James Tanton, (PhD, Mathematics, Princeton University, 1994) and Guest of Honour and Advisor at Infinity 2023 organised by Aditya Birla World Academy, opens on techniques to make the discipline of Mathemetics simpler, easier and interesting for students
James Tanton is PhD in Mathematics from Princeton University and a Mathematician in Residence at the Mathematical Association of America in Washington DC. He is deeply interested in bridging the gap between the mathematics experienced by school students and the creative mathematics practiced and explored by mathematicians. He has worked as a college professor for a decade and as a high-school teacher for a decade.
Tanton speaks to BW Education and discusses about other techniques to assist the students in Mathematics. Excerpts:
What are your views on UK PM Rishi Sunak’s plan to make Mathematics a mandatory subject for all children in the UK until they turn 18, considering that India already follows this practice and the benefits it brings?
This is a yes and no answer because currently, the state of Mathematics education for elementary, middle and high schools across the world is in a troubling state. So much of it revolves around memorising formulas and getting the correct answers to sums and problems under pressure and speed. None of this makes for a joyful learning experience, leading to maths becoming a dreaded subject for many. In fact, a survey conducted a couple of years ago revealed that every four out of five children in Classes 7-10 across India fear maths and this fear grows as they move to higher classes.
As a mathematician and teacher, this is saddening to learn because I’ve spent decades of my life unfurling the sheer joy of mathematics and to think that students today aren’t experiencing any of that and are instead stuck with a subject they fear and dread, is not a comforting thought. If we are really serious about having children learn mathematics compulsorily till age 18, we have to work to change the way we teach it and instill a sense of joy and wonder in the process.
Mathematics has engaged and fascinated humankind for thousands of years. And it is not because of answering questions under pressure and at top speed, but because it has helped us to think and discover answers to complex problems. For instance, if we are teaching students standard long-division algorithms, the goal here isn’t to get the right answer as fast as possible because even calculators and technology can do that. The objective should be to teach them the structure of numbers and help them understand what led to the answer. We have to be able to teach them how to think; if you are not teaching thinking, then I say, don’t do it. Teaching mathematics has to move beyond finding answers quickly and correctly. Instead, we have to infuse it with the joy of storytelling.
Take for example the reason why we have a base 10 system, it is because of our anatomy. We have 10 fingers on our hands and the most common number systems have 10 digits. In fact, the term ‘digit’ used for numerals actually originates from the Latin word ‘digitus’, meaning finger or toe, reflecting the way we use our fingers to count. In some regions of the UK and Europe, counting typically starts with the thumb and ends with the little finger. In contrast, in India, counting is done by using the lines between the segments of the fingers, allowing each finger to represent four numbers and the entire hand to represent 20.
Each of these processes tells a fascinating story about cultures and people and their role in shaping the history of mathematics. We have to be able to teach this to students so that they can make these interdisciplinary connections. It is only then that they can truly appreciate a fascinating subject like mathematics and not fear it. So I have no trouble teaching mathematics till age 18, but we have to make it all about the human experience, thinking, problem-solving and joy.
What are your views on Maths education in India and globally?
In education, both in India and globally, a common belief is that success in mathematics is solely measured by passing standardised tests. However, this is an incomplete and narrow view of mathematical aptitude. Mathematics is a creative process that involves finding solutions to novel problems through deep thinking and contemplation, much like a writer would approach their craft. The emphasis on speed in teaching mathematics in schools detracts from the true essence of the subject, which is about modelling and problem-solving. While procedural fluency is important, it should not be the sole focus in teaching mathematics. Instead, a more comprehensive approach that values creativity and critical thinking should be encouraged.
Key takeaway educationists can pick up from Indian mathematician’s study versus global and vice versa.
