5 Science-Backed Strategies to Actually Learn Math (Not Just Memorize)
Let's be honest—most of us were taught to memorize formulas, not to actually understand math. But what if there's a better way? One backed by cognitive science, not just "study harder"?
You know the feeling. You spend hours studying for a math test, everything makes sense the night before, you walk into the exam, see the first problem and... blank. Total blank.
Or maybe you can solve problems when they look exactly like the examples in your textbook, but the moment the question is worded differently, you're lost.
Here's the truth: you're not bad at math. You were just never taught how to actually learn math. Most traditional teaching focuses on memorization and repetition—which works great for tests, but terrible for real understanding.
The good news? Cognitive scientists have spent decades figuring out how our brains actually learn complex subjects like math. And their findings might surprise you.
Strategy #1: Spaced Repetition Beats Cramming (By a Mile)
Remember pulling an all-nighter before a calculus exam? Yeah, we all did. But science says that's literally the worst way to learn.
The Science
When you cram, information goes into your short-term memory. It's there just long enough for the test, then vanishes. Spaced repetition forces your brain to actively retrieve information multiple times over days or weeks—which moves it into long-term memory.
How to Actually Use It
Learn a new concept today
Let's say you just learned the quadratic formula. Work through a few problems until it makes sense.
Review it tomorrow
Don't look at your notes. Try to solve 2-3 problems from scratch. Struggle is good—it means your brain is working to retrieve the information.
Review it again in 3 days
By now, you'll have forgotten some of it. That's perfect. Forcing your brain to remember strengthens the neural pathway.
Review it again in a week, then a month
Each time, the intervals get longer. Eventually, the concept becomes permanently stored in long-term memory.
Pro Tip: Use a Calendar
Set calendar reminders to review specific topics. "Review quadratic formula" on Tuesday, Friday, next Thursday, etc. Sounds tedious, but this is how you actually remember things.
Strategy #2: Stop Re-Reading. Start Retrieving.
You read through your notes three times. Everything makes sense. You feel confident. Then the test comes and... nothing.
Here's why: re-reading creates the illusion of knowledge. Your brain recognizes the information ("oh yeah, I've seen this before"), which feels like understanding. But recognition ≠ recall.
The key principle:
Learning happens when you struggle to retrieve information from memory
How to Practice Active Recall
❌ Don't do this:
- • Read your notes over and over
- • Watch solution videos passively
- • Highlight textbook passages
- • Copy examples without thinking
✅ Do this instead:
- • Close your notes and try to solve problems from memory
- • Write out explanations in your own words
- • Do practice problems BEFORE looking at solutions
- • Test yourself constantly—even if you fail
Yes, it's harder. Yes, you'll make mistakes. That's the point. Every time you struggle to remember something and eventually succeed, you're strengthening that neural connection.
Strategy #3: The Feynman Technique (Explain Like I'm Five)
Richard Feynman, Nobel Prize-winning physicist, had a simple rule: if you can't explain something in simple terms, you don't actually understand it.
This is brutal honesty for your brain. You can fool yourself into thinking you understand something. But you can't fool a 10-year-old.
The Four Steps
Pick a concept you "know"
Example: derivatives in calculus.
Explain it to a child (or your dog)
Out loud. Actually speak it. Pretend you're teaching a smart 10-year-old who knows basic math but nothing about calculus.
"Okay, imagine you're driving a car. The derivative tells you how fast you're going at any specific moment. If you look at your speedometer, that's kind of like taking the derivative of your position..."
Identify the gaps
You'll stumble. You'll say "well, uh, it's just... you know..." That's where your understanding breaks down. Write down every point where you got stuck.
Go back and learn those specific gaps
Now you have a targeted list of what you actually don't understand. Go back to your textbook, ask a teacher, watch a video—but only focus on those specific gaps.
Repeat until you can explain it smoothly
Try explaining it again. Still struggling? Keep going. When you can explain it clearly without notes, you've actually learned it.
Warning: This Feels Slow
The Feynman Technique takes longer than just reading notes. But that's because you're actually learning, not just skimming. One hour of this is worth five hours of passive review.
Strategy #4: Mix It Up (Interleaving)
Most students study in blocks: spend two hours on quadratics, then two hours on logarithms, then two hours on trigonometry.
Feels organized, right? Problem is, your brain gets lazy. After solving 20 quadratic problems in a row, you're not really thinking—you're just pattern matching.
