not provide opportunities for people in public schools, with fewer resources. This has to be different, it has to reach everyone. It's not just looking at a high average, because that average means that there are very good students, but also students who don't have opportunities. We look good in the photo, but it's not the photo we want. I want this group, with diversity, which is now strongly reaching Chilean universities, for everyone to advance, in the step that each one can take. Now Chile is giving free university studies to students from the lowest strata of society. So you will no longer just have brilliant students at universities, who attended private schools and who you don't have much to teach, but now you need to support these students who arrive and you need teaching tools to meet this diversity. So learning is not just seen as an average grade, a number, but it has to be seen as an opportunity that guides people to take another step.
In your view, then, do Brazilian universities have more space for diversity?
I think so. When I studied at unesp, I had colleagues from different states and this already has a richness, different ways of speaking, different accents. And these differences are met in a better way. In Chile, recently, we have been receiving a lot of immigrants, people of different races, which we didn't have before. So you have to open up more through the language, through your preparation, through the ways of treating people, and I found that this occurs in a very interesting way in Brazil. I have always been very well attended to, very well treated here. It is a country that welcomes people from abroad, but Chile shows a certain resistance because it is the first experience, in many years, of receiving immigrants. Now there is an explosion of these people and we have to look at these differences. They have to be looked after, they need to work, they are people who have difficulty speaking, because they speak other languages. This has to be in schools, and immigration is allowing this, this openness of not just looking at the student's competence in tests, this mercantilist vision, but we have to serve everyone, with great respect. Now we have this obligation to have disciplines that address diversity, and project-based modeling, teacher training, favors this.
How does teacher training work in Chile? What changed with this free offer?
Now teacher training has greater resources. The Ministry of Education decided that in previous governments, during the period of (Michelle) Bachelet, to pay more attention to the evaluations of pedagogy and medicine courses, two important areas, health and education. In the case of medicine, you don't need to encourage people to follow the course, they really look for it. To encourage studies in teacher training, the government started giving scholarships, even before they were free. So those who have the best results are free and receive a scholarship, and those who have a reasonable result do not receive a scholarship, but also pay nothing. There is then support for teacher training and projects to improve pedagogy careers. This is valuable, because you help this movement with education. After that came free tuition, which also helped students who did not achieve high scores, but wanted to study pedagogy, who could obtain free tuition through their social strata. So we got a diverse group that can study and can dedicate themselves to undergraduate studies.
And is this diversity also reflected in the classroom as well?
This is what is expected, because the scholarship that students receive is called "teachers vocation scholarship". So the student knows that, if he is going to study, it is because he has a vocation for it. And then he has to study for three years in public schools, then he can work wherever he wants. So the government wants these teachers with vocation to arrive in public schools first. And there are other challenges, society is undergoing very strong changes, which are now also affecting school students. They are no longer silent students, who graduated during the dictatorship. Now we have different students, so we need to understand these social changes in the students who arrive at schools, and who need to respond to these differences, these social changes. This is a challenge for the teacher, offering good mathematics teaching in a different way.
Currently there is no way not to ask about the political situation in Chile. But even to relate it to our conversation, how much of the reality of education in Chile is present in this wave of demonstrations? Is there a relationship with these social changes that you mentioned?
Yes, there is a large participation of schools, especially secondary schools and universities. These are students who, in 2006, were already protesting. Part of these scholarships, the free ones, come from this movement called "Penguin Movement", because the uniform they wear, with a white blouse and black coat, looks like a penguin. They held protests and achieved changes. But now the issue has gotten out of control, it's very difficult, because the issue of retirement has come into play, so the entire middle class, everyone is wanting change. And me too! There is no one who does not recognize that this system, which has been in existence for 30 years, should have been attended to much earlier. Now it's too late and it will be done by force. This leads to a crisis, to despair. And among these, there are those who cause problems for commerce, for stores, for working people. Stores need to close, so whoever has a store needs to fire employees, because the store has already been robbed seven times during the protests. So you have the peaceful march, but also the excessive violence. There is also police violence, which is outdated, which still has the idea of dictatorship. So they are receiving support from the police in Spain to train police officers to deal with this different society. People have legitimate needs that need to be met. This is the conflict that occurs there, now there has been an agreement for a new constitution, things have become calmer. But the protests returned, because just a change in the constitution doesn't solve much.
Returning to the issue of mathematics, and thinking about the need you point out to offer an education that looks at this new society, what benefits can teaching mathematics with this focus bring to people?
I think the gain is very big, because there are people who have some kind of trauma with mathematics from elementary school, people get blocked. They do what they can, but this also marks their opportunities for professional development. This is important because mathematics is in almost every profession. Previously in Chile, it was only from the 9th level onwards that students had classes with specialists in mathematics teaching. Then, during the assessments, they began to realize that the students did not have mathematical reasoning at the 8th level. So they started working from the 7th level, they didn't just leave the generalist teachers. This allows students to develop with a teacher who understands that, if mathematics is not difficult for him and it is what he likes, he has to teach students in a way that engages them and does not allow them to experience trauma. The gain is for society that has a good performance in tests, that manages to enter a university. If the student is traumatized, they have fewer opportunities for development. Teacher training has to be continuous, they have to respond to new perspectives, new ways of teaching, innovate, because students are different. What works at one school may not work at another, so it's difficult.
Here in Brazil, many people think that mathematics has no relation to their daily lives, which favors the difficulties you point out. Does this also happen in Chile?
Yes, a subject that is talked about a lot there is the granting of credit, finance companies offer credit to people, sometimes to the elderly, who are less able to defend themselves, and they have no idea what the rates are charged, how much it will have to pay. Or people who are going to buy a piece of furniture, anything, and buy it in installments, don't know that they can pay double because of the interest. That's why mathematics, firstly, has to be for life, for financial issues, for daily life, which is very interesting. People get into debt, but they don't know that if they saved a few months, they wouldn't be paying interest for so long. These subjects need to be considered in training, in basic education, it has to be teaching for life. We call this contextualized mathematics, situated in the world, in the problems of daily life, that has meaning for people. If the problem is not contextualized, it produces a cognitive shock. The theoretical problem has to come from a context, so that the student understands what is happening and it makes sense to him. This prevents trauma (laughs).
Finally, based on your experience in Chile and the contact you have with Brazil, are the prospects for the future of teacher training positive?
(thinks) it's difficult! (laughs) It is a process of developing these new ways of looking at the context, at the culture, at the democracy in which the student can choose. This makes teaching progress in some way. I think that, just as teaching and research processes evolve, society also evolves in some way. We may be late and stuck, so we need to continue. A teacher who graduates now will work for at least 30 years, so he has to look far ahead to continue progressing in teaching, because people evolve and what we think now is right, I don't know if in five years it will remain valid, in ten years, in twenty years. I have to reinvent myself, have this ability to evolve so I don't stay still. Teachers need to be able to understand whether students are integrating this knowledge about the world, assimilating, transforming and returning knowledge to the world.
