how to improve problem solving skills quora

Stack Exchange Network

Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

How can I improve my problem-solving ability?

Everyone says the same thing: "a real programmer knows how to handle real problems." But they forget how they learned this ability or where: it's not taught in schools.

What can I do to improve my ability to tackle complex programming problems? What strategies have worked for you? Are there specific areas I should be focusing on, like algorithms or design patterns?

• self-improvement
• problem-solving
• 3 Two useful books mentioned in Code Complete are: Conceptual Blockbusting by James Adams, and Lateral Thinking by Edward De Bono. –  mctylr Commented Jan 17, 2011 at 17:09
• 1 AH! I forgot to post in here back when it just had a few answers. –  Mark C Commented Jan 19, 2011 at 5:33

26 Answers 26

A few techiques that might or might not work:

• Look at existing solutions to common problems, e.g. design patterns. Maybe you find something similar that at least partially resembles your problem. Search the web.
• Act as if the problem has already been solved, and trace what follows back to the solution to make. For example, instead of designing the API for a class, just write the code that makes use of the class, with method calls as you would like them, and then implement that API.
• Do something else, e.g. surf the net or play solitaire, and wait for inspiration to happen.
• Think of the person you like most, and pretend you want to impress her with your problem solving skills. What would be an extremely impressive solution?
• Check the problem for inherent contradictions or conflicting requirements, and state exactly what they are and what compromise could be made. Often, when such conflicts exist, but you are not aware of, you tend to discard one possible solution after another because you cannot perfectly satisfy all requirements.
• If you already have a possible solution, but it feels "dirty" (copy-paste, global variables, spaghetti code etc.), use it anyway and make it better afterwards
• The last point is excellent. Sometimes to solution to the problem is to just get it working for most cases and then see where it needs to be improved. –  JeffO Commented Jan 11, 2011 at 13:20
• 4 However, be aware that the number of "I'll fix it later"s which turn in to "I've fixed it"s is (at least in my experience) fractionally small. –  Gareth Commented Jan 11, 2011 at 16:09
• 3 Gareth: True, but the idea is not to make it better next week, next month or whenever, but immediately after getting it to work. It's meant as a method to crack hard nuts. –  user281377 Commented Jan 11, 2011 at 18:27
• 3 I don't surfing the net as a way of waiting for inspiration to happen. You need idle brain cycles to get inspiration to happen, and surfing the net is a way of wasting those idle brain cycles. Instead, go shopping, or take a walk, or take a bike ride, clean your apartment -- do something that doesn't take much brain power. Inspiration will come more quickly under those circumstances. –  Ken Bloom Commented Jan 16, 2011 at 17:08
• 1 Geek: I know that #4 sounds a bit paradoxical, but sometimes, it really works for me; especially in situations where more than one approach seems possible and the problem is the selection of one of those approaches. #6 means not to be too restricted by the usual don'ts in our profession. Sometimes we have internalized rules like "avoid global variables" to the point that we unconsciously reject every solution that makes use of such deprecated technique. –  user281377 Commented Jan 17, 2011 at 7:15

Use R-mode or L-mode thinking as required

R-mode is the creative, non-verbal approach we commonly associate with the subconcious. L-mode is the linear, logical, verbal approach associated with your "inner voice".

If a problem appears to be intractible it is probably because you are attempting to solve it using the incorrect thinking mode. For programmers, the default thinking mode tends to be L-mode so it may work for you to switch it off temporarily and access R-mode.

How to access R-mode thinking

There are many ways, but perhaps try the Poincare method (named after the famous mathematician).

Write down everything you know about the problem. Immediately solve all the easy aspects of it (if any). Pick a single item from the remain "hard problems" list and then go off for a walk where you won't be disturbed or distracted.

Don't try to analyse the problem during the walk, just let your mind wander and observe any interesting images or sensations that arise that could be related to the problem. Let them coalesce. If inspiration strikes immediately stop the walk and return to write down the insight that you have gained.

Rinse and repeat until all problems have insights. Then start exploring the insights.

Book recommendation

Also reading Pragmatic Thinking and Learning may help you become a better problem solver. (I seem to be referencing this book a lot recently...)

