Snehal: I’m Snehal Deshpande Roy, an engineering graduate, and have been teaching math for 10 years now.
After the birth of my first child, everything changed for me and my husband. We became more family-oriented and hence I opted for early retirement. We ended up deciding that we want to homeschool both our children which now has other students as well.
Sriram:Do you think there’s a fear of math in children?
Snehal: Not at all. There’s no fear of math in my children. The first reason would be they don't have any fear of evaluation. Also, they have ample time to discover what they have learned. But yes, I did come across fear for math while I was teaching kids who go to school.
Sriram: Why do you think there’s a fear of math in students who go to school?
Snehal:It’s mainly because we have created a problem & solution structure. If I ask that same child to write an essay or story, you’ll see there’s no fear of math.
Why is that?
Because there’s creativity and one can write an essay in many different ways. Whereas, in math, we are so used to treating it as a subject where there’s a problem and there’s only one way to solve it.
“For children, math is like passing a bridge between two mountains. If they don't use the bridge, they’ll fall in the valley of errors.”
That’ll create fear or anxiety. If we start teaching the subject creatively and start welcoming different approaches, I’m sure there’ll be less fear of math in children.
Sriram:What are the real-life benefits of learning mathematics?
Snehal: Every discovery that has changed the world today has been inspired by nature. That happened because of their understanding of math and those people were able to connect it to the outside world.
For example, One person found this randomness in the clouds, trees, and mountains very interesting. He made a theory about factors that changed the world.
After that one electrical engineer creates an antenna using the knowledge of factors. This antenna can take signals for more than one frequency. That went on evolving and we ended up with a mobile phone.
So basically, the reason we have a mobile phone is because of the factor model which was inspired by nature. There are endless real-life applications if you can connect mathematics to the real world.
Sriram: Do you think mathematics helps you look at the world and nature very differently?
Snehal: Yes, it does. Let’s talk about people who are good at mathematics. Maybe they found some way of connecting to the subject which made it easier to understand. They have a broad understanding of what is happening beyond calculations.
That’s what makes math an easy subject for these specific individuals. Whereas, the people who are not good at mathematics are maybe trying to remember or mug up everything.
For example, Brain has 7-8 slots for short-term memory. Let’s say that all of them are maxed out and you are receiving further information. This will overwhelm your brain.
Whereas, if you find a way to connect what you’re learning to something outside, you don’t have to mug it up anymore and hence have a way of recalling it. It becomes your muscle memory and then when you work on that subject, you find it very interesting. Imagination is a big part of learning mathematics.
“Imagination is a big part of learning Mathematics.”
Sriram:Is intuition and guessing important for mathematics?
Snehal:Yes, Intuition and guessing are really important.
For example: While teaching geometry, we give students the whole house that is readymade and asks them to recreate it. And if they can’t do it on the first go, we say there must be a lack of understanding. Whereas, we need to show them how that house is built, where are the guts & roots and what is the process that has gone behind.
This requires a lot of guessing, thinking, and intuition. Intuition and guessing will help you develop much needed critical thinking, which can be used in solving new problems.
“ Intuition and guessing will help you develop much needed critical thinking.”
Sriram:Do you feel that imagination, guessing, and intuitions were more predominant in the ancient world and hence we were able to build things like Pyramids, the Taj Mahal, etc.?
Snehal: Actually, yes. We always wonder how it's so accurate.
There's a lot of math involved in it considering the accuracy in that architecture. We could say that some of them did have the understanding of mathematics but there was also a huge part of intuition, guessing, and imagination involved in it.
Sriram: What are the implications for higher and specialized education? Let’s assume maths is started at a higher level, how should it be approached?
Snehal:I would say that mathematics should be taught at an early stage but the way of teaching it should be refined. It has to be nurturing in a way that even if you go for higher levels, you should be able to think creatively. There’s something called intellectual defense.
When you have gone through one structure for many years and suddenly you’re asked to do something different, your mind becomes rigid. You can't think creatively. To think creatively, you have to be more flexible. The intellectual defense is the phase when you become rigid. That’s where most of us go and it’s the biggest problem in the industry.
“To think creatively, you have to be more flexible, without intellectual defense.”
Sriram:As a mathematics teacher is it possible for you to make everything interesting and relatable?
Snehal:Math itself is derived from the outside world. It was created so that we can connect. The only reason why we could not find any resemblance with the outside world in a few concepts of maths is because of our way of understanding.
"Why is math so important?"
Maybe because of democracy. In ancient times, all the deals were discussed/finalized in one room. But as society grew, everybody had their own opinions. That's when people thought numbers are one of the ways where people can universally come at one level.
Sriram: Do you think that numerical skills are inherent?
Snehal: Probably one of the biggest misconceptions in the world today is that being good at math is an inborn talent. It’s not an inborn talent.
"Do you know how to play basketball the moment you’re born?"
No. It’s a skill which you have developed. The only requirement is you should be interested in learning. If you put in hard work, you'll become good at playing basketball. It’s the same with everything else. We don't know how to speak when we’re born but we never expected that speaking a certain language is a natural talent.
Just like that, maths is a skill. Just by being anxious or rigid, you’re closing the doors. You’re putting intellectual defense right in front of you. The moment you become interested, you become a learner. And the moment you become a learner, you start putting hard work and become good at mathematics.
Sriram: What tips would you like to share with people who think mathematics is some kind of a black box?
Snehal: I would advise starting seeing the numbers differently. Try to see how you can connect them to the real world. Let's say there is a headline in a local newspaper stating ten thousand people were infected in the area. If I sit and look at the number 10,000, I would realize that this is a false number because the total population in this area is around 10,000.
That would mean that everyone is infected by COVID. But that’s not the case. The moment you find a way to connect to numbers, it makes you quite consciously aware of your surroundings. Mathematics is designed to give a reality check of the social and physical world around you.
Sriram:Are there some real-life examples that you would like to share?
Snehal: One of my students was good at mathematics, whatever we used to do in class was very easy for him. We came across one problem which he just couldn't solve. I was just sitting there and watching him struggle. He came up to me and said: “why don't you try this?”. I started doing calculations with him as if I am his assistant. After 40 minutes of struggle, we couldn't solve the problem. He said, “I’m so glad I finally found something that I do not understand”.
He was having pleasure in the fact that he is stuck somewhere. I asked him to stay with that feeling and come up with a solution. And in the next class, we managed to solve the problem. That was a really good moment for us.
One student was really good at math but very academic. The moment you asked him anything out of the syllabus, he used to shut off. We had seen visible changes through the months when we had been taking the course with him. His thinking process changed drastically. He ended up creating a website for maths for younger kids.
"How do you know that you understood a subject?"
The moment you understand it, you have the urge to share it with other people. That is what happened with one of my students and that makes me feel really happy.
One of my students was pretty weak at math. He used to travel a lot during his younger years. His family was going through a transition from one country to another. This happened to him when he was around 8-10 years old and this is the time where you learn the basics of mathematics like multiplication, division, etc. He never really got the essence of it.
Even if he got promoted to the next grade, those concepts stayed the same. After that everything was coming on top of it and he was making mistakes because the concepts were not clear. We went back and talked about the basics. The moment concepts got clear, he became good at mathematics.
Sriram: Let me turn it around, what have you learned about mathematics?
Snehal: One of the most important things that I have learned because of my teaching is the approach towards the subject. I am one of those students who were afraid of geometry. But when the approach changed, everything just became so easy.
To teach students, I happened to push myself to be a better person who understands mathematics. If I wouldn't have been a teacher, probably I wouldn't have bothered so much to make these connections to the real-life world from mathematics.