Most people feel like math skills are an innate talent.
In high school, I was the same way. I figured that the “good at math” gene missed me and there was no chance of me doing anything in my future that required crunching numbers, writing computer programs, or science.
I was one of those high school students who actually took pride in my lack of math skills. I avoided challenging myself with more difficult and interesting math and science classes.
Beyond what was mandatory, I only took biology classes so that I could avoid math-heavy physics and chemistry. If I couldn’t rely on memorization to pass, I didn’t want anything to do with it.
I ordered my high school transcripts to get a look at my math grades. I was a terrible math student.
It should come as no surprise that I struggled in high school to even get a C in my high school math classes.
Even when I graduated in 2003, I figured that getting a degree in anything that didn’t require math was a waste of money. So I tried again. This time, my failure would cause me to fail out of college in my third semester in 2004.
Fast forward 14 years to 2018.
At the age of 33, I not only graduated from Duquesne University with a B.A. in Physics and a minor in Mathematics, but I always was making $1000 per week tutoring high school students in physics, chemistry, and math.
Academically, I didn’t get lower than a B in any of my math classes. Professionally, I was doing such a good job tutoring that I had to turn down work.
How did I go from being a mediocre student in high school who barely understood basic math concepts to getting a degree that’s so math intensive that you automatically get a math minor by completing it?
How did I go from someone who was terrified of trigonometry and doing derivatives to someone who got several high school students through AP Calculus and AP Physics?
How to Get Better At Math
This article details the step-by-step methods I used to grasp basic arithmetic, higher-level calculus, and every level of math in between.
If you want to get better at math, this article will take your abilities to the next level. You’ll be a better math student and feel more confident when you face off against numbers.
1) Believe That You Can Learn Math
This is the single biggest hurdle you’ll face. That’s why it’s the first step to getting better with math. You have to sincerely believe that you can learn math.
Most people who have trouble understanding math have simply convinced themselves that they can’t learn it. They believe that they just weren’t born with a mind for math. I know this not only from observation, but from personal experience as well.
I used to think the same thing about myself. I would rationalize my lack of math ability by telling people that I’m great at memorization, but figuring out math wasn’t my thing. However, two things changed my mind about my so-called lack of innate math skill.
You’re likely at least as smart as a typical math major
Despite the fact that the average IQ of majors is higher, the average SAT score of someone who studies math is a bit more modest.
The average SAT score of a math major–someone who devotes 4 years to studying math–is only 1238 (out of 1600).
If that sounds high, I’ve tutored students to even higher SAT scores who started out in the sub-1000 range. Even if the future math majors score higher on the math section (which makes perfect sense), these findings suggest that overall, they aren’t any more intelligent than most people who go to college.
When I saw this, I figured that it was possible for me to get better at math.
Growth Mindset Comes From Your Achievements Elsewhere
The second thing that gave me confidence that I could get better at math was my experience in boxing.
I started boxing at the late age of 22. However, despite this late start, I went on to have a very successful career and overcame many challenges throughout the process of becoming a boxer. At first, boxing may seem unrelated to improving at math, but I did not start boxing with any natural talent.
I worked hard, paid my dues, and watched myself go from a stumbling amateur to a national champion. My mentality with boxing was that I was going to succeed, no matter what.
When I restarted my math education in my late 20’s, I took the same approach. I figured that if I could succeed in boxing with a late start, then getting better at math and science should be no problem at all.
These two events shifted my mindset. They got me to see that there was nothing inherently special about the people who are good at math. At the very least, if I was smart enough to get into college, then I was smart enough to do math.
I also saw that I did one challenging thing by working hard. Think about other areas in your life where you’ve met challenges but didn’t have any initial talent or advantage.
2) Take Your Math Education Into Your Own Hands
If you’re like most people, you were educated in a public school system.
You had limited/non-existent resources for improving your math ability outside of the classroom. If you got a bad explanation or had to endure a subpar math teacher, there was nothing you could do to get better.