• 4 Pragmatic Thinking and Learning was excellent –  Brad Cupit Commented Jan 11, 2011 at 19:26
• Ref: drawright.com/theory.htm (what R-mode and L-mode is) –  mctylr Commented Jan 17, 2011 at 17:04

Ask someone else...

No seriously. You biggest resource can be the person sitting next to you. Don't even ask them for the answer to the problem, ask them to sit next to you and let you explain the problem.

Often you'll work it out as you verbalise it.

Sometimes the other person will ask a question or point out a detail which will unlock the mental floodgate.

Eventually you will learn to verbalise things in your head without the use of a puppet, and spot the key details in the problem quicker.

And if all else fails at least they might be able to show you a technique which you wouldn't have thought of using.

• Asking others or forming study groups is an excellent way to learn. –  Gary Commented Jan 19, 2011 at 7:43
• i do the same, just to get idea from me and this is one of the best way. –  Viswa Commented Oct 18, 2013 at 4:29
• This technique is known as Rubber Ducking, excellent article about it in coding horror codinghorror.com/blog/2012/03/rubber-duck-problem-solving.html & wiki is also helpful en.wikipedia.org/wiki/Rubber_duck_debugging –  spats Commented Jan 11, 2014 at 14:55

Actually my short answer is "solving more problems". But the point is: Really concentrate on the problems and don't give up. Don't ask for help on StackOverflow or whatever. (Reading StackOverflow is ok of course!) Try hard until you get a nearly working solution, then you nearly reached your goal. And continue until you have a satisfying solution.

For me problem solving is two things:

• problem solving strategy
• persistence and frustration tolerance

Point 2 is really crucial in my opinion because it forces you to change your thinking the longer you are stuck with a problem. It also allows you to spend more time with problem solving allowing you to even more improve your skills. ;-)

By the way, I recommend you to read Edward de Bono. Though I aquired my problem solving skills mainly by studying Physics, his writing is really interesting.

Well and my problem solving toolkit is this:

• randomly try something
• read random articles/blogs/posts about the topic I am concerned with (or a closely connected topic)
• making a nice drawing
• split the problem into multiple but simpler problems
• do something else
• Google something that is related in some way to the problem
• talk to others about the problem
• make a TODO list
• write down stuff you know about the problem's effect so you can more easily find patterns

Please note that most of these tools can be applied recursively.

And my algorithm is this:

• Which tool of my problem solving toolkit makes most sense at the moment?
• Problem not solved? Continue with 1. ;-)

Step 1. is a tough decision, but you make better decisions the more you practice.

Oh and I nearly forget the most important ingredient:

Think positive about the whole process. Don't think "I hope XYZ will now solve the problem." Rather think: "If XYZ doesn't work then I know that YZX can't be the problem source and I will check if ZYX works." Problem solving can be fun sometimes in particular if your process of finding a problem ends up to be elegant and informative.

• I searched this page for the word "Physics" to see if someone already wrote about it. Mathematics is the other one. –  Mark C Commented Jan 19, 2011 at 5:34
• The value of studying physics with regard to your problem solving ability is hard to overstate, I think. –  Mark C Commented Jan 19, 2011 at 5:35
• +1 for thinking positive. If you find yourself getting worked up then your problem solving ability is impaired. Look at the problem as it giving you knowledge. –  Gary Commented Jan 19, 2011 at 7:49

Start working on the skill of identifying problems as well. Sometimes you have to recognize there is a problem before you can solve it. In school they require too many answers and not enough questions out of students.

Find people around you that solve problems and ask them how they go about it.

Be prepared to be wrong. You won't improve if you keep them all to yourself and you won't be of any use.

• +1 for "In school they require too many answers and not enough questions out of students." this is soo true and take time to learn to ask the right questions... check everywhere there are so many examples of bad question –  Rémi Commented Apr 3, 2014 at 15:32

The main benefit of a computer science education for software engineers is the ability to create and understand abstractions. Abstractions are used to encapsulate common functionality, such as String class methods, into tight, reusable packages that allow us to focus on the bigger problem.

Learn to recognize and create Abstractions :

But most importantly, abstractions teach us how to break a problem down into smaller, more manageable chunks . When combined with a science background, the combination of those skills can create an engineer capable of cutting through the noise and getting to the heart of the problem.

