“No subject has the ability to make you feel as stupid as mathematics”

And it is mathematics that is the protagonist of this conversation, from Inês' point of view, who attributes to it the characteristic of being the field that has the ability to make a person feel stupid, questioning their intelligence, but at the same time sharing characteristics with letters. Don't miss a word of this testimony:

[VÍDEO YOUTUBE]

We are only complete beings when we master letters and science

By default, or even by socialisation, we tend to think of education in terms of two poles: Literature and Science, Portuguese and Mathematics. In fact, logical mathematical reasoning is important for developing the ability to argue, for example. The two fields can be so closely related that, according to Inês Guimarães, they can have a symbiotic relationship.

There are many people who argue that this division that has been created between literature and science is very damaging, and I think so too. Because I think that the two fields can have a symbiotic relationship. And, for example, people think that mathematics doesn't require creativity, that creativity is something for the arts. This is wrong. Mathematics needs a lot of creativity. People think that in literature you don't need to have good reasoning skills, which is wrong. In order for a person to be able to articulate what they want to say rigorously and to convey the information in a precise way, they need to have good reasoning skills.

For Inês, we are only complete beings when we master letters and science. Although they are different fields, they are related. A connection that few notice and even fewer understand. This is because mathematics is considered by society to be the most challenging of the school subjects. According to our guest, this idealisation is due to the unique characteristics of the subject. Mathematics is characterised by the fact that it exists only in everyone's head, that it is not based on facts and that it is highly abstract. According to Inês, it is this last characteristic that gives mathematics its great power.

In the specific case of mathematics, what is it that makes mathematics different from other fields, and what is it that justifies so much time spent on explanations and everything else? Mathematics isn't just about knowing facts. It's not just about acquiring knowledge. You can't see mathematics, it only exists in your head. It's something very abstract. That's where its power comes from: it's something highly abstract that you can apply to an infinite number of situations. Other fields end up being more tangible. Mathematics is about ideas.

The fact that maths involves imagination, projection and abstract thinking is what sometimes makes it too complicated for most people to be a successful subject. For all these reasons, Inês points out that no subject has the ability to make a person feel as stupid as mathematics. That when you get a maths question wrong, you think your intelligence is being attacked. This is a misconception, says Inês, but it also happens because society has cultivated the idea of associating intelligence with mathematics.

People shouldn't think like that, they shouldn't feel attacked because they can't solve something in mathematics. But I think even in society itself this idea has been cultivated that intelligence is associated with mathematics and it has nothing to do with it. You can be intelligent and be bad at maths, and you can be good at maths and not be so intelligent.

Giving crutches to someone who can walk but is too lazy to run

Mathematics is the subject with the most hours of teaching, support and tutoring. Children are often given extra tuition in this subject early in their schooling, perhaps out of concern for their parents, because it is a challenging subject, or simply out of conscience. From our guest's point of view, it's ultimately a preventative measure, but it's like giving crutches to someone who can walk but is too lazy to run.

And I think there are a lot of children who are doing badly and their parents get worried and say 'let's go to private tuition'. They don't even give the child time to adjust. Sometimes it's normal to have a bad result and it doesn't mean that they have to go to private tuition and have a lot of difficulties. Then there are those who go to tutoring as a preventive measure. I don't think that's helpful either. Because I think students need to be independent, they need to cultivate more independent learning.

Inês argues that children need discipline and perseverance from an early age. Enrolling in tutoring at a young age is often synonymous with a lack of will, desire and commitment. It's not good for them to have someone in the background thinking for them. Inês isn't against tutoring, but she doesn't see the benefits of it when you're very young, because she thinks it might be necessary at some point. Then there are a lot of people who get good marks in maths, but they're nothing more than imitation monkeys. Our guest explains:

In school maths you can get more or less good results by memorising recipes. Like "OK, when a problem like this comes up, I'll do this step, and then this step... and it'll work". If you ask a more conceptual question to see if the student has really understood the concept, they probably won't be able to answer you. Why is that? Because they're used to following these recipes and doing these typical exercises. As soon as you present them with an exercise that is a little bit different, they won't do it. Because they don't have that conceptual knowledge, it's a mechanical knowledge: they've mechanised a series of techniques, but they haven't developed their reasoning. They haven't understood the concepts in depth.

 

In this context, it is important to understand and study mathematics from a conceptual point of view, so as not to fall into the trap of mechanising the subject. And perhaps the starting point at this level is to restructure school textbooks, which Inês Guimarães believes are full of rubbish.

I have mixed feelings about textbooks. Because on the one hand I think it's good to have a source of information, where you have everything, and for a good student, a student who really wants to delve into things well and rigorously, it can work. But in general I feel that textbooks are too dense, have too much information and end up not being very engaging. I think if I were doing a manual I'd probably go for something simpler. I really feel that maybe we need to take this step.

A maths teacher is a decisive factor in whether a person likes maths or not.

And if it's not the textbooks that convince a student, it could be the teacher. That's what happened to Inês. Although she already had a taste for maths, it was in the seventh grade that she began to develop an almost love for it. And it was all thanks to the teacher who told her that she didn't know anything about maths. 

One day I was doing an exercise and I got it wrong, or I can't remember exactly, and the teacher told me to go home and tell my parents that "every day I realise that I still don't know anything about maths". In other words, the teacher told me to my face that I didn't know anything about maths. I said "I'll show him I can do it", it was like a shock. And so I started studying maths every day from Year 7, solving problems almost all the time. Total obsession. I'm not saying it's healthy.

Despite the harsh words, which were almost a shock, they served as a click for Inês to cultivate maths in her life. And this is what often happens in schools: teachers can really make a difference in our lives, depending on how we receive and deal with the message they give us.

And one thing we have to be very careful about is that a maths teacher is a determining factor in whether a person likes maths or not. If you get a bad maths teacher you could be traumatised for life, if you get an excellent maths teacher you could discover a passion you didn't know you had.

Mathematics is a constant presence in Inês' life, who curiously didn't pursue a career in teaching, but is now diving into computer science.

Watch the full episode on YouTube, Spotify, iTunes or Google Podcasts.