Fortunately, that’s no longer the case. There are a plethora of free/low-cost materials online. If your teacher isn’t getting the job done, here is a short list of things you can do to get better at math:
- Youtube videos
- Khan Academy
- Download problem sets solutions
- Download pdfs of textbooks
- For more problems, buy more used textbooks and study guides
You’ll need resources to get better. There’s no way around that. You’ll need to do many practice problems to truly grasp many of the basic concepts necessary for math success. Fortunately, there is a solution on the internet for almost any problem somewhere. You can check if both your process and solution are correct.
Take advantage of all of the free math resources on the internet. You need to practice math to get better at math.
If the explanations you get in class aren’t helping you, then there are great Youtube channels and websites out there that do an excellent job of explaining ideas.
3) Master The Fundamentals of Arithmetic
Now that you’re armed with the proper mindset and know how to acquire math resources to practice with, let’s lay out the plan to increase your understanding of math.
When most people use the word “arithmetic”, they just mean working with numbers and general mathematics. They aren’t incorrect, but that’s too general for our purposes. In this case, we’ll be more specifically using arithmetic to mean the four basic operations you perform on numbers.
Those operations are addition, subtraction, multiplication, and division. These are the basic arithmetic operations.
These are the basic building blocks of all mathematics. They are present in all levels of math and permeate your daily life in many seemingly non-mathematical situations.
Many of us think we understand them, but we get tied up adding negative numbers, quickly multiplying double-digit numbers, or working with fractions.
Here is a list of basic arithmetic skills you should you must master:
- Performing the basic arithmetic operations on negative numbers
- Performing the basic arithmetic operations on fractions
- Quickly being able to multiply one or two-digit number by another two-digit number
- Quickly being able to estimate how many times one number can be divided into another
The goal isn’t to become a human calculator that can perform amazing feats of mental math. Machines are faster and at this point, it looks like you’ll always have access to a calculator (I’m old enough to remember when they used to tell us that we wouldn’t always have a calculator).
The goal is for you to get comfortable working with numbers. We never have to do this for words because we always speak, write, text, and type. With numbers, you have to develop a feel and fluency with them. Arithmetic practice is the way.
4) Learn To Read Math
There are 3 levels to being able to read math.
Level 1: The symbols and their meaning
You have to know that “¾” means “divide 3 into 4 equal parts. You have to know the difference between “ -3 + 0” and “3 - 0”. This might seem obvious, but I’ve found that a lot of people’s lack of mathematical aptitude derives from not knowing basic stuff like this.
Make sure you know the symbols. You should not have to think about what it means when you see |-4|. You may not know the answer, but you have to make sure that you at least know what it’s asking you.
Level 2: Synonyms of the symbols and the numbers
The essence of math is the way one thing can be exchanged for another. In this way, we can make problems easier to work with.
“5/7” is the same thing is “5 *(1/7)”. Depending on your problem, one form may make more sense to use than another. This doesn’t just work for the numbers as well.
Learn different ways to express the same idea. For example:
- Adding a negative number is the same thing as subtracting its positive equivalent.
- Multiplication is the same thing as adding the same amount together as many times you’re multiplying it.
- Dividing a fraction by a number is the same as multiplying by that number’s inverse.
These are just little examples of learning how to look at math as an interchange of ideas.
Some versions of ideas are easier to work with than others. Sometimes, we just need a different perspective to help us realize that we really do understand what’s going on.
Level 3: How the symbols and the numbers work together
I could have simply titled this section, “The Order of Operations”. That would cover most of what this section says and will sort out most of the issues that you have when it comes to getting better at math.
In case you forgot, the order of operations is as follows:
We usually learn this with the mnemonic “Please Excuse My Dear Aunt Sally”. If you do nothing else in your math career, I recommend you learn this and all of the implications of it.