Learn to solve problems using the Scientific Method :

When troubleshooting a production application where a hard-to-find problem exists, sometimes it helps to actually break the application further (in a non-production environment) in order to eliminate several variables in order to isolate and eliminate one.

In summary, the scientific method, learned from taking all of the Physics electives and other science electives required for a computer science degree, helps solve these problems as if we were trying out a placebo and a new drug trial on a series of volunteers. Like scientists who sometimes have to make something worse in order to make it better, sometimes we as engineers must do the same.

Scientifically thinking in this manner can -- in general -- only come from having experience in a science background. Sometimes solving a problem can't be perceived as a linear path from A to B.

In short, study computer science, study other scientific fields, learn functional programming. These will help you think like a scientist and to think outside the box.

• Exactly. Break big problems into smaller problems. –  Bill Michell Commented Apr 3, 2014 at 13:12

It is all dependent on what type of problems you are aiming to solve, but learning to think logically if you already don't is a good thing.

All in all, and you are gonna hate me for saying it, but practice makes perfect. I didn't get pulled out of my mother's womb knowing how to be a good problem solver and no one else did. You need to practice and learn how to do things on your own. If you are still in school and don't have programming/computer science type classes, math and science are also quite good for fostering development of these skills.

I think what you are looking for is computer science heuristics.

When it comes down to what 99% of us do in the trenches, there really isn't anything new under the sun. So you might see a problem and recognize it as a DP problem, or another one as a problem that could benefit from memoization, etc...

How do you gain this knowledge? A proper CS degree is a good place to start... Not Software Engineering or Information Systems, but that stuff that most undergrads complain about "not being practical".

You can do this on your own, but it'll probably be harder. I'd start with these two courses:

Intro to Algorithms

Great Ideas in Theoretical CS

My answers relate specifically to coding but can be applied to anything.

• Step away from the keyboard. Talk a walk, go for a run, talk it over with a colleague over a coffee
• Become 10 years older! My experience has helped me enormously.
• Use Binary chop. Split the problem into two and narrow the problem: repeat.
• Remember Sherlock Holmes: When you have eliminated the possible, whatever remains (no matter how strange) is the answer
• Check your test data. Well over half of my really tricky problems have been caused by faulty data and not faulty code or algorithms.

In terms of practice, I can tell you what I do. I'm more interested in applied math, than programming, but applied math as applied to computing is programming of sorts. I see problems and solutions around. Before (or sometimes after, if say my job requires a timely solution), linking to a known solution -or existing code library, I like to ask myself: "If this were a virgin problem -i.e. you won't be able to find a canned solution, how would you proceed?" If the answer is somewhat straightforward consider writing a solution (analytic, or a computer program to solve it). Ignore complicating end cases,-you are interested in exloring approaches, and algorithms, not reinventing an existing library. If the solution will require too much effort, don't program the full solution, but at least think about the sorts of data structures and methods that you would want to use. Also think about alternative methods.

There's a great SO question on this.

My answer was:

The best way to improve is to practice! Subscribe to the RSS feed at: http://www.mensa.org.uk/puzzles/ and take time to complete them as they come out. A puzzle-a-day desk calendar (e.g. http://www.calendars.com/product.asp?PID=1&MGID=-1&IID=46387&cm_mmc=Affiliate_Program--performics--k137666-_-DDI%20Link ) is a good idea too as it will give you regular, bite-sized, and varied problems to solve. While these will invariably be off topic from the problems you will find yourself facing, the variety is important as it will force you think in ways you haven't before, which is really what problem solving is all about. Edit: Also check: http://www.mindtools.com/pages/main/newMN_TMC.htm for good problem solving tips.

Playing chess is an excellent trainer for solving programming problems. The layers of problems and the logic trees relate very nicely. It also helps you to think ahead and plan before going down a suboptimal path and wasting time.

Chess also requires a balance between the left and right “thinking modes.” If you become too analytical, you can get bogged down in trying to calculate everything, which is impossible. However, every creative inspiration needs to be checked with a calculation to make sure it fits with the concrete reality of the situation. Hard problems are just like this.

Chess demonstrates how study and practice lead to solid improvement in a very linear fashion. This is true with program problem solving as well.

