A translation of my interview with Spanish daily Newspaper ‘El Economista’ discussing maths education. You can read the original version here.
Mathematics continues to be in many cases the bone subject of some students. The focus of this problem for much of society has fallen on the way numbers are taught, but is this really the problem? Tom Crawford has a doctorate in mathematics and currently works as a popularizer and professor at the University of Oxford. His goal is to share his love for mathematics and spread it through lectures, radio shows, interviews, etc.
How should mathematics be taught in schools?
Through stories. Teaching through storytelling is an incredibly powerful tool and one that is not used enough in math. For example, when teaching trigonometry, instead of just stating the formulas, why not explain WHY they were needed in the first place? By ancient architects trying to build monuments, by explorers trying to estimate the height of a distant mountain. These are the reasons that mathematics developed and I believe that teaching it through these stories will help to engage more students with the subject.
Are teachers prepared to teach this subject correctly?
I don’t think teachers are to blame – they are told to follow a particular curriculum, and due to their heavy workload, they don’t have time to develop engaging lessons at the heart of their design. Of course, there are ways we can help teachers by providing examples of ways to make math content more interesting and engaging. This can be through storytelling or applications to topics of interest to students, such as sports and video games. This is what I am trying to do with “Tom Rocks Maths”, for example, see my video teaching Archimedes’ Principle answering the question “how many ping pong balls would it take to lift the Titanic from the bottom of the ocean?”.
From your point of view, what should a math teacher be like?
The most important thing is to have a passion for the subject. The level of enthusiasm and interest shown by the teacher in presenting a subject will be passed on to the students. Just as enthusiasm is contagious, so is a lack of it. Beyond passion, there is no typical profile of a math teacher. Anyone can be a mathematician, and it is very important that people do not feel that they have to conform to a particular stereotype to teach the subject. I have always been myself and I hope that as a public figure in mathematics I will inspire others to do the same.
“The level of enthusiasm and interest shown by the teacher when presenting a subject will pass to the students”
Sometimes this subject becomes very complicated for some students, not so much because of its difficulty, but because of the way in which it has been taught. What should be done with these students?
The trick is to find a way to explain a topic that resonates with a particular group of students. Let me give you an example from my research: the Navier-Stokes (NSE) equations. For students who have no real interest in math, I would try to get them involved by explaining the $ 1 million prize that can be won by solving these equations. For students who are more interested in real-world applications, such as Engineering or Biology, I would tell you how the aerodynamics of a vehicle or the delivery of a drug into the bloodstream are based on an understanding of Fluid Mechanics and the NSE. If the students are sports fans, I can explain how equations are used to explain the motion of a tennis ball through the air, or to test the perfect training in road cycling. Finally, for students who are already enthusiastic mathematicians, I would explain how equations work in almost all situations, except for some extreme cases where they result in “singularities”, which as a mathematician are the ones you are most interested in understanding. Once you know the interests of your audience, you can present a topic in a way that helps them engage with the material.
Can you come to hate math?
It is certainly possible, though of course oblivious to a mathematician like me. I think this feeling of “hatred” is related to the way the subject has been taught or to a lack of understanding. If you did not enjoy your math classes at school and harbor negative feelings towards your teacher, you will begin to develop negative feelings towards the subject. This is not because you don’t like the subject, but rather because of the way it was taught to you. Similarly, if you don’t understand the math, it is very easy to develop a “fear” of the topic, which can quickly turn into hatred due to feelings of inadequacy or stupidity if left unaddressed. It’s all about finding a way to approach the topic that fits with the knowledge and experiences you already have. If you present a problem abstractly by manipulating random numbers to find a given total, then most people will have a hard time, regardless of their mathematical ability. But the same problem presented in a relatable situation suddenly becomes understandable. Here is an example:
(a). Using the following numbers, make a total of 314: 1, 1, 2, 5, 10, 10, 20, 20, 50, 100, 100, 500.
(b). You go shopping and the total is ?? 3.14. What currencies would you use to pay for your items?
They are the same question, but in (a). the problem looks like a math question and in (b). It is an everyday situation that people all over the world are used to. They both require the same math to solve, but even people who “hate” math could tell you the correct answer to (b). using your own real life experience.
Women are at a great disadvantage compared to men when it comes to entering a STEM career, why do you think this is happening?
First of all, as a man, I am certainly not qualified to answer this question, but I will at least try to give you my opinion based on my personal experience. At the high school level, I think the difference is less severe (see this link for example ) and even in college there are slightly more women than men studying science-based subjects (see this link). BUT, the problem occurs after this. In graduate programs and beyond, there is a distinct lack of female researchers, and this is further amplified in higher-level positions. One explanation could be that academic ‘tenure tracking’ positions exist for life, and many of the men who now hold these positions have done so for the past 30-40 years and were employed when we were doing a lot of work. worse when addressing the gender gap. Now that awareness of these issues has increased and overall we are doing a much better job of addressing them than 30 years ago, hopefully we will start to see more women in leadership positions in the next few years, it will only take a short time for the effect to be seen. I also think that in general, There are not enough female role models within many subjects (especially math) who have reached the pinnacle of their field (through no fault of their own), and as such there is a lack of role models for young women. researchers The achievements of female mathematicians such as Maryam Mirzakhani (2014 Fields Medal) and Karen Uhlenbeck (2019 Abel Award) should be celebrated even more precisely for this reason.
“There are not enough female role models within many subjects (especially mathematics)”
Do you consider that mathematics is given enough importance in the educational world?
In the past maybe not, but attitudes are certainly changing. With the increasingly important role that technology and algorithms play in our lives, people are beginning to realize that we need to better understand these processes in order to make informed decisions, and math is the key to doing so. Employers are certainly aware of the invaluable skill set that a mathematician possesses, and as a result, more and more students are choosing to study the subject at grade level and beyond to improve their competitiveness in the job market. Ultimately, attitudes are changing for the better, but there is still more to do.
In your opinion, what is the best way to teach this subject?
Storytelling is key to making your material as engaging as possible and knowing your audience’s interests allows you to present the topic in a way that is more engaging to them.
What is the current status of mathematics research at the university?
I think the main problem facing research mathematics is the relatively recent trend in short-term research results. Most of the funds available to mathematicians require the continuous publication of new results or results that can be easily used in an applied environment. The issue of continuous publication means that researchers feel the need to publish a new manuscript every few months, leading to very little progress at each step, and a large amount of time spent writing and formatting an article rather than performing a real investigation. In many cases, the work would be much clearer if it were published as one piece in its entirety after several years of careful work. The momentum of short-term research results means that it is now very difficult to study mathematics just because you have to be able to convince your funding body that your work has real-world applications that will be beneficial to you. society within the next 5-10 years. To show why this is a disaster for mathematical research, let’s take the example of Einstein and his work on relativity. Now viewed as one of the most fundamental theories in physics, his work had no practical applications until the invention of GPS 60 years later. In today’s market for short-term results, it is highly unlikely that Einstein’s work was funded.