By THOMAS HUKAHU
A WEEK ago, I shared on social network the death of Stanford mathematician Professor Maryam Mirzakhani and a few comments by friends had me pointing out essential things that students studying mathematics should keep in mind.
I also stated some startling points made by the Mirkzakhani, an Iranian, after reading an article that announced her death as well as contribution to the pure mathematics world.
There was one point that caught my attention. Mirkzakhani’s daughter described her mother scribbling equations on paper as like “painting”.
I learnt through years of studying the subject, as well as its sister-science of physics, that the best students in those subjects approach them as artists at work.
Students should study maths in the same way that people learn to paint. I call this the artist’s approach to learning. Someone who approaches the subject as an artist will dig deeper – and learn more, so he or she will become more confident in time and progress well in the subject.
How does someone learn to paint? By playing in a soccer field or painting while walking? No, you have to find a desk, sit down with your tools – the paintbrush, easel, and board – and paint. You can sit for one to two hours to paint. Nothing attractive will emerge on your drawing board if you think 15 minutes is sufficient for a good painting.
The same goes for maths. Students who want to do better in the subject must sit down with their notebooks, textbooks and review concepts learnt as well as completing all given exercises.
I call this mode of locking yourself in a chair for an hour or more a day “the artist’s approach” to learning. The serious student of the piano will do the same. They do not study the piano by walking along a road. They sit for an hour or more each day and work on finger exercises and going over different pieces.
The same applies to maths.
I tell students that I learnt this the hard way when I bombed my first test in grade 11, scoring about 11 out of 30, a kind of mark that I have never obtained in all of my school life. It was a shell-shock and I questioned my own abilities then.
However, it was the guidance given by my teachers to get me to actually sit down for an hour every afternoon and practise maths that actually saw me improve my marks.
That routine was the thing that had me walking through university without too many problems. I had learnt to properly study the subject when I was in grades 11 and 12.
There was a point made in the article on Mirzakhani that also caught my attention. She was known to be a self-professed “slow” mathematician.
Let me explain. There is a wrong perception that we have of brilliant mathematicians or scientists. We think that they are whiz kids – or child prodigies – and continue to be stellar scholars all through life; or they are human beings who can calculate sums very quickly.
The truth is some of the brilliant mathematicians of today are not that fast. Mirzakhani is said to be one – she said so herself.
Another Fields Medal recipient, French mathematician Cedric Villani has admitted “he is not good with computation of numbers” – like he cannot regurgitate the answer to a sum thrown at him. However, that has not stopped him from progressing in exploring the wonders of maths.
The important point here is that you do not have to be good with number computation to be a brilliant maths student, although possessing that ability can help you a lot. Algebra, trigonometry and basic geometry do not require students to be good with number computation. They have to follow processes or steps to solve problems.
From my years of learning and teaching maths, and the related subjects like physics and chemistry, I have found these important for students:
1. Spend one hour or more daily on maths;
2. Always complete all your homework daily. One day’s work builds on past day’s work;
3. Review all notes taken in the day;
4. Go over problems and examples given in class.
5. Attempt problems similar to what you did in class in supplementary texts:
6. Ask when you do not understand – ask your peers and ask your teachers.
As in learning painting, the piano or violin, or playing football, the student who spends more time on reviewing the basics and other stuff will always do better than the others. Practice makes permanent.
If you have completed all given work – work from your textbook – look for other sources, like other textbooks and complete problems that are similar to what you are learning in your course.
Today, the internet is filled with resources – Word documents or PDFs of all sorts of topics in calculus, geometry or statistics.
Download files and notes and do exercises listed in them – exercises that are similar to what was given in class. In a way, students today should be able to do better than students in the past because the internet is full of resources.
Even top universities in the world are sharing their material in open-source course material. Videos of professors lecturing on different topics are also posted online.
Take the time to explore those to supplement what you learn in class. The more enriched you are, the better you will do in maths.
By THOMAS HUKAHU