Laura Morera, PhD in Mathematics Didactics from the UAB, explains that mathematics is taught in many educational centers in a friendly environment, building knowledge among all students, leaving no one behind and introducing the challenge component, especially for the most seasoned. “This scenario is not only possible, but also desirable, and not only in primary education but in secondary education as well”, points out the co-author of Learning to teach mathematics in compulsory secondary education .
"We have come a long way in understanding how mathematics is taught and little by little it is spreading in schools, but, like everything else, the changes are gradual." He attributes this slowness to many factors, but focuses on teachers, both in the lack of knowledge of the subject (which occurs more among primary school teachers), and in classroom management (which fails more among teachers ESO) and in the didactics of mathematics. "You can give a master class in mathematics, but if you can't make them listen to you...".
He has 17 years of teaching experience in primary, ESO and university. And she is responsible for didactics at Innovamat (an organization that promotes competent and personalized learning of mathematics).
In a classroom there are students with a predisposition to understand mathematics and others who do not understand them and who worry them. They start from very different situations. How does the teacher get everyone to follow the same rhythm?
In reality, no one should be afraid of mathematics, thinking that "they are not good at it." And the truth is that mathematics anguishes less and less. It is true that it is a hierarchical matter that must lay the foundations well so as not to be left behind. But it is also true that now he returns over and over again to the same concept, giving new opportunities to learn. Some will understand it the first time, others, at another time. And fewer and fewer errors are penalized or destructive feedback is given.
The demolishing “you haven't tried hard enough”.
Now it's, okay, you still don't know how to do it, but keep going, I'm going to accompany you and, with the right clues and your effort, you're going to get it. The key is that learning is built among all students and if one does not respond appropriately, nothing happens, another will explain it. The focus is not on the error but on contributing to know more.
There is also the question of time. "Solve this in the shortest possible time."
Time is good for teachers to see what strategies each student is using. Lets you see which of your 25 students is struggling. But this strategy can be experienced as a competitive situation and can block some students. In this sense, it is good news that the new curricula introduce the socio-emotional factor. There are many teachers and professors who already work like this.
Why have the math skills of Catalan schoolchildren fallen?
I don't think it's crashed down. The exams have become more complex and there are students who have not learned in a competent way. I think that's part of the problem there. If you don't learn to reason, you can't do it on a test.
For example?
It is one thing to identify a series of triangles and quite another to ask what kind of figures you can use to build a rigid structure. Arguing is more difficult than solving contents of A, B, C...
Can a student who studies in a competitive way solve a non-competitive exam?
Yes, but the other way around is very difficult. If you understand the process and know how to reason and deduce, you can answer a specific operation.
With competency teaching, is there enough time to give the entire curriculum?
There are teachers who think that they cannot give "contents" and "processes" with the assigned class hours. But there can be rich activities, of a competence type, that develop both. In mathematics, the contents are given many times from different perspectives. It is like an iceberg, the content is the tip of the iceberg, if you know how to add you have many things that support: numbering, packaging, decomposing... If one day you do not remember by heart how much 7 6 is, you have strategies to find the alternative of 6 6 1 If we always build learning like this, you get a more solid and connected knowledge.
Competence and personalized learning. Will failing in math go down?
Sure. We already have evidence that teaching constructively reduces failure.
Despite the measures, there is still a bias between girls and boys.
Many variables have been identified in this question and an answer is being provided. Like referents and models. Changes are slow, but it is getting better.
What about gifted students interested in numbers?
Classes should be high-ceilinged and low-floor so everyone can participate. You can give certain students new challenges in that same activity, without advancing the agenda. For example, you can ask them not to put only one answer but to look for all the existing possibilities. With the prime numbers you can propose that they see if from the number 4 to 100 they can find an even number that is not obtained with the sum of two primes (Goldbach's conjecture, still open). They're going to love that.
Why do I have to learn the square root? That's what the students ask.
The important thing is not so much knowing how to solve it as understanding the operation and learning strategies to obtain solutions. In the future, we are going to have to adapt to unpredictable situations and we need everything that learning mathematics brings us.
Are teachers prepared for these changes in teaching?
There is a base of teachers trained decades ago and some have not been updated with training. Some would improve their classes with didactics of mathematics (what activities or skills are necessary to understand a new concept) and how to manage the classroom (generate learning opportunities). Others need to reinforce knowledge about the subject. The important thing is to continue training continuously. A teacher can always be a better teacher.
