Top 8 'Problem-Solving-Pattern' Study Techniques to take for free for finally acing your STEM exams. - Goh Ling Yong
Staring at a page of STEM problems can feel like trying to read a foreign language. You see familiar symbols and numbers, you’ve memorized the formulas from the textbook, but when it comes to actually solving the problem, it’s like your brain hits a brick wall. Sound familiar? You’re not alone. This is the classic struggle for students who rely on rote memorization to get through subjects like physics, chemistry, engineering, and advanced math.
The hard truth is that memorizing a list of equations is like memorizing a dictionary to learn a language—it gives you the words, but not the grammar or the ability to form a coherent sentence. Acing your STEM exams isn't about how many formulas you can recall; it’s about recognizing the story the problem is telling you. It's about seeing the underlying pattern and knowing exactly which tool (or formula) to use and why.
This is where "Problem-Solving-Pattern" study techniques come in. These are methods designed to train your brain to stop memorizing and start recognizing. They shift your focus from "What's the answer?" to "What kind of problem is this?" The best part? They are all completely free and only require your time and a shift in perspective. Let’s dive into the top eight techniques that will transform your study sessions and your grades.
1. The "Problem-Type" Feynman Technique
You've probably heard of the Feynman Technique for learning concepts: learn something, then try to teach it to a five-year-old. We're going to adapt this brilliant method specifically for problem-solving. Instead of explaining a concept like "torque," you're going to explain how to solve a category of problems, like "static equilibrium torque problems."
The process is simple. After you solve a problem, grab a blank sheet of paper and pretend you’re creating a tutorial for a friend who is completely lost. Don't just list the steps; explain the why. Start with, "Okay, the first thing I do when I see a problem like this is look for these keywords..." Then, explain why you chose a specific formula, what each variable represents in the context of that problem, and how one step logically leads to the next.
Example in Action:
For a kinematics problem, you might say: "The problem mentions 'constant acceleration' and asks for 'final velocity,' but gives no time. This is a huge clue! It tells me the pattern is to use the v_f² = v_i² + 2ad formula, because it's the only one that connects initial velocity, final velocity, acceleration, and displacement without time. I'm choosing a coordinate system where 'up' is positive because..." This forces you to internalize the logic, not just the math.
2. Reverse-Engineering Solved Examples
Textbooks and online resources are filled with solved examples. Most students just read them and nod along, thinking, "Yeah, that makes sense." This is a passive learning trap. To turn it into a powerful pattern-recognition tool, you need to work backward.
Cover up the solution and try the problem yourself first. Once you're done (or stuck), look at the very last line of the official solution. Then look at the second-to-last line. Ask yourself: "What mathematical or logical step did they take to get from this line to the final answer?" Continue this process, moving up the solution one line at a time.
This technique forces you to see the solution not as a magical reveal, but as a logical, step-by-step construction. You’ll start to see why a certain substitution was made three steps earlier or why they chose to simplify an expression in a particular way. It deconstructs the pattern, making it much easier for you to reconstruct it on your own later.
3. Problem Chunking by Underlying Principle
How is your textbook organized? Usually by chapters: Chapter 1: Vectors, Chapter 2: Kinematics, Chapter 3: Forces. This is logical, but it can trick you into using the "Chapter 3 formula" for a "Chapter 3 problem." On an exam, problems are mixed up, and you don't have that clue.
"Chunking" is the process of re-organizing problems yourself, but instead of grouping them by chapter, you group them by the fundamental principle they use. Create a document or a section in your notebook titled "Conservation of Energy Problems." Go through your textbook and homework and pull every problem that is solved using conservation of energy, whether it involves springs, gravity, inclined planes, or pendulums.
Doing this reveals that five seemingly different problems are actually just variations of the exact same pattern. Your brain starts to associate the setup of the problem (e.g., an object changing height and speed) with the principle (conservation of energy), no matter what chapter it came from. This is one of the most effective ways to prepare for the mixed-bag nature of final exams.
4. The "What If" Scenario Drill
True understanding isn't just about solving the problem as it's given; it's about understanding how the system behaves. Once you've successfully solved a problem, don't just move on. Spend two minutes playing the "What If" game.
Ask yourself questions that change the constraints of the problem and predict the outcome. This tests the boundaries of your understanding of the pattern. It pushes you from simply executing a memorized procedure to truly reasoning about the physics or mathematics at play.
Specific "What If" Questions to Ask:
- Physics: "What if friction was NOT negligible? Which term would I add and where?" or "What if the launch angle was 0 degrees? How would the final equation simplify?"
- Chemistry: "What if this was a weak acid instead of a strong acid? How would the equilibrium calculation change?"
