The Four Stages of Learning Math

Everyone (yes, EVERYONE) who learns new math struggles at first and then slowly puts the pieces together. The only difference is that the people with more experience learning math know what to expect and how to push through it. This is the key to not only understanding math but really to doing anything tough in life.

Think about how it feels when you start a new topic in math. Can you identify these stages in your process? Do you let yourself get caught up in frustration before you push through?

  • Stage 1: Bewilderment – I’m sorry. The fact that no one uses this word anymore made it all the more important to me that I manage to use it in a sentence today. Anyway, back to our topic: This is the stage where you have literally no idea what is going on. All you know is that someone is writing symbols on the board and they might as well be making them up. You try to look in the book and it looks more made up than the stuff you saw on the board! Pushing through this stage means asking tons of questions and truly reading your math book. When I say reading, I mean sitting with a pen and paper and trying the examples right along with the book.
  • Stage 2: Stumbling – You know you have hit stage 2 when you can do problems in the book, but only if you have your notes. In other words, you get the first step or two and then get stuck. BUT — All it takes is a look at the notes or an example (and a few minutes of frustration) and you can figure out where to go. A lot of people get stuck here because they haven’t learned that the frustration they’re feeling is no different than “feeling the burn” when working out. Those little trip ups and times when you are trying to find you mistake? Those are exactly the moments your brain is building the connections it will need for the next problem.
  • Stage 3: Robotic Understanding – After a while of working problems and stumbling about you will find yourself at this stage. Things are starting to feel much different now. While you may not always know WHY you do certain steps, you can do problems on your own and are getting the right answers most of the time. You’re seeing connections between this and things you learned before even though some of the ideas are still fuzzy. This is a good place to be and a place to be careful! Plenty of people figure they got it at this stage and stop practicing/studying. Don’t fall for that! Keeping the work up now will pay off with…
  • Stage 4: True Understanding – Truly understanding a math concept or idea means that you can work problems that use it (even if you get stuff wrong here and there – that’s normal!), see how it is connected to other ideas, and even be creative with it (as in do a problem that is different from anything you have seen and apply this new idea to it). In my personal experience, there are probably 100 levels of “true understanding”. Even with all my experience, there have been times where I suddenly realize something about a topic I learned 10 years ago! If you are taking math class, you won’t necessarily reach this stage until you have had a few new topics that your mind can start to connect together. In my experience, the difference between accepting being in the “robotic understanding” stage and pushing to the “true understanding” stage is what separates the A/B’s from everyone else.
  • Your goal: Next time you are feeling overwhelmed and frustrated learning math, remember: It is part of the process. You will have to find your own way to push through it, but I am hoping just knowing this much will keep you motivated!