Problem-solving ability applies in a wide range of situations beyond just solving math exercises. Analytical thinking and problem-solving skills are integral to many different jobs, from accountants and computer programmers to detectives and even creative professions like painting, acting, and writing. While everyone's problems may differ, certain methods help you take a targeted approach to problem-solving, such as the approach first proposed by mathematician George Polya in 1945. By following his four principles – Understand the Problem, Plan a Solution, Execute the Plan, and Review – you can enhance your problem-solving skills and systematically tackle any challenge.
Steps
Understand the Problem

Clearly Define the Problem. This step may seem quite simple but is actually crucial. If you don't fully understand the problem, your solution may either be ineffective or completely fail. To define the problem, you need to ask yourself questions and observe the situation from different perspectives. For example, are you facing only one issue, or does it involve multiple problems? Can you restate the problem in your own words? By dedicating time to the problem, you will gain a clearer understanding and be better equipped to formulate a solution.
- Try formulating a question. For instance, as a student with limited funds, you want to find an effective solution to this problem. What is the issue here? Is it about income – are you not earning enough? Is it about overspending? Or perhaps you're facing unexpected expenses, or your financial situation has changed?

Set a Goal. Clearly defining your goal will help you understand the nature of the problem. What do you want to achieve? What do you want to discover? Remember, you need to explain what you know or don't know about the issue and find ways to gather data that can help you reach your goal.
- For example, your problem might still revolve around money. What is your goal? Perhaps you never seem to have enough money to go out on weekends, see movies, or visit bars. You've decided your goal is to have more money to spend. Great! With a clear goal, you'll be better positioned to identify the problem more effectively.

Collect Data Systematically. Along with identifying the problem and goal, you should gather relevant data about the issue to understand it better. Collect data, seek opinions from relevant experts or individuals, search for online resources, books, or any other medium. Once you have the data, organize it. You can rewrite, summarize, or even graph it. While this step may not be necessary for simpler issues, it becomes essential for more complex problems.
- For example, to address your money shortage, you should gather as much information as possible about your financial situation. Collect data from your most recent bank statements, and meet with your bank representative. Track your income and spending habits in a notebook, then create a spreadsheet or graph to illustrate your income and expenditures.
Develop a Plan

Analyze the Data. The first step in finding a solution is to examine the data you’ve gathered about the issue and analyze its significance. As you analyze, look for links and relationships between pieces of information to gain a deeper understanding of the broader situation. You may start with raw data. Sometimes, you will need to break the information down into manageable parts or organize it by relevance or importance. Tools such as charts, graphs, or cause-and-effect models can be highly useful during this phase.
- For instance, now that you have all the bank expenditure reports, review them. When, how, and where did the money come from? Where, when, and how did you spend your money? What is the general pattern in your financial situation? Is your principal amount still intact, or is it depleted? Are there any items you can’t account for?

Formulate Feasible Solutions. After reviewing the data, you realize that you've depleted your principal amount – this means you’ve spent more than you've earned. The next step is to brainstorm potential solutions. There's no need to evaluate them immediately. Simply brainstorm or reverse your thinking. This process includes asking yourself, “How could I have created this problem?” and then reversing your answers. You can also consult others to see what they would do.
- Your problem is the lack of money, and your goal is to have more money to spend. What are your options? Come up with feasible solutions without evaluating them right away. Perhaps you could earn more by taking on a part-time job or apply for a student loan. On the other hand, you might try to save by cutting down on spending or reducing costs in other areas.
- Here are a few strategies to help formulate solutions:
- Divide and Conquer. Break the problem into smaller parts and brainstorm solutions for each one separately.
- Use Analogy and Similarity. Try to find similarities between the current issue and a previous problem you’ve solved. If you can relate your situation to one you've already dealt with, you may apply the same solutions.

