Barcelona Metropolis

The pedagogue, who founded the Ton i Guida school in the Verdum neighbourhood, defends a mathematics useful in life that help mature thinking and that avoid suffering children.

[Interview: Joan Bramona Pedagog and Roser Cabacés Mestra // Editing: Marga Pont and Jordi Casanovas]

Born in Barcelona in 1931, Maria Antònia Canals i Tolosa graduated in Exact Sciences and did a teaching degree. In 1956 she began working in the Talitha school in Barcelona’s Sarrià neighbourhood, whose methods were drawn from the new teaching currents of the first third of the 20^th century. In 1962, set on bringing her approach to the neediest sectors of society, she founded the Ton i Guida school in the Verdum neighbourhood, where she was head teacher until 1980. Ton i Guida later joined the city’s network of public schools and eventually merged with Pla de Fornells to form the Antaviana infant and primary school.

A founding member of the Rosa Sensat Teachers’ Association, Canals has poured a lot of her professional efforts into teacher training: at the University of Vic, the University of Girona and the Autonomous University of Barcelona; at the Rosa Sensat summer schools; and on courses and seminars throughout Spain. She has also penned numerous publications on maths teaching.

In 1992 the Perímetre group – one of the groups of teachers created under her influence – together with the mathematics team at the Educational Sciences Institute (ICE) founded the Girona Association of Maths Teachers (ADEMGI), which Canals chaired until 1996. She also chaired the Catalan Federation of Entities for Maths Teaching (FEEMCAT) for several years.

Since her retirement in 2001, Canals has continued working to improve maths teaching as Director of the Office for School Maths Materials and Research (GAMAR), an organisation she founded in 2002 at the University of Girona, where this interview was held one November morning. Since 2014 she has also been Director of the Rosa Sensat Association’s Centre for Activities and Reflection on Maths Education (CAÀREM), which she also helped to create.

Maria Antònia, what does mathematics give to us?

To those of us who like it, a significant degree of happiness, and for those that don’t, a certain inferiority complex I believe, although I could be wrong…

In your opinion, what type of maths should we be teaching to children?

Maths that is useful for life. It should be like a mind game that helps to mature the child’s thinking and teaches them to deal with lots of different things. And it should allow them to be relaxed and happy, not make them suffer.

What do fine motor activities bring to this type of learning?

Like Maria Montessori, I think that it helps to build more mature thinking. The contact between physical and mental action creates a conceptual framework that is rooted in realty, instead of being “out there”… Dexterity is essential, especially in early childhood.

And conversely, what should we stop doing as part of maths teaching?

Lots of things. We shouldn’t smile at the child who finishes first, because speed shouldn’t be rewarded. We shouldn’t ignore a child when they tell us something that is not quite the answer we were expecting. We shouldn’t pay so much attention to the official curriculums, which are rather far removed from reality. The relationship with the child should be based on the present, on what is happening, on the space where they are working… The curriculum shouldn’t be the same for children in a little village in the Alt Empordà area as for children in Barcelona, for example.

What role should imagination and creativity play?

Alexandre Galí, a great pedagogue from the period of the Spanish Republic, asserted that mental calculation is a question of imagination. Piaget also spoke of imagination as a space in between physically handling things and the concept, the most abstract part. Imagination is necessary; children discover numbers when they imagine them. I once met a teacher who said that in the case of language, each word should have a place in the child’s imagination. And so in the same way, in mathematics, each number, each quantity, each category of figures and each concept has a place, and the imagination takes what we feel with our hands and situates it within the mind.

As regards creativity, people tend to associate it just with the arts, but it has to be present in everything, because it’s a basic human ability that is more developed in some people than in others. It’s unnatural to always make a creative child do the same tasks and not let her invent things.

And what do you have to say regarding autonomy and freedom?

I don’t like freedom, I prefer autonomy. I recall a quote from Montessori: “Autonomy, for us, shows our love for children”. Giving a child autonomy not only means that you let them do what they want, but also that you help them to do everything they are capable of with a bit of effort. If we don’t do this, we are clipping their wings.

And on the matter of play?

The other day, at a talk, I explained that I’d heard about some children who played hide and seek behind a see-through curtain. And they know it’s see-through. Yes, they’re aware that they’re not hiding, but they play at hiding themselves. Play has an enormous value in itself. I’d dare to say that, first and foremost, it’s the most important subject in education and in schools. As soon as young children start to walk and to be autonomous individuals, they start to play. We adults haven’t explored this enough; play is a huge area we need to look at.

When a teacher is working with children who are just starting school and they ask me what they should do, I tell them: “First, spend a whole term just playing, and then we’ll talk about what to do.” Playing with them, interpreting the game and changing it based on this interpretation, helps teachers learn to do their job.