5) Think In Pictures
A big breakthrough I made in math was when I realized that everything could be represented with a simple picture. In fact, the entire branch of geometry (and to a lesser extent, trigonometry) relies on visual representation to teach its concept.
There are a few key visual representations you should familiarize with to improve your math skills.
The Number Line
If you understand the number line, you have a visual model for every arithmetic operation possible. You’ll understand why multiplying two negatives gives you a positive, why you can’t take the square root of a negative number, and why we need imaginary numbers.
The Cartesian Plane
The real benefit of the Cartesian Plane is that it trains you to see relationships between things.
Specifically, how one quantity changes based on how another one changes. Algebra gives a lot of people fits because they get confused with addition of letters to the number problems.
All the letters represent variables, or something that does not have a set value. The equation that the letters appear in merely shows the relationship between the two (or more) changing quantities.
The cartesian plane may just be dots and lines, but it demonstrates a real-world application of math. Everything depends on something else, and the cartesian plane allows us to see that relationship with all the distracting noise stripped away.
Area, Volume, and The Fun Math Behind Shapes
The visual representation of any number squared is a square. The visual representation of any number cubed is a cube. That is either painfully obvious or you just had your mind blown.
The real fun begins when you start to see it applied to other shapes.
There are some beautiful relationships between the 2 and 3-dimensional versions of shapes. The idea isn’t to memorize the exact relationships but to see that nearly every math idea has a real physical component that can help you grasp the underlying concepts that seem to be abstract.
This not only makes learning math purposeful, but I always felt like understanding the physical ideas behind the numbers made it more fun and interesting.
Much of math becomes easier to study if you figure out the visual representations of an idea. Everything you learn can be represented on the number line, the cartesian plane, or in the form of a shape.
6) Use Technology To Help You Learn Math
With today’s technology, you can go extremely far without a teacher. When it comes to solving math problems, there are tools that will solve the problem for you. Unlike a simple calculator, these tools also walk you through the steps.
These are fantastic for figuring out where you went wrong while also showing you how to solve the problem correctly.
I spent an entire year working on math problems from various books I downloaded, and nothing helped my math skills improve faster than running my work through one of these programs for feedback.
The three I recommend are:
Regardless of which tool you select, remember what the purpose of using these types of problem solvers are:
You want to push yourself as hard as you can to solve the problem. Only after you’ve given a good effort do you check to see that your answer is correct.
Checking the answer without pushing yourself to the limit of your knowledge and ability is no better than asking someone for the answer. If you do it this way, you never actually improve your problem-solving capabilities.
7) Take Time To Understand The Math Concepts
The goal isn’t to become a human calculator or a math genius. It’s certainly not to memorize a bunch of different math problems.
Sadly, school trains you this way because they depend on funding and it’s a lot easier to teach you to pass a test than actually learn.
The goal is to understand the concept. This is why you need to find great supplemental resources as well as take notes and challenge your thought process.
When I was improving my math skills to get my degree, I spent a lot of time on the site www.betterexplained.com. I even reached out to the writer of the site to personally thank him for all of his explanations. Another favorite site of mine was Paul’s Online Math Notes.
Both of these sites did a fantastic job of explaining any new concepts I had trouble with and illuminating old mathematical concepts I never quite understood.
In addition to the notes from their website, I also took a lot of notes and asked myself a lot of questions. By asking myself questions, I forced myself to dig deep and truly grasp the material.
There is nothing that facilitates learning more than asking the right question.
A Summary Of How To Get Better At Math
- Believe that you can learn math
- Take your math education into your own hands
- Master the fundamentals of arithmetic
- Learn to read math
- Think in pictures
- Use technology to help you learn the math
- Take time to understand the math concepts
If you work on solving problems and avoid memorizing everything but the math basics, you will go far in whatever math courses you have to take.
This is the general strategy I used to go from a failing math student to getting a degree in physics. I believe that anyone is capable of becoming better at math if they follow these steps.