What does a teacher need to know?
That children must acquire certain skills before understanding a concept. Brick by brick a concept is built, and it is necessary to ensure that no one skips any. The students have to practice afterwards. The more the better. We recommend that this practice be done through technology because that way the teacher sees how the class is going. They are small photos that allow us to detect those who have not understood it and the brick that they do not know how to lay. If you help yourself at the moment, much better than waiting for the evaluation to finish. In the end, what teachers want is for the maximum number of students to go as far as possible.
Mathematical societies have raised an uproar over the reduction in hours of mathematics in the early childhood and primary education grades. The institutes complain about how the students arrive. On the other hand, the aptitude test to be a teacher in Catalonia (one of the few communities that takes it) leaves 4 or 5 out of 10 unfit and they are examined for 4th ESO content.
Teachers know about education and perhaps do not always have enough training in the specific subject, be it math or language. In secondary it is the other way around, they are graduates in the subject, very specialists, but their knowledge of didactics or classroom management comes from a one-year master's degree. Hence the importance of continuous training, which is not easy because teachers do not always see it as necessary. But they must think about the following, that they can give a great master class in ESO, but if they don't manage to be listened to... This is a very complex and demanding profession that should be highly regarded by society.
In contrast, few mathematicians want to be teachers.
I studied at the UPC and I was the only one who wanted to be a teacher. It's a shame. It seems like it's an easy profession, followed by those who aren't good enough to go to consultancies, banks, or PhDs. Actually, the best should go because a teacher helps individuals to be better, have better values, understand the world better. And with this they do good to society, the world is better. And the reward of seeing the excited face of a student who has understood something is priceless. It is also true that the difference in salaries between companies and schools does not help.
How can you earn that prestige?
I give the example of soccer. Many people watch matches, follow broadcasts, read interviews with athletes, coaches, and referees in the press. We all also have experience in education and it does not have the same impact. More examples of good teachers should come out.
Maybe someone who likes pure mathematics doesn't like to teach.
There are stereotypes with mathematicians. When I say that I am a mathematician, people tell me that I don't look like a mathematician. And what is a mathematician like? I ask. In the end, he is someone who likes math. The series that characterize us with the stereotype of an introverted boy, with glasses, always in the library, hurt us a lot. They push girls away, for example.
Was it difficult for you to make the decision?
When I was little, I already put the dolls to learn. And later, I helped my classmates with materials that I invented. I already knew my vocation. My doctorate is on didactics of mathematics.
And you no longer work as a teacher?
I decided to teach teachers and professors because the repercussion is greater than if I taught. Innovamat is in 1800 schools, close to 350,000 students. But many times I run away and the teachers let me teach with them in their classes. Last year I was a co-teacher in an ESO class. I learn a lot. Practice and research feed each other. And I am a volunteer at Estalmat Catalunya, a project of the Royal Academy of Exact, Physical and Natural Sciences to stimulate mathematical talent.
Do math teachers have to be mathematicians?
They can come from other professions if they like math and teaching. Personally, the one who says "I am a veterinarian and I teach mathematics" bothers me. No, I reply, you are a mathematics teacher, although you trained as a veterinarian. If I were a math teacher and I had to do 2 hours of biology or physics, I would have to learn the subject, soak myself up, and transmit passion. If you transmit the basics, without passion, the students do not learn enough.
Scopes and projects, do they drown out mathematics?
The best thing for meaningful learning is to touch all the contents and processes from different areas. I am not against anything as long as mathematics is not reduced. There are brutal projects that come from various disciplines. There are others that start from one subject and make connections with others. That's fine, let's accept that mathematics is relegated to being an instrument, but this can happen if, instead, in another project that same course they are the main subject. Fractals, for example, and then you connect with history, art, biology...
How will AI impact teaching?
He is yet to study. It can be used to help teachers find more activities or as a virtual tutor for a student with difficulties. To evaluate. I play. I throw problems at him and if he doesn't solve them well I give him clues. Be careful that I have asked you for a 5-figure number and you have only given me 4. And he apologizes and gives me another piece of information. And I answer again. Now you have given me 5, but it does not meet the fact that they are even... I think that an activity could be done with the students proposing that they connect with the chat, that they give them a problem that they do not know how to solve, and that they have to achieve, without giving them the solution direct, that the chat ends up doing well. Correcting this conversation gives me a lot of information about the students. Your level of reasoning and communication.
