When Math Feels Hard, This Is What to Do Next Step-by-step strategies to build confidence in challenging math

When asked to imagine a truly difficult challenge, many people immediately think of advanced mathematics. Complex equations, abstract theories, and intricate logic can make math seem like one of the most intimidating academic subjects. But here’s the truth: mathematics is a skill—one that anyone can learn with the right approach and persistence.

If you're reading this, you probably already believe that improvement is possible. You’re motivated to sharpen your problem-solving abilities. The next logical question is: how can you actually get better at math?

The answer is simple but powerful: you need to engage with math consistently, especially the hard parts. And more importantly, you need effective strategies to tackle the types of problems that stump you. This guide will walk you through practical techniques for working through—and eventually solving—those seemingly insurmountable math problems.

Why Difficult Problems Are the Key to Growth

Tough problems aren’t just barriers—they're opportunities to stretch your understanding and achieve breakthroughs. The more you challenge your current skill set, the more you grow. However, when you encounter problems that halt your progress, it’s crucial to have a method for breaking them down and finding your way through.

Let’s look at exactly how to do that.

Step 1: Understand the Core Idea Behind the Problem

George Pólya, a Hungarian mathematician, wrote in his book "How to Solve It" (1945) that when facing a difficult problem, you should:

"Find the simpler problem hidden within."

This advice is golden because mathematics is cumulative—each complex concept is built upon simpler, foundational ideas. If you struggle with a problem, it's often because one or more of these underlying components isn’t fully mastered yet (1).

Step 2: Break the Problem Into Simpler Parts

When you face a complex question—one involving several steps or mixed concepts—dissect it. Identify each mathematical operation or idea involved. For example, a summation problem with a fractional exponent involves two distinct topics:

• Understanding summation notation
  Interpreting and evaluating fractional exponents
  Instead of wrestling with both concepts at once, practice them separately.

Example Breakdown:

Let’s say you encounter this problem:

∑i=14(43/2)\sum_{i=1}^{4} (4^{{3/2}})i=1∑4​(43/2)

This combines summation with an exponent involving a fraction. If either concept is shaky, you might get stuck. So split the task:

1. Practice summation on its own with easy expressions like:
   ∑i=14(i+i2)\sum_{i=1}^{4} (i + i^2)i=1∑4​(i+i2)
2. Work on fractional exponents separately, such as:
   43/2=43=64=84^{3/2} = \sqrt{4^3} = \sqrt{64} = 843/2=43​=64​=8

Once you master each part, you’ll be better equipped to solve the original, more complex problem (2).

Step 3: Use Simple Numbers to Focus on Concepts

Large numbers, decimals, or complicated fractions can distract you from what really matters: the concepts. When practicing, simplify the numbers. Use small, whole values that are easy to manipulate mentally. This keeps your focus on understanding operations, not doing tedious calculations.

Tip:

If you’re stuck on a tough problem filled with ugly numbers, create a similar problem with smaller values. Once you solve that, go back to the original.

Step 4: Fill the Gaps in Your Understanding

Sometimes, even when you simplify a problem, you still can’t solve it. That’s usually a sign that you need to revisit the foundational concept.

At this point, your next step is to review the theory. Here's how:

• Go back to your textbook or class notes.
• Look for solved examples that mirror the concept.
• Watch tutorial videos or read explainer articles.
• Try guided practice problems that show step-by-step solutions.
   

Step 5: Use Tools Like WolframAlpha or Symbolab

When you're truly stuck, it can be helpful to see how the problem is solved step by step. There are online tools designed specifically for this purpose:

• WolframAlpha: Extremely powerful, but full step-by-step solutions require a paid subscription.
  
   
• Symbolab: A bit slower to use, but provides free step-by-step solutions and is very helpful for understanding the process.
  
   

⚠️ Caution: Don’t use these tools as a shortcut. First, make an honest attempt to solve the problem yourself. Then use the solution to learn the process, not just to get the answer.

Step 6: Re-Solve the Problem Without Help

Once you’ve reviewed the steps or followed an example, go back and try the original problem again—on your own. This is where real learning happens.

If you’re able to solve it correctly from scratch, you’re on the path to mastery. If not, identify exactly where you’re struggling and repeat the process (3).

Step 7: Don’t Rush—Mastery Over Speed

It’s tempting to race through homework or assignments, especially when you're on a deadline. But rushing through math means:

• You may guess instead of truly solving.
• You skip the critical thinking process.
• You miss the opportunity to solidify your understanding.
  
   

Take your time. Your goal isn't just to finish—it’s to fully grasp the ideas, so you can use them again in exams, future classes, or real-world applications.

Remember: Mastery means you can’t get it wrong—not that you got it right once.

Closing Insights: Confidence Comes from Consistency

Improving at math—or any challenging discipline—is about believing you can get better, and then showing up every day to prove it to yourself. With each problem solved, your confidence builds. That confidence then fuels more practice, and the cycle continues.

To quote the brilliant physicist Richard Feynman:

“The best way to learn is to try and fail and learn why you failed.”

Quick Recap: Your Roadmap to Solving Hard Math Problems

1. Break the problem down into smaller, manageable parts.
2. Isolate and master each concept separately.
3. Use simple numbers to focus on understanding, not calculation.
4. Review and study when you don’t understand something.
5. Use learning tools like WolframAlpha and Symbolab (but don’t rely on them).
6. Re-attempt problems without looking at the solution.
7. Take your time—real understanding comes from effort, not speed.
    

Ready to Level Up?

By applying these strategies, you can train your brain to handle the toughest problems in math. And once that confidence kicks in, the only direction you'll move is forward. Happy problem solving!