Playing chess can also help you get a good grasp on how much there is to learn. Even though you have been programming (or playing chess) for 10 years, you aren't a grandmaster yet.

• I have found my mind sharpened with regularly playing chess. –  Paul Nathan Commented Jan 18, 2011 at 17:41

I have recently been solving the problems at Project Euler . The problems are of varying difficulty. The solutions don't usually require large amounts of code, but you do have to consider many factors like run-time of your algorithm. You can use any language you like, as you just enter an answer. There is a good write-up of an optimal solution for many problems, and lots of discussion about each problem. Try to solve one problem every day and you will be amazed how much your problem solving and analysis improve. For extra credit, try solving the same problem in many languages, such as a procedural language (maybe C++), a scripting language (like python) and a functional language (like F#).

I come from a science background, so when I look at a problem, I tend to use tactics from the Scientific Method . I especially like to set up "experiments" based on hypotheses and use "controls", so I'll build something and then change/add only 1 thing about it and see what the result is of that one change/addition and if I'm not getting the result I need, I'll switch it back and change something else. This works well for troubleshooting/debugging code. Sometimes you get the answer you seek, but you always learn something new doing that even when you fail. I also like to learn through reductionism -- taking something that already exists (always good to start with something you may not understand, but you know works) and looks complex to me and seeing if I can break it down into its component parts and learn how they work first. It's sometimes easier for my brain to handle learning like this instead of approaching a problem holistically and I can use that knowledge to build other similar complex things myself. I also recommend reading books on logic and reasoning choosing works from both classical and modern thinkers (start with Aristotle and work your way up). They can give you some of the foundations of basic logic which you can use to help in problem solving in computers. And, of course, if you can't solve a problem and you've been working on it for awhile, take a brain break. Ruminating on a particular aspect of an issue is sometimes detrimental. Everyone needs breaks :)

The hardest part of problem-solving is "Perceptual Narrowing".

You pick something that appears to be the problem and doggedly go after that until you're exhausted and making no progress.

The way to do this is to be sure -- absolutely sure -- you really understand the problem. "Solving the Right Problem" is the most important part of problem-solving.

Sometimes they call this "thinking outside the box". "The box" is a narrow viewpoint that may not include the real, fundamental problem. Thinking outside the box is to look for the right problem to solve.

There are numerous books on strategies for avoiding the narrowing that goes with premature focus on the wrong problem.

Mostly the trick is to identify what the real outcome is supposed to be. Then figure out what blocks that desirable outcome.

Honestly I think everybody is different, so everyones road map to becoming a better problem solver is different. You can learn from other people's experience, but in the end you have to forge your own path. This is essentially learning something the "hard way", but it's effective in this case.

Here is how I started to improve my problem solving, though I am not a great problem solver yet, just a better one than I was last year. I was given a new project at work that involved extending a piece of open source time tracking software, by adding three new reports for management. This software was written in a language I had never used and it was poorly documented and highly obfuscated. I dug in and did a ton of research and then I just worked on the reports in baby steps, once I had basic functionality I improved upon them and then finally I added more features.

So, in other words, I recommend you find some sort of sink or swim real world project to work on. If you are currently employed as a programmer, find a project or ask your boss for one. If this scenario isn't possible find one outside of work, maybe contract/freelance work or something. I solve problems very well and very quickly when I have to and I retain that knowledge because of the intensity of the project. If this won't work for you then just do what everyone else on this thread suggests :).

The answer is itself in the Question by coming out with different solutions. There are always more than one solutions (e.g. Sorting can be done in different ways viz. Bubble Sort, Selections sort etc.) you just need to choose a way you can do it (Sorting) efficiently. Try with different next time and so on..... And books for Problem solving..... None You can not learn Problem solving skills from books, more code you will execute more knowledge you will gain. Good Luck

It's easy for a programmer to mentally attack a problem by visualizing how to solve the problem with their favourite programming language. Just like the classic carpenter who sees all problems as nails when his favourite tool is the hammer.

I think the best problem solving exercises comes when you get above the practical level and just think in terms of "this is what I would need in order to solve it in an optimal way". In some cases you may have to learn (a lot of) new stuff to apply the solution at all, but the key point is that your ability to work out a solution shouldn't be limited to your historical and existing techniques.