What Interleaving Looks Like
❌ Blocked Practice
- • Problem 1: Quadratic
- • Problem 2: Quadratic
- • Problem 3: Quadratic
- • Problem 4: Quadratic
- • Problem 5: Quadratic
- • Problem 6: Logarithm
- • Problem 7: Logarithm
- • Problem 8: Logarithm
Feels easy, but you're not really learning
✅ Interleaved Practice
- • Problem 1: Quadratic
- • Problem 2: Logarithm
- • Problem 3: Trigonometry
- • Problem 4: Quadratic
- • Problem 5: Logarithm
- • Problem 6: Trigonometry
- • Problem 7: Quadratic
- • Problem 8: Trigonometry
Harder, but forces your brain to discriminate
When you interleave, your brain has to constantly figure out which strategy to use. "Wait, is this a derivative problem or an integral?" That extra work builds stronger, more flexible understanding.
How to Start
Create mixed problem sets. If your textbook groups problems by type, intentionally skip around. Or find practice tests that mix topics—those are gold.
Bonus: this is exactly what tests do anyway, so you're practicing under realistic conditions.
Strategy #5: Always Ask "Why?"
This one's simple but powerful: never accept a formula or rule without understanding why it works.
Most students learn that a² + b² = c² and stop there. But why does the Pythagorean theorem work? Where does it come from? What's the geometric proof?
Questions to Ask Yourself
Why does this formula exist? What problem was someone trying to solve?
Where does this come from? Can I derive it from first principles?
When would I use this? What's a real-world situation where this matters?
What happens if I change this variable? How does the equation behave?
How does this connect to other concepts? Is this related to something I learned before?
Every time you answer a "why" question, you're building connections in your brain. Math isn't just a collection of random rules—it's a web of interconnected ideas. The more connections you make, the easier everything becomes.
Real Example: The Quadratic Formula
Don't just memorize x = (-b ± √(b²-4ac)) / 2a. Ask:
- • Why does completing the square give us this formula?
- • What does the discriminant (b²-4ac) actually tell us?
- • Why are there sometimes two solutions, sometimes one, sometimes none?
- • How is this related to the graph of a parabola?
Answer these questions, and you'll never forget the formula. Plus, you'll actually understand what you're doing.
Bonus: Dealing with Math Anxiety
Let's address the elephant in the room. Maybe you're reading this and thinking "yeah, but I'm just not a math person."
Here's the truth: "math person" is not a real thing. Stanford researcher Carol Dweck's work on growth mindset has shown that believing you're bad at math actually makes you worse at math. It's a self-fulfilling prophecy.
The Growth Mindset Shift
❌ Fixed Mindset:
- • "I'm bad at math"
- • "This is too hard for me"
- • "I give up"
- • "Other people are naturally better"
✅ Growth Mindset:
- • "I'm learning math"
- • "This is challenging right now"
- • "I'll try a different approach"
- • "I can improve with practice"
Every time you struggle with a problem and eventually solve it, you're literally rewiring your brain. The struggle IS the learning.
Putting It All Together: Your Weekly Study Plan
Okay, so how do you actually use all this? Here's a realistic study schedule that incorporates these strategies:
Sample Weekly Study Plan
Monday: Learn New Concept
• Watch lecture/read textbook
• Work through 3-4 example problems
• Try to explain it using the Feynman Technique
• Total time: 60-90 minutes
Tuesday: Active Recall
• Close your notes
• Solve 5-6 problems from memory (struggle is good!)
• Review any problems you got stuck on
• Total time: 45 minutes
Wednesday: Mixed Practice
• Create a problem set mixing Monday's topic with older topics
• Interleave different problem types
• Total time: 60 minutes
Thursday: Learn Second Concept
• Same process as Monday for a new topic
• Total time: 60-90 minutes
Friday: Spaced Review
• Review Monday's topic (spaced repetition)
• Quick active recall practice on Thursday's topic
• Total time: 45 minutes
Weekend: Mixed Review + Deep Dive
• Create a big mixed problem set (all topics from this week + previous weeks)
• Pick one concept you're struggling with and use Feynman Technique
• Total time: 90-120 minutes
Total Weekly Study Time: 5-7 hours
That's way less than most students spend "studying" (aka re-reading notes). But it's infinitely more effective because every minute is high-quality learning.
The Bottom Line
Learning math isn't about how many hours you put in. It's about how you study those hours.
These five strategies—spaced repetition, active recall, the Feynman Technique, interleaving, and elaborative interrogation—are backed by decades of cognitive science research. They work. Not because they're magic, but because they align with how your brain actually learns.
Yes, they're harder than passive re-reading. Yes, you'll struggle more in the short term. But that struggle is the whole point. That's where the learning happens.
So next time you sit down to study, close the textbook. Open a blank piece of paper. And start testing yourself.
That's when you'll know you're actually learning—not just memorizing.