Summary

Andrew Plummer, a math tutor, shares insights on effective learning and teaching strategies gained from his experience tutoring high school students, emphasizing the importance of belief in one's ability to learn, passion for the subject, and the ability to explain concepts in simple terms.

Abstract

Andrew Plummer began tutoring math with no prior experience, initially believing he was effective due to his students' affirmations. However, he later realized his teaching approach was flawed. Through his journey, he learned crucial lessons about education: firstly, that a belief in one's learning capacity is essential; secondly, that passion for the subject matter significantly enhances the learning process; and thirdly, that true understanding is demonstrated by the ability to explain complex concepts in layman's terms. Plummer uses these insights to teach math, statistics, economics, and data science, and he imparts these lessons to his students to foster better learning outcomes.

Opinions

The author initially overestimated his tutoring effectiveness, mistaking polite affirmations for genuine understanding.
Overcoming the belief that math is only for certain types of people, like Bill Gates or Mark Zuckerberg, is crucial for learning.
Grit and perseverance are key differentiators between those who succeed and those who do not, as argued by psychologist Angela Duckworth.
Connecting math to a field of interest, such as data science, can make learning more engaging and effective.
The author emphasizes the importance of being able to explain concepts simply, suggesting that if one cannot do so, they likely do not fully grasp the material.
He encourages students to find value in math by relating it to their career aspirations, such as law or business, where data literacy is increasingly important.
The author advocates for teaching new skills in an entertaining way if they are not directly related to one's goals, citing his own experience with a math professor who used engaging stories.

What High School Students Taught Me About Teaching

And how I use these lessons to learn anything.

I started tutoring math to high school students in December 2018. I had zero tutoring experience — outside of helping a friend with their calculus homework — but the tutoring center desperately needed a math tutor, and I desperately needed to pay my tuition.

I remember my first day on the job. I wore a dress shirt (no tie, thankfully), black pants, and formal footwear. Meanwhile, everyone else (including the manager) wore jeans and a sweater.

At the time, I thought that my first tutoring session went great. When I asked my student if she understood a concept, she would respond,

“Yes, this makes sense.”

I always only had to explain a topic once — I was that good.

Over time, I realized that my first tutoring session had, in fact, gone horribly wrong. I had covered the material too quickly for anyone to understand, I had used words she was unfamiliar with, and I had dressed like a stern math teacher who, if we were at school, she would have avoided.

Thankfully, I’ve learned a lot since then, about teaching, and, conversely, about what it takes to learn anything.

1) If You Don’t Believe You Can Learn It, Then You Can’t Learn It

Math comes easily to some people.

The Latin symbols, shifting equations, and seemingly unnecessary formalism makes intuitive sense to them.

I wasn’t like this.

Math was for Bill Gates and Mark Zuckerberg, and not for Andrew Plummer.

In fact, I hated math up until about four years ago. When I entered university, I planned to study English Lit., attend law school, and then use the income from my novels to retire early.

I thought math had its purpose, sure, but I also thought that I was excluded from its grand design. Math was for Bill Gates and Mark Zuckerberg, and not for Andrew Plummer.

American psychologist Angela Duckworth argues that the difference between the people who find a high degree of success and everyone else is not that they are geniuses (and we are not); rather, the difference is that they exhibit a level of grit that we do not.

They believe that they can do it, eventually.

It was only when I started believing that, yes, if Bill Gates can learn math, then so can I, that I started to learn math. It was not a problem that I didn’t understand the concepts immediately (or after hours of studying); I knew I would understand it eventually.

One of the first stories I tell my students is the time I had failed my first calculus test in university, despite studying for weeks. The story surprises all of them. They know that I’m good at math now, and it had not occurred to them that there might have been a time when I was bad at math.

Why do I tell them this story? Because I hope that it shows them that anyone can learn math, even the non-Bill Gates’s of the world.

2) If you’re not passionate about something, then you won’t learn it

I have gotten the following question from each of my students:

When will I ever need to know this stuff?

It’s a fair question. And I empathize with the students who will likely never need to solve trigonometric identities or find the derivative of a non-linear function.

It is difficult to learn a new skill you see zero value in.

One reason it became easier for me to learn math is because I knew it was importance for data science, which I was becoming increasingly interested in.

Not only did my passion for data science make me work harder in my math courses, but it also made math more approachable. I sought out math courses — linear algebra, econometrics, mathematical statistics, etc. — and I engaged more with my professors. The result was that I learned math more easily, and more quickly, than would have been the case if I had not seen its value.

If you want to learn a new skill, then connect that skill with what you love.

Many of my students want to become lawyers or businessmen.

Well, data literacy is becoming an important skill in both law and business!

Sometimes, a student’s goals are entirely separate from math. In that case, I explain the concepts in a way that is relatable and, hopefully, entertaining.

If you have to learn a new skill (like math for school), and you cannot find how that skill is related to your goals, then teach yourself in an entertaining way. (One of my math professors told funny stories about some of the ways that math theorems were devised. I always enjoyed his class).

3) If you can’t explain a concept in layman terms, then you don’t understand it

Many of my students require tutoring because they are performing poorly in math (Duh).

As a result, telling them to ‘isolate x’ is unhelpful because they don’t know what you mean by ‘isolate’.

Being forced to explain a concept in layman’s terms taught me which parts of the concept I was having troubles understanding.

Why can you not divide by zero?
What is the intuition behind Pythagorean’s Theorem?
What does it mean to ‘isolate x’?

If you’ve recently learned a new topic, then practice teaching that topic to someone who is unfamiliar with the field. If you find yourself unable to answer their questions, or if they leave the conversation more confused than when you began, then it is likely that you don’t understand the concept very well.

Re-read your textbook, work on practical examples, or use Stackoverflow until you’re able to explain the concept to a non-expert. They don’t need a rigorous proof but they should leave the conversation with a general idea of what you’re talking about.

Conclusion

I’ve used all of the above to teach myself math, statistics, economics, and data science. These are also the lessons that I share with my newest students, and they’ve found them helpful.

Be persistent, seek value, and keep it simple.