An old practical example for me is that I learned how to implement efficient cooperative multitasking when I realized that my problem didn't actually need preemptive threads, even though I usually would have gone right ahead to my comfort zone banging up all those mutexes (that eventually always seem to stop being comfortable at some point..).

In application development, many of the problems we face are either our own invention or the invention of the idiot we inherited that screwed up code base from. Resolving a problem most often comes down to finding the source . Often, once we find where it's happening, mere competence is what is needed to solve it.

To that end:

• Learn your platform.
• Learn your tools.
• Learn what tools are available for your platform that you haven't encountered yet.

All the brain training in the world is useless without information for the brain to use. In order to solve a problem, you must know what the possibilities are first! Even then, it's a lot quicker to work with good information rather than just a description of the problem.

I might speculate til the cows come home on why something is taking too long to execute. But if I say "lets get some data first", I might see that a whole lot of exceptions are being thrown and realize I could change this to an if statement instead. Without knowing how to collect the information, knowing that on my platform exceptions take quite a bit of overhead, and that there's a way to check before try that is faster, I'd never solve the problem.

There's two parts to your answer:

a) Technique's for the actual problem solving

b) Making your brain inherently "better" at thinking and problem solving

There's always been some great answers on technique (assume you know the problem etc) so I'm not going to cover that as much. As for training your brain, there's a couple of things you can do to cross those synapses and build more interconnections

1) Learn a new language, a real language (like french, or chinese might be a good bet these days)

2) Learn to play a new instrument

3) Do something artistic like paint, draw or sculpture

4) Play scrabble or do crosswords

5) Dance like you mean it. No, I'm not kidding. Dancing has been shown to have an impact on your brain and thinking

6) Broaden your experiences, innovative solutions came come from applying a theory in one field in another so study different fields and areas you find interesting

7) Exercise, exercise is crucially important to improving the thinking process

Finally, I'm going to offer my best tip for solving hard problems: take a long walk. I've found that it works miracles for clearing out your head and letting one contemplate problems

My advice would be to throw out the book!

Not literally of course. What I mean is, enter a topic area you have little experience in, and solve hard problems there, without learning about existing solutions. Rely on nothing but your creativity and critical thinking and perhaps a reference manual.

You might design an image format. Or a web server. Or a compression scheme. File system. Kernel. Artificial intelligence. Programming language. Computer vision system.

Something you find interesting, that is reasonably complex, and which you never learned about. Don't read about it: just jump straight in. Experiment. Make mistakes. Reinvent the wheel.

Don't ask for help. Stay away from tutorials. Stay away from the theory. Don't pull a solution off the shelf.

• We learn best from mistakes.
• It gives you an opportunity to practise coming up with solutions creatively, rather than regurgitating and adapting old solutions.
• You are forced to evaluate your ideas. You can't evaluate them without developing a good understanding of your tools, of the problem you're solving, and of the idea you wish to evaluate. This leads to a deeper understanding of the topic than you would otherwise develop. (Feel free to read about the tools you are using, just don't read about the problem you're trying to solve.)

Make a few attempts, and once you feel happy with what you've achieved, leave it for a few months. Then come back fresh and see if you can find a new perspective. After that, it's time to start reading about the problem and how others have solved it (or talking with people). At this point, instead of saying to yourself "yes, that makes sense" while you read, you'll say "yes, exactly ", or "well, to some extent", or "wow, that's clever".

In other words, you'll think much more critically about what you read, and you'll find it much easier to understand and remember because you already have a large "mental framework" to attach it to. You'll feel good about those things which you discovered independently, and you'll walk away with a heap of new knowledge.

Don't try to make your solution perfect. Just prove to yourself that you can solve the problem. Adopt a "can-do" attitude, and if you feel daunted by the problem, remember that the person who first solved it probably knew about as much as you do (in fact, they didn't know it had a solution!).

Problem solving isn't something that can be taught or even learned by reading. The only way to get better at solving problems is to solve problems.