- Math: "What if the integration bounds were from zero to infinity? Would the integral still converge?"
5. Create a "Problem-Type" Flowchart
For complex topics with multiple solution paths, a flowchart is your best friend. This is a visual map of the decision-making process your brain should follow when it encounters a problem. It's the most literal way to document a problem-solving pattern.
Start with a box at the top that says, "New Problem." Then, create decision diamonds based on the key features of a problem. For example, when studying integration techniques in Calculus, your first question might be, "Can I solve it with a basic rule?" If no, "Does it look like a candidate for u-substitution? What am I looking for?" If no, "Is it a product of two functions? Maybe Integration by Parts."
Mapping it out visually clarifies the hierarchy of choices and helps you build a systematic, unflappable approach. When you get to the exam, you won't be randomly trying formulas; you'll be mentally following the clear paths you laid out in your flowchart. This method, as we often emphasize here on the Goh Ling Yong blog, is about building a repeatable system for success, not just hoping for inspiration.
6. Deliberate Practice with Interleaving
Imagine you're trying to learn three different tennis serves. Would you practice Serve A 100 times, then Serve B 100 times, then Serve C 100 times? This is called "block" practice, and it's how most students study. They'll do 20 problems of the same type in a row. It feels productive, but it's not effective for long-term learning.
A far better method is "interleaving." Practice Serve A, then B, then C, and repeat that cycle. In study terms, this means mixing up different problem types in a single study session. Do one projectile motion problem, followed by a circular motion problem, followed by a work-energy problem.
This feels harder and more frustrating initially because your brain can't go on autopilot. For every single problem, it's forced to ask, "Okay, what kind of problem is this? What pattern do I need to retrieve?" This active retrieval process is what builds strong, flexible memory pathways. It simulates the exam environment and trains the most critical skill: correctly identifying the problem pattern from the start.
7. Build a "Keywords & Triggers" List
Every STEM discipline has its own jargon. The wording of a problem statement is packed with clues—if you know how to recognize them. Keep a running list in your notebook with two columns: "Keyword/Trigger Phrase" and "What It Means / What to Do."
This list becomes your personal Rosetta Stone for translating word problems into mathematical setups. By actively looking for and documenting these triggers, you'll train your brain to spot them instantly, cutting down on confusion and saving precious time during exams.
Examples for Your List:
- Trigger: "Starts from rest" or "is dropped" -> Meaning: Initial velocity (v_i) = 0.
- Trigger: "Smooth surface" or "frictionless" -> Meaning: The force of friction (F_f) = 0.
- Trigger: "Inelastic collision" -> Meaning: Momentum is conserved, but kinetic energy is not.
- Trigger: "At STP" (in Chemistry) -> Meaning: Use standard temperature (273 K) and pressure (1 atm).
- Trigger: "Find the tangent line" -> Meaning: I need to find the derivative to get the slope.
8. Keep a Detailed "Error Analysis" Journal
Getting a problem wrong is not a failure; it's a data point. The most successful students don't just check the right answer and move on. They perform an autopsy on their mistakes to understand why they went wrong.
Dedicate a section of your notebook to an "Error Journal." When you make a mistake, don't just correct it. Log it. Write down the problem, your incorrect solution, and then, most importantly, analyze the root cause of the error. Be specific. "I got it wrong" is useless. "I used the wrong formula" is slightly better. "I used a kinematics equation for a problem with non-constant acceleration" is a diagnosis that leads to a cure.
The goal is to find the flaw in your pattern-recognition process. Were you tricked by a keyword? Did you misremember a condition for a certain theorem? Writing it down solidifies the lesson. Over time, you’ll see your own personal patterns of error and can work specifically to fix them. As Goh Ling Yong often advises his students, self-awareness of your common mistakes is the fastest path to improvement.
Your Path to Acing Your Exams
The journey from being a "formula-memorizer" to a "pattern-solver" is a game-changer. It’s the difference between feeling anxious and overwhelmed by STEM subjects and approaching them with confidence and a clear strategy. These eight techniques are not quick fixes or magic tricks; they are training exercises for your brain. They require deliberate, focused effort, but the payoff is immense.
Instead of spending another three hours passively re-reading your textbook, commit to trying just one of these techniques in your next study session. Pick the one that seems most interesting to you and give it a real shot. You’ll be actively engaging with the material in a new way, building the mental muscles you need not just to pass your exams, but to truly master the subject.
So, which one will you try first? The Flowchart? The Error Journal? Share your choice in the comments below!
About the Author
Goh Ling Yong is a content creator and digital strategist sharing insights across various topics. Connect and follow for more content:
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