Talk to us about your biggest influences in maths and teaching.

I don’t have many influences, because I haven’t read much – I don’t really like reading, and I’m also a very slow reader; a teaching book might take me two years to get through. I do like poetry, and when I was young I used to like crime fiction, but not anymore. And I love reading the Gospel. There are people who believe they know something when they’ve read it. I, on the other hand, need to see it or touch it.

Maria Montessori was the first pedagogue to make an impression on me, because when I was little I went to a Montessori school, and my aunt worked with her in Rome. At the beginning I liked everything about Maria Montessori; now I like a lot of aspects but not all of them. For example, I don’t like her approach to numeracy.

In terms of maths education, a clear influence is Dienes. I met him once when he came to Barcelona, when Franco was in power, and he gave a wonderful conference. And I also very much like Piaget, who’s not a pedagogue but a psychologist. I only know Piaget because I’ve read his work, whereas I know what Decroly did because I’ve been to Brussels twice to visit his school.

I’ve learnt a lot of interesting things from Decroly. All of his students’ maths learning is done through measurement. When I went there, there was an architect in charge of the geometry workshop. A child might want to go there because she has a half-made toy which she’s keen to finish, so she goes and talks to the teacher. I found it wonderful. If I were younger and I had the time, health and money, I’d go back to Brussels to see that workshop again, instead of reading Decroly.

And what do you think about Alexandre Galí?

The Franco regime dismissed him and then tried to defeat him during the early years of the Thalita school. But he wasn’t morally defeated; that’s what I most liked about him when we used to visit him at his home. Whenever we talked to him about the children, his eyes would twinkle – his green eyes. He fascinated me! What I remember most is how he got the children to write. Nowadays they don’t know how to write, something which is as important, or even more so, than reading. Writing, just like speaking, means knowing how to express what you’re thinking to others. He placed great importance on writing and he had a whole method which I’ve used myself in my classes.

Another person who has influenced me is Constance Kamii, a student of Piaget. From her I’ve learnt how important it is that students shouldn’t see or touch the material when they’re resolving mathematical problems. They see it beforehand, they touch it and move it about, but not when they’re counting. I find it delightful. It helps to build mental representation. It’s a method I like much more than the Montessori one.

In your opinion, what difference is there between a model based on discovery and understanding and one founded on mechanical processes and closed responses?

Those who choose a closed model want to resolve their own problems as teachers. In contrast, a model based on discovery and understanding focuses on the needs of this young person I have before me, the boy or girl, and not on my needs as a teacher. I think almost the only essential requirement is drive. Some people think that to be a teacher you need a good curriculum, a good inspector – I doubt they exist, not for maths anyway – a good classroom, good weather… If you need all this, you should go and look for another job.

Due to their family situation, by the age of four some children have already grown up and need to fight for their emotional survival. At school, that stops them from immersing themselves in spontaneous activity and play – they’re held back by something deeply embedded in them. How can we combine an educational system with circumstances that are sometimes complex, with children who might be deprived of affection, attention, health…?

I don’t know, it’s very difficult. On our way back from a trip to the Sahara, my colleague from GAMAR Miquel Mallent told me something that made a deep impression on me. In an area where people live in the middle of a vast desert, deprived of everything, he visited quite a big school, without many resources, and he assured me it was a very good school. The conditions are always good or bad compared to a situation that you imagine.

You’ve always taken this into account. When you went to Verdum, how did you adapt your teaching methods to the possible lack of resources?

I decided that I should turn every deficiency into an educational opportunity. For example, we didn’t have a playground; the school was a large hut in the middle of a piece of waste ground. As there was no fence, we had to teach the children not to run away at break time. This is no easy task, because as soon as he sees an opportunity, an angry child will run away. I also remember Miren, a girl with Down’s syndrome, something which I had no idea how to deal with, but then I thought she should offer a way to educate the other children. I had a very serious talk with them and told them that if anyone made fun of Miren, they would be suspended from school for several days, “because we can’t allow anyone to make fun of Miren, as it’s damaging to the class and damaging to her”. And they understood, even though they were only four to six years old. I used to say to them: “Show her how to walk up the stairs, how to wash her hands”. And Miren even learnt how to jump into a moving skipping rope! They did that off their own bat, I didn’t ask them to do it. Miren’s difficulties became a learning opportunity for the others; they learnt to respect her and she made us re-evaluate a lot of things. It happens to all of us: life’s hurdles can help us to grow if we know how to approach them well.

As teachers we’re forced to take into account the reality of our surroundings...