There are different techniques and methodologies to problem solving that you can read about, and you can read about tools and technologies that you can use to solve problems in a particular domain. Unless you continually think about problems, try to come up with solutions (come up with multiple solutions for every problem and evaluate them against each other), and then evaluate your solutions against the solutions developed by others, you won't get better at problem solving.

I recommend picking up a copy of Pragmatic Thinking and Learning: Refactor Your Wetware by Andy Hunt . It's a book about understanding how you think, react, and learn. It brings in relevant theories from behavioral theory and other cognitive sciences. It's specifically geared toward software developers, but applicable to any knowledge worker.

For newbies in programming like myself I recommend the book "Think Like a Programmer". In the first chapter it covers such problem solving techniques as restating and dividing the problem, starting with what you know, reducing, analogies and experimenting.

Then there are more advanced techniques with examples in C++: solving problems with arrays, pointers and dynamic memory, classes, recursion, code reuse. I cannot comment on this part because it's too hard for me yet.

I solve as many problems as possible. I also like some puzzle books like this one . I also tinker with problem solving games, like math games involving prime numbers or something, sudoku, the Tower of Hanoi, etc. Just find things to solve. Also, code it out when possible.

Bye solving a LOT of problems!

you start with easy problems and you move up to more harder problems once the easy ones become a routine instead of problems.

Don't keep yourself to theory, do more practice. With practice comes experience.

• The Overflow Blog
• Ryan Dahl explains why Deno had to evolve with version 2.0
• Featured on Meta
• We've made changes to our Terms of Service & Privacy Policy - July 2024
• Bringing clarity to status tag usage on meta sites

Hot Network Questions

• Postdoc supervisor has stopped helping
• Adverb of Place vs. Predicate nominative
• Visualizing histogram of data on unit circle?
• Ethics application: secondary analysis of anonymous data without "future use" consent
• "Show single Polygon" Atlas Filter Expression
• How to remove a file which name seems to be "." on an SMB share?
• How should I respond to a former student from my old institution asking for a reference?
• \includegraphics not reading \newcommand
• "Knocking it out of the park" sports metaphor American English vs British English?
• Calculate the sum of numbers in a rectangle
• Who gave God the name 'Jealous' as referred to in Exodus 34:14?
• How to add a segment to an Excel radar plot
• Why are swimming goggles typically made from a different material than diving masks?
• If you get pulled for secondary inspection at immigration, missing flight, will the airline rebook you?
• Should I be worried about this giant crack?
• Retroactively specifying `-only` or `-or-later` for GPLv2 in an adopted project
• Did anyone ever ask Neil Armstrong whether he said "for man" or "for a man?"
• A world without entropy
• Aberrant Mind spell swapping
• Is the Shroud of Turin about 2000 years old?
• Why is global state hard to test? Doesn't setting the global state at the beginning of each test solve the problem?
• The hat-check problem
• Is this misleading "convenience fee" legal?
• Travel to UK with temporary passport as EU citizen

Growth Tactics

How to Improve Problem Solving Skills in the Workplace

Jump To Section

In a career spanning over two decades in leadership and management, I’ve found myself at the epicenter of problem solving in the workplace more times than I can count. The nature of managing teams and leading projects means that each day comes with its own set of challenges, each presenting a new “fire” to extinguish.

This relentless demand for solutions has served not as a setback, but as a rigorous training ground for honing my problem solving skills. I’ve come to realize that the capability to effectively solve problems is not just an asset but a necessity in the fast-paced and ever-evolving workplace. The journey of refining these skills is continuous, demanding both dedication and a willingness to adapt.

This article aims to share insights and strategies on how to enhance problem solving skills in the workplace, drawing from lessons learned through firsthand experiences. Here, we’ll explore why cultivating strong problem solving abilities is crucial for professional growth and organizational success, and how you can systematically improve these skills to navigate the complex challenges of today’s work environment. Let’s dive in, and uncover the means to turn problems into opportunities for innovation and advancement.

Understanding the Importance of Problem Solving

In the modern workplace, the ability to tackle difficulties effectively is not a luxury, it is an absolute necessity. Problems can arise from a variety of sources: internal challenges, market competition, technological advancements, or unforeseen global events. Employees and leaders alike who excel in problem solving become invaluable assets to their organizations. But what makes problem-solving skills so crucial? Let’s unpack this.