Evaluate the solution and make a choice. After analyzing the raw data, it's crucial to assess the viability of each option. In some cases, this means testing a scenario or conducting an actual experiment. In many other cases, it could involve simulations or a “thought experiment” to understand the consequences of a given solution. Choose the solution that best fits your needs, seems likely to produce results, and won't introduce new problems.
- How can you save money? Consider costs – only use money for basic needs like tuition, food, and housing. Could you reduce costs in another way, like finding a roommate to share rent? Can you borrow money from a student support fund just for weekend fun? Can you reduce study time to take a part-time job?
- Each solution will present its own set of circumstances that need to be evaluated. Go through each situation carefully. Your financial issues will require a specific budget, but also a personal evaluation. For example, can you cut back on basic expenses like food or housing? Are you willing to prioritize money over studying or taking out loans?
Implement and Evaluate the Plan

Implement the solution. Once you've chosen the best solution, it's time to put it into action. Start with a small-scale test to measure its effectiveness. Keep in mind that unexpected issues may arise during this phase, especially if you haven't properly structured the problem or accounted for certain factors in your initial analysis and evaluation.
- You decide to reduce costs because you're unwilling to borrow money or shift study time. You can establish a detailed budget, cut back on a few small expenses, and commit to testing the solution for one month.

Review and assess the results. After implementing the solution, you need to monitor and evaluate the outcomes. Ask yourself if this solution is truly helping you. Does it move you closer to your goal? Are there new issues emerging that you couldn't foresee? It's time to revisit the problem and your approach to solving it.
- The results of your test will likely be mixed. On the one hand, you've saved enough money in a month to enjoy a weekend outing. But a new problem arises: now you have to choose between spending on necessities like food and buying a new pair of shoes, which isn't covered in your budget. You may need to explore a different solution.

Adjust if necessary. Remember, problem-solving is a cyclical process. You’ll come up with multiple potential solutions, and each needs to be evaluated individually. If you solve the problem, you've found the right solution. If not, you'll need to seek alternative solutions and restart the process. Revisit your initial solution and adjust it if it isn't effective. Try another approach, implement it, and assess the results. Repeat this process until you've successfully solved the problem.
- After a month, you abandon your first budget draft and find a part-time job. You secure a work-study position at your university, set up a new budget, and now you have additional income without cutting back too much on your study time. You've found an effective solution.
Sharpen Your Skills

Regularly exercise your brain. Just like physical muscles, your problem-solving skills require regular practice to improve their strength and function over time. In other words, you need to “work out” your brain. Numerous studies show that activities like brain games can make your mind more flexible. There are plenty of games or exercises you can try.
- Crossword puzzles are a great option. For example, in the game “Split Word,” you need to arrange letters to form words related to a specific theme, like “philosophy.” In “Tower of Babel,” you need to memorize and match foreign-language words to the correct images.
- Math puzzles can also test your problem-solving skills. Whether the problem is related to numbers or words, it will engage the brain's analytical areas. For instance: “Hùng’s current age is half the age he was 6 years ago when he was half his current age. How old will he be in 10 years when his age doubles the previous number from 10 years ago?”

Play video games. For years, video games were seen as tools that made you “lazy in thinking.” However, recent studies have shown that they can actually improve certain cognitive functions, such as spatial awareness, reasoning, and memory. But not all types of games produce the same results. While first-person shooter games can enhance spatial reasoning, they aren't as effective at developing problem-solving skills as other types of games.
- You should play games that require strategic thinking or analytical skills. Try puzzle games like Tetris. Or, if you prefer role-playing or strategy games, you could try titles like “Civilization” or “Sim-City.”

Pursue a hobby. Hobbies offer another way to keep improving your problem-solving skills. Choose one that involves active problem-solving or stimulates the right areas of the brain. For example, learning a new language can activate both hemispheres of the brain, triggering regions responsible for analysis, reasoning, and problem-solving.
- Web design, software programming, puzzles, Sudoku, and chess are also hobbies that require strategic, systematic thinking. Any of these activities can help you enhance your overall problem-solving skills.
