Irma Saiz and Mathematics

Irma Saiz is a mathematics professor and creator of many of the math books used today in Argentinian schools; she tells us today about her motivation to make young people fall in love with her favorite subject. She is a charismatic, funny and tremendously intelligent woman, ideal to open Boost section!

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She studied Mathematics at the Universidad Nacional del Sur in Bahía Blanca, Argentina; she researched in France for two years: one year at the Université de Lyon with Maurice Glaymann and another year at the Sorbonne in Paris with Gérard Vergnaud. Subsequently, she completed a Master’s Degree in Pedagogy of Mathematics at the Centro de Investigaciones y Estudios Avanzados del Instituto Politécnico Nacional in Mexico.

She has been a consultant in the design of new curricula for compulsory schooling and teacher training in Mexico, Chile and Argentina. She has given courses and talks on topics related to the learning of Mathematics in the above mentioned countries as well as in Spain.

She has developed research and publications for both students and teachers and presented research reports. She recognizes herself as someone very interested in modifying the relationship with mathematics that some children and adults have with mathematics and has spent a lot of time in the classroom, observing classes and students at work.

Interview to Irma Saiz. Corrientes (Argentina), April 2022

Sonia Megías: This afternoon, we are at Irma Saiz’s house. She is a math professor; I’m so happy to have her with us! According to what many people tell me, her math books have marked “a before and after” in the teaching of mathematics in Argentina. Good afternoon, Irma. How are you?

Irma Saiz: Fine! Shall I sit down?

SM: Yes, please! Let us know how you get boys and girls hooked on math through your books.

IS: Well, that’s exactly what we try to do. On one hand, because math is a marvel, it’s beautiful, it’s elegant, it’s very natural, and it’s the first science that humankind developed. Mathematical ideas and regularities are taught to us at an early age, and it comes to children naturally. So, we encourage children to discover that beauty, and the elegance of mathematics.

Beauty, not in the abstract sense of observation, but the beauty of making it by yourself. That’s why our books are called Hacer matemática (Making Mathematics). How do children learn to speak? By talking, by trying out how to use a word or not, and by making mistakes… And there’s always some help from adults, but it’s not like “Now I’m going to teach you how to talk”. It’s not like that.

The traditional way of teaching math has been: I teach you, you try to understand what I taught you, and then you repeat it. But I don’t agree, that’s not how one learns! It is by experimenting, by trying to do things with the teacher’s input, yes; but that idea of being taught and then repeating…. buff!

Math, as an Argentine mathematician says, has bad press. People talk badly about math. Either it’s loved or it’s hated.

SM: And you achieve that love towards math through your books, right?

IS: Sure, that’s the goal! But yes, we get children to enjoy math, because they feel very involved in the learning process: they give their opinions, they discuss…

"Hacer Matemática", uno de los libros escrito por Irma Saiz junto con Cecilia Parra.
“Hacer Matemática”, uno de los libros escrito por Irma Saiz junto con Cecilia Parra. / “Hacer Mathematics”, one of the books written by Irma Saiz together with Cecilia Parra.

SM: For how long have you been doing this job?

For twenty-five years already! We published our first books twenty-five years ago, together with my colleague Cecilia Parra, at a distance, traveling to meet each other. Today, thanks to technology, we have fewer problems! Actually, our books brought us a lot of satisfaction! We even know mothers whose children don’t use our books at their own school, but they encourage them to work on them anyways in the summertime, since the teacher’s help is not needed to solve the problems.

SM: Oh, how nice that is!

IS: Of course, the teacher can and should give them much more.

SM: You have also elaborated books for adults and teachers alike; and you have also participated in compilations…

Yes, one of the first ones was this one, called Los niños, los maestros y los números (Children, Teachers and Numbers), which talks about when children first learn their numbers. There are research articles which appeared in Mexican magazines, and this particular one is also for teachers…

It states: “Children have to build upon knowledge”, and well, how are they going to build it if they do not know how to build? And when you listen to little children (it used to be at age six), but now it’s from the age of four onwards, anc they say for example: “oneteen, twoteen”. Nobody taught them that, and they didn’t hear it from anybody, but they have discovered that there are many numbers like that: sixteen, seventeen, twenty-five. So, this shows us how kids are thinking in items such as abstract numbers.

We have another example from a colleague: A boy was playing in the little square in front of their house, and suddenly he shouts “Mamaaaa!” She goes running to see what’s going on, and the child asks “After 1000 follows 2000 or 1001?”. Do you see what I mean? He’s playing soccer, he’s 6 or 7 years old, and he’s already thinking. That’s what we mean when we say that math is elegant: that it has its own logic, which is also very accessible to students. Like all learning, it is necessary to practice, but it happens on the other hand, not by learning the multiplication table by heart.

SM: Before working on math books, you were a teacher, of course. You already knew the breeding ground.

IS: Yes, I did. I have worked with many teachers, and I was in the classroom watching. Actually, what I found even more interesting was observing classes even though I was not the teacher, because the teacher doesn’t have too much time to observe; they have to be there interacting with students. On the other hand, from outside this exchange situation, one can see many things, including how students are working.

We used to work on teamwork and collaboration. How groups collaborate in learning, which allows them to compare, to interact with each other, to fight mathematically. Students are not supposed to ever fight with a teacher, of course. The teacher is the one who knows. But among them, it is not clear who is the one who knows, and who is the one who does not, so they ensue in arguments in order to defend their ideas; and that is precisely what learning is all about.

Problema Irma Saiz y las matematicas
Problema incluido en uno de los libros de matemáticas escritos por Inma Saiz. / Problem included in one of the math books written by Inma Saiz.

SM: One last message, as a summary for our readers: What do you want to tell us about math to encourage others?

IS: That it’s marvelous, and that everybody should get into mathematics! Because it is a pleasure to think and reason, and to fight, as much as they can, for a different mathematics. There are already calculating machines, which do a 235 x 418 multiplication in a second and do it very well, but they can’t solve problems… for the moment! We don’t know what will happen when artificial intelligence continues evolving… But for the moment, we have to do with children what an “almost-free-little-device” does not do. Right?

SM: Thank you very much, Irma. It was such a pleasure to be with you today!


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