Of course. What you can’t do is say: “We don’t have a playground? Then we can’t do that…” What do you mean you can’t?! It’s like when you go to the mountain, and there are people who say: “No, you can’t climb that”. What do you mean I can’t? It was in this way, by taking on challenges, that mountaineering was born and how the great mountaineers were forged. And this is basically how the world makes progress in any type of field.

What is your opinion of the alternative educational models that are more respectful towards children?

Thankfully they’re becoming more popular and they’ve made some groups of teachers sit down and think. But I don’t place so much value on the models as I do on schooling itself, otherwise I wouldn’t have worked in schools all my life, because it’s the collective that educates the child. I’ve never had children, but when I was young I thought about what I would do with my children, if I had any: would I send them to school, with all the nonsense you get there? It’s a very delicate issue. Now I think that I would have sent them to school…

I remember when Ovidi Montllor visited us at the school, at Verdum. Ovidi was from Valencia, and he’d come to live in Barcelona for one or two years. He had a daughter who was ten or twelve years old. He told us “I’m a communist, and of course I want my daughter to go to a public school, but the thing is that they’re all Francoist. And because I don’t want to send her to a religious school either, I thought the least bad option would be to send her here.” He assured me that he didn’t mind if she learnt nothing (“Oh no, she should learn”, I told him), he just wanted his daughter to be happy. And the girl came and she was happy for the two years she stayed, because she felt welcome. Schools weren’t created to make children happy, but their happiness is the first prerequisite. If they’re not, there’s really no point.

So in your opinion, this is how we have to teach children: by paying attention to their happiness.

Children must be happy, but it’s not a question of making them happy to make their education more effective, but rather as the first prerequisite. In this life, we should be happy. And children are the weakest people because they don’t yet have the tools to defend this right, and we have to help them to defend it. If a child doesn’t learn at school, what’s the problem? There is none. They’ll learn some other way. The world itself has a lot to teach us. But we live in a society that’s set up like this: from six to fourteen, everybody needs to be in compulsory education. But what if they don’t want to go? In the same way, from the age of twenty onwards, or whenever, everyone should be happy at work. This might be a communist principle, but in any case it’s elementary; for me, it’s a Christian principle.  

Sometimes we have to remind ourselves of these obvious truths.

When I went to Verdum, people would say to me: “Oh, how difficult, and what a bad time you must have of it…” Well, no, I didn’t have a bad time of it; I still know those children from Verdum, they came to see me when I broke my leg, they care for each other… How could I have a bad time if the children were wonderful?

There was a child of eight years old; he was short, and he seemed younger. He didn’t know anything at all… Well, he knew a lot of things we didn’t know about, like how to get a knife and go rob someone on the street if he needed money. He had a lot of brothers, including an older one who went robbing with him. He finished his second and third years without knowing how to read or write. But he knew all about counting, because when he went out to rob people he also had to count. Our aim was for him to spend a few hours in a normal environment instead of being on the street, and for him to be happy at school. When he went into the fourth year he still wasn’t learning, and us teachers were very concerned. He didn’t learn because he didn’t want to, because if he had wanted to, he had all the resources he needed. Fortunately, children have the ability to close themselves off completely. I had to find another way to get Pepe to feel at least the slightest will to learn to read and write, and so I thought it would be a good idea to get him to teach something to me. He came on all the outings, he loved them, and he used to climb the trees…! He was incredibly good at it. So I said to him: “Look, Pepe, you have to teach me something which you do very well and I don’t know how to do. And while you’re here at school, I want to grab the chance to learn it.” That caught his attention. “And what is it”, he asked me. “To climb trees.” He gave a start...! “Right away, Miss!”

Pepe was one of the best teachers I’ve ever had, because he had a technique! Goodness, I was gobsmacked. I climbed up a very tall tree, scared stiff. But I took the chance… What’s more, I really did enjoy learning to climb the tree, truth be told. He must have learnt to do it by instinct, like monkeys do. And from that day on, his attitude changed and he showed an interest in learning to read and write. The fifth year teacher, Jordi, did a fantastic job with him, because he entrusted him with editing the school magazine, and he had to read all the articles to decide whether to accept them or not. That’s another example of how an obstacle can be turned into a means.

As a teacher, what do you think is missing in the relationship with children?

I can’t say what’s missing, because I haven’t worked with children for many years, and I don’t have much experience in how they react nowadays. I can only say what I see in other teachers. A lot of them have good relationships with their students, but they don’t think this is so important, when in actual fact it’s the most important thing. Teachers nowadays have been spoilt by textbooks; they feel lost without one. But in fact the problem with teaching is the system as a whole, even though teachers are the most important part.