India boasts a rich and illustrious mathematical heritage going back thousands of years. The country has nurtured countless mathematicians and groundbreaking mathematical concepts. Take for instance one of the greatest milestones in the history of mathematics – the Hindu-Arabic numeral system, which represents an infinite number of numbers using just ten symbols (0-9). It is one of the most notable contributions to the discipline of Mathematics because, as compared to previous systems like the Egyptian system, where each number had its own symbol, this system made it much easier to write and manipulate large numbers.
Similarly, the roots of modern-day trigonometry lie in ancient India. A branch of Mathematics that deals with the relationships between the sides and angles of triangles, Trigonometry was originally developed for the purpose of solving astronomical problems in ancient Greece and the knowledge travelled to India possibly along Roman trade routes. The earliest known reference to trigonometry in India is in the text ‘Suryasidhanta’ from around 400 CE. Indian astronomers made significant contributions to the study of circular motion, which was eventually translated into Arabic and Persian and brought to Europe. In the 1500s, European scholars saw the mathematics being done in India and Spain and used this as the basis for a textbook on triangles, which later became known as Trigonometry.
Despite having access to all these beautiful and powerful origin stories, students in India and abroad don’t learn about this and the modern education system has sadly lost out on this connection between storytelling and teaching maths. Stories and narratives can serve as powerful tools of inspiration, helping young people across the world to develop a passion for mathematics over time.
Why are inter-school competitions such as Maths Infinity needed on National and Global Platforms?
While I have personally never been a fan of competitions, I do understand that they can be exciting and motivating and can actually encourage students to hone their mathematical skills. Also, for those students who thrive on competition, it can be a great opportunity to boost their self-confidence and help provide a sense of accomplishment in the field of mathematics. Also, more importantly, Maths competitions require students to collaborate and work with each other which can help build valuable teamwork skills. National-level maths competitions can, thus, be a valuable experience for students, providing opportunities to learn, grow and achieve recognition for their skills.
Maths and gender bias, what could educators do to make it gender-neutral?
I think that Maths has somehow always been enmeshed in this narrative of it being a high-powered subject that requires speed, efficiency and winning – these are all attributes that are typically associated with the male psyche. This idea is perpetuated in our current education system, where the emphasis on winning under speed has affected the way Mathematics is taught in schools, without benefiting either girls or boys.
Imagine what we could accomplish if we could break out of this misplaced narrative and approach mathematics from a more holistic perspective that involves more thinking and creativity. Take for instance students writing an expository essay on why it took humankind so long to come up with the concept of zero and why it was such a hard number to understand. Elements like this make Mathematics a more inclusive subject that can cut across barriers of race, gender, politics and geography and help make it a loved subject that brings students together.
Quick tips on how to love your Maths.
My number one piece of advice would be to banish the notion of treating Maths through a solely formulaic lens that focusses on getting students to find answers to problems at speed. Loving mathematics can only happen if we work to find the stories behind mathematical concepts. Most Maths taught in schools may seem sterile, but there is a rich history and fascinating stories behind each concept.
For example, the word ‘fraction’ comes from the word ‘fracture’, which relates to breaking bones. It makes sense as a fraction is a piece of something. Similarly, the English word ‘sine’ has its roots in a series of mistranslations that began with the Sanskrit term ‘jyaardha’, which means ‘chord half’. This term was frequently abbreviated by Aryabhata to ‘jya’ or ‘jiva’. During the translation of Hindu works into Arabic, the word was transcribed phonetically into the Arabic word ‘jiba’, which had no meaning. Since Arabic is written without vowels, later writers interpreted the consonants as ‘jaib’, meaning ‘bosom’ or ‘breast’. In the 12th century, when an Arabic trigonometry work was translated into Latin, the translator used the Latin word ‘sinus’, which also meant ‘bosom’ and evolved to mean ‘fold’, ‘bay’, or ‘gulf’. This Latin word is now the English ‘sine’. Imagine if students could keep learning such stories; we could transform the way mathematics is taught in India and around the world and eventually create a powerhouse of insightful young people who don’t hate the subject.
