Problem-Solving in STEM: Remembering Complex Formulas and Equations
For students and professionals in STEM (Science, Technology, Engineering, and Mathematics) fields, the ability to remember complex formulas, equations, and constants is a cornerstone of success. The traditional method of rote memorization—repeating an equation until it sticks—is often tedious and leads to a fragile memory that can fail under pressure. Instead of wishing for a perfect, eidetic photographic memory, you can use a powerful, systematic approach that transforms abstract mathematical and scientific information into vivid, memorable images and stories.
1. The “Mental Image” Method: Personifying Variables
This is one of the most effective ways to remember formulas. Instead of seeing a collection of abstract letters and numbers, you turn them into memorable characters and objects that interact with each other in a mental scene.
- How it works: Take a complex formula and give each variable or constant a concrete, visual identity. For example, let’s consider the formula for force, . You could visualize a person named Fred (for F) hitting a giant mass (for m) with a giant axe (for a). The image is active, a little absurd, and links the abstract concepts to a concrete, unforgettable scene. For the quadratic formula, , you can create a memorable story. “Negative B” is a bee with a negative sign. “plus or minus” is a plus and minus sign. The square root sign is a square root. The story goes like this: A “Negative Bee” got into a fight with a “plus or minus” sign. The “Negative Bee” then went and “squared a bee,” but the bee was so angry it “minus’d” and “four” of the angry “ants” (a) and “caterpillars” (c) got into the fight. The whole scene fell over a “2a” cliff.
- Why it works: This method leverages the brain’s natural ability to remember stories and characters. By personifying the variables, you create a powerful semantic and visual link that is much more durable than simple, abstract recall.
2. The “Equation Palace”: Organizing by Location
Just as a Memory Palace can be used to remember a list of words, it can be used to organize and remember a list of complex equations.
- How it works: Choose a familiar location, such as your house or a lab. For each major topic or chapter, assign a specific room. For each key formula within that topic, create a vivid mental image and “place” it at a specific location in the room. For example, in your “Physics Room,” you might place the formula for force () on the front door, the formula for kinetic energy on the sofa, and the formula for gravitational potential energy on the bookshelf. To recall the formulas, you simply take a mental walk through your “Physics Room.”
- Why it works: This technique leverages your brain’s powerful spatial memory. The physical location acts as a powerful retrieval cue that makes it easy to remember the order and content of each formula.
3. The “Color-Coding” System
This is a simple but effective technique that uses visual cues to add an extra layer of encoding to your notes and work.
- How it works: Assign a specific color to different types of variables or concepts. For example, in a thermodynamics class, you might use one color for temperature, another for pressure, and a third for volume. In your notes and when you are solving problems, always write these variables in their assigned color.
- Why it works: This system helps your brain organize information visually. When you are looking at a complex equation, the colors serve as a visual shorthand that helps you quickly identify and understand the relationships between the different parts of the formula.
4. Active Recall with Spaced Repetition
The goal is not just to encode the information but to make sure it sticks. Active recall is the process of retrieving information from memory without a cue. Spaced repetition is the strategy of reviewing that information at increasing intervals over time.
- How it works: After you’ve used a mnemonic technique to remember a formula, close your book and try to write it down from memory. Do this a few hours later, then the next day, and then a few days later. This forces your brain to work to retrieve the information, which strengthens the memory trace. You can use flashcard apps that are built on the principles of spaced repetition to manage this process for you.
- Why it works: The act of struggling to remember something actually strengthens the memory. By forcing yourself to retrieve the information right as it is about to be forgotten, you are telling your brain that this information is important and should be stored in long-term memory.
By combining these methods, you will move beyond a superficial understanding of formulas and develop a deep, lasting knowledge of the concepts they represent. You won’t just be remembering; you’ll be truly learning and mastering the language of science and mathematics.
Common FAQ
1. Is it a good idea to just memorize the formula without understanding the concept? No. While these techniques can help you remember the formula itself, a true master of STEM understands the underlying concepts. The techniques should be used to support your understanding, not replace it.
2. Can these techniques help with remembering constants and long numbers? Yes. You can use the Major System, a mnemonic technique that converts numbers into letters and then into words, to remember long strings of digits like the value of Pi or physical constants.
3. What if my mental images are too weird? The weirder, the better! The human brain is naturally wired to remember things that are emotional, strange, or unusual. Don’t be afraid to make your mental images as bizarre and vivid as possible.
4. Can I use these techniques for coding? Yes. You can use these techniques to remember lines of code, the order of a program’s structure, or the syntax of a new language. You can create a mental story or a Memory Palace for a sequence of commands.
5. How long does it take to get used to these techniques? You will see immediate results. With consistent practice over a few weeks, these techniques will become second nature, and you will find yourself automatically applying them to new information.
6. Do these techniques help with test anxiety? Yes. Test anxiety is often a result of a fear of forgetting. By building a reliable and robust memory system, you will feel much more confident and in control during an exam.
7. Can I use these techniques for proofs in mathematics? Yes. You can use a Memory Palace to remember the order of steps in a proof. For each step, you can create a vivid image and “place” it in a specific location in your palace.
8. What’s the biggest mistake students make when studying STEM? The biggest mistake is relying on passive learning, such as rereading a textbook or watching a lecture. To master STEM, you must be an active participant, solving problems, engaging with the concepts, and using active recall.
9. Can I practice these techniques with a study group? Yes. Study groups are a great place to practice these techniques. You can work together to create memorable images or stories for complex concepts, and you can quiz each other using active recall.
10. What if I’m not a “visual learner”? While some people have a natural inclination toward visual learning, everyone has the ability to create and manipulate mental images. These exercises are designed to build that skill. With practice, you will find that you can create mental images more easily.