Marta Mata thought that teaching could not be separated from politics; she had a comprehensive vision that I admired greatly. At the Rosa Sensat Teachers’ Association she taught us the importance of having a political stance – it didn’t matter what kind, but it clearly demonstrated. Well, I’ve never known how to do that… I’m more suited to entrenching myself on the front line. Teachers don’t all have to be the same. I think it’s highly necessary that there are some who are very politically aware and act on their beliefs; if this weren’t the case, we wouldn’t have managed to keep Catalan in schools, for example. Teachers as a collective are too credulous, too weak in the face of structures. There are some structures which are inherently bad and which we should fight against. But nowadays teachers aren’t up for fighting, they just want to do their work and go home afterwards and have a peaceful life.

At one point, just like Marta Mata, you felt you had failed in the context of schooling.

We had this feeling a few years after democracy was restored. During the dictatorship we ran into lots of difficulties, but we had never felt like a failure. In any case the entire country was a failure, not just the world of teaching. We thought that everything would work out because we had fought hard, but in the end we saw that fighting didn’t resolve anything. Marta may have died without ever fully having the feeling of professional failure, because she was a natural optimist, the same as me. But all of us from that generation felt it a little bit. Personally, I felt it when democracy had returned, when I left the Ton i Guida school to go to the Autonomous University of Barcelona. I set off with high hopes, thinking we could influence the new generation of teachers, and I saw how they came back from their work placements perturbed and with different values: they paid more attention to what they saw in the schools than to what we had to tell them. It was one of the moments when I felt the greatest sense of failure, and I lost a lot of my belief in university. The truth is I don’t know how teachers should be trained. I’ll never know as long as I live…

And what’s happening in the world? There’s enough misfortune and injustice to give us a sense of failure… As I have faith, I think that God created the world and that he guides it in one direction or another, even though we don’t understand it. The world evolves very slowly and we’d need to have control over the fourth dimension to perceive it. The fourth dimension is time. When we’re dead, we’ll be able to access the fourth dimension and we’ll see everything a little differently.

With this optimistic vision, what advice would you give a new teacher who is just starting out?

I have a lovely niece who has studied teaching, and even though I always thought she had everything it takes to be a teacher, I never dared give her any advice. They themselves have to find the keys to working in a world that’s not mine anymore. All I know is that doing maths and working in education makes me happy...

What have you been working on recently?

The day I retired, when they gave me the Jaume Vicens Vives prize for quality university teaching, was like a new start. I didn’t even know the University of Girona had put me forward for the prize. A part of the prize money went to the university for research. I don’t know what proportion, but I thought it was excessive because I blurted out: “But I’ve never been able to do research!” Afterwards I understood, because the university needed to give the person who had won the prize a workspace and infrastructure for as long as they wanted, and I’m not ready to stop working yet…

First of all I just decided to compile activities, materials. I had a lot of things that I used to use in the teacher training classes. Then I thought about gathering together teachers once a month. And that was over ten years ago… I only placed one condition on doing this work: that no one should phone me beforehand, because if they did, I wouldn’t get a moment’s peace all week. They found that hard to accept. One Monday a month – we call it an open day – they come and ask whatever they want. With the money I also got an intern who had been a student of mine at the university, who told me we should create a website. He said that in this day and age, you’re nobody if you don’t have a website. And that’s how the website came about.

The relationship with the teachers has been built up slowly, and with only a few of them. I don’t have much contact with the Faculty of Education. First I just gathered materials, then I set up the website and received teachers, and over the past few years we’ve been creating materials. I still discover new things when I’m making materials. One of my most recent projects was a curriculum for teaching maths from three to eight years. Eight years is a key moment for maths teaching, because it’s when children start to learn fractions and negatives. Nobody understands fractions; most teachers don’t know enough about them, I see that from the conversations we have.

My work has slowly become a new profession which isn’t teacher training in the classic sense of the word, and at the same time I’ve been learning from the teachers. But I got to the point where I felt I needed more contact with the Rosa Sensat Association. Since October 2014 I’ve been coming to Barcelona one week a month, to another office that I set up at the Association’s headquarters, where I’ve done things that hadn’t occurred to me in Girona. It’s called CAÀREM – the Centre d’Activitats i Àmbit de Reflexió per a l’Educació Matemàtica (the Centre for Activities and Reflection on Maths Education). I wanted it to have a grave accent somewhere, so that all my Spanish friends, of which I have many, could see that in Catalan we have a grave accent. I found it pretty hard to hit upon a word with a grave! 

What would you still like to learn? What are the main things you are curious about?

I’d like to see some of the universe’s different galaxies. Because of course, they say there are a lot of galaxies… And I can’t even imagine our own… And the fourth dimension, which I mentioned before. And I’d like to learn things related to maths or education; I’m not