Have you ever tried solving exercises while your brain burns, and then you reach the exams always getting grades lower than expected?
If so, you've probably felt like you've never actually "grasped" the concept. And chances are, you probably tend to get stuck whenever you're faced with a new problem — not knowing how to proceed.
And even after practicing a similar problem 20 times, you fail to solve it during the exams.
You've done more than enough practice problems...but it doesn't do shit
Remember that Friday exam you just took?
You studied so hard for it.
You've solved all the problems, studied all the lectures, did all the past exams that were available — everything that you should. EVEN IF YOU FELT LIKE YOU DIDN'T HAVE THE TIME TO DO EVERY SINGLE EXERCISE IN THE WORLD.
The worst part?
When you do feel like you know your concepts, when you feel like you've practiced enough...you just lose it completely when you're tested.
You're still using up all of the allotted time — not even having the chance to double-check your answers.
What's going on?!?!?
FACT: There's a right and wrong way to learn problem-based subjects
You've probably heard the top students that the best way to get better at solving is to 'practice, practice, practice'...except it means something different for them:
- They already know how to practice intuitively and can't possibly teach you the specifics because they've been doing this since they were young
- They have a base of prior knowledge already, and since mathematical subjects are cumulative, they already have the advantage that you don't.
In short, they already knew how to learn the concepts properly and how to apply those concepts to different problems.
The former requires encoding (rather than memorization) and the latter requires both mathematical intuition and fluency.
And if you've been thinking that you're just not cut out for it, let me share with you something real quick...
With the right method, you, too, can develop your math skills
No, I'm not talking about "developing a growth mindset" and simply expecting magic. I'm talking about the approach to develop your skills. The action steps.
Myself, I didn't fall into that "Straight-A" category.
I failed Calculus 2 back in college, almost twice.
I failed Statistics 101 once.
Almost failed trigonometry.
And if I didn't sacrifice my entire life to studying? I would NOT have passed Advanced Engineering Mathematics.
It certainly made me think that "engineering probably is not for me" — that I shouldn't have been accepted for that degree.
And well, I did take almost 7 years just to finish my 5-year course, while my peers were gaining valuable job experience ahead of me. Does that sound a bit "confirming"?
Fast forward to today, I've passed my Engineering board exams (with just above 50% passing rate) finishing with top scores, and now taking my Master's Degree in Electronics Engineering.
So what changed?
When I started preparing for my Board Exams, I've learned how to learn problem-solving subjects.
I started with none other than Barbara Oakley's content in Coursera. Then discovering Active Recall. Then Anki.
After making myself the guinea pig and constantly reflecting upon my experiences...
I've learned how to learn concepts in problem-solving in a way that allows me to apply them, and how I can gain mathematical intuition and fluency by practicing in a "purposeful" way.
So here's what I've learned along the way...
To be more specific, let me share with you a couple of things I've learned that were most helpful in my journey:
- comprehending formulas by extracting meaning (and there are three ways to do that) instead of merely breaking them down into multiple cards
- making flashcards that help you solve problems (3 types), i.e. aid problem-solving
- using the right materials to get a fast feedback loop, instead of waiting for your professor to correct you when it's already too late
- focusing on developing fluency and mathematical intuition
- using purposeful practice for acquisition, feedback, and correction of your "solution library" (per se)
- filtering what should go into your problem sets and what shouldn't
- knowing that simply understanding a solution once isn't enough — that you need to maintain knowledge, too (there's a simple guideline for reviewing your "main deck")
- doing interleaved practice with filtered problems, so that you're not just doing mindless repetitions aka "university ceremony"
- leveraging past efforts to prepare for problem-solving exams with less stress
It doesn't matter if (you think) you're not a math person, or gym person, or whatever.
If you use the right process long enough, then you will become a math person, anyway.
It's also about the system, not just the goal.
And speaking of systems, I designed a course that will help you ace your problem-solving exams.
It's called Better Solving with Anki, and it's the culmination of my experience that has helped me go from a college student who's "not so good" at math to a national top passer in the Engineering Board Exams.