Value in the Workplace

First and foremost, problem solving is directly linked to productivity and efficiency. A workforce adept in identifying issues quickly and proposing viable solutions can save a company from costly downtime and resource wastage. It is the oil that keeps the organizational machinery running smoothly.

Beyond the immediacy of resolving specific issues, problem-solving skills foster a proactive mindset. Rather than waiting for directives, employees who are skilled problem solvers take ownership and initiative. They are the ones who anticipate potential roadblocks and ward them off before they impact workflow.

Innovation and Adaptation

The constant push to find better, faster, and more cost-effective methods gives rise to innovation. When employees approach problems with a creative mindset, they often discover new ways of doing things that significantly improve operations. This adaptive quality ensures that a company is not just reacting to change but is staying ahead of it, prepared to pivot and embrace new opportunities.

Team Dynamics and Morale

A culture that values and develops problem-solving skills is also conducive to stronger team collaboration. When everyone brings their problem-solving ‘A-game’, it creates a synergistic effect where the sum is greater than its parts. Moreover, teams that solve problems together experience heightened morale and job satisfaction. Overcoming hurdles collectively strengthens workplace harmony and builds a sense of camaraderie and trust.

Risk Management

The strategic side of problem solving involves risk management—identifying potential issues before they become actual ones. Effective problem solvers are able to extract lessons from every challenge and apply them to future scenarios. This makes the business more resilient and able to handle adverse situations with more agility.

Measure of Leadership

Finally, for anyone in or aspiring to leadership, being a competent problem solver is a defining characteristic. Leaders are often judged by their capacity to navigate through crises and lead their teams to success. It’s not simply about extinguishing fires; it’s about doing so in a way that instills confidence and maintains or even boosts momentum.

Essential Problem-Solving Skills to Develop

To flourish in today’s complex business environment, mastering a set of core problem-solving skills is imperative. These skills serve as the toolkit for dismantling difficulties and turning them into opportunities. Here are some crucial abilities that professionals should foster:

Analytical Skills

The bedrock of problem solving is the ability to break down complex information into manageable parts. Analytical thinkers can dissect a problem and understand its components, which makes finding a solution more straightforward. Developing sharp analytical skills allows you to evaluate data methodically, recognize patterns, and isolate the variables that influence outcomes.

Critical Thinking

Critical thinking goes hand-in-hand with analytical capabilities. It involves questioning assumptions, evaluating arguments, and considering the validity and reliability of data before making decisions. By honing critical thinking, you reinforce your judgment and decision-making processes, ensuring that your solutions are well-founded and not just spur-of-the-moment guesses.

Creative Thinking

While analytical and critical skills are important, sometimes the best solutions come from outside the proverbial box. Creative thinking unlocks innovative solutions to problems that may not be apparent using traditional methods. Cultivating creativity isn’t just for artistic pursuits; it’s about looking at challenges from fresh angles and being open to unconventional ideas that can lead to breakthroughs.

Emotional Intelligence

Problem solving is not solely an intellectual exercise; it often involves managing emotions and interpersonal relations. Emotional intelligence (EQ) empowers you to understand and manage your own emotions and those of others. High EQ leads to better communication and collaboration, which is essential when you’re working through problems in a team setting.

Decision-Making Skills

All the analysis, critical thought, and creativity ultimately aim at making decisions. Timely and decisive action is often required to resolve issues before they balloon. Training yourself to weigh the pros and cons and then confidently make choices is an essential component of effective problem solving.

Strategic Planning

Strategic planning is about seeing the big picture . Those skilled in strategy are able to formulate step-by-step plans that lead to solutions, considering both short-term results and long-term implications. This forward-thinking approach is invaluable for moving from problem identification to successful execution of solutions.

Adaptability and Flexibility

In a world where change is the only constant, being adaptable and flexible is key. Problems often don’t follow a script, and you need to be able to pivot and adjust your plans as new information or variables come into play.

Persistence

Finally, an often-overlooked aspect of problem solving is the persistence to follow through. Some problems are more complex and stubborn than others, requiring sustained effort and the resilience to face setbacks.

By intentionally cultivating these skills, you will become better equipped to face the multitude of challenges that the workplace can throw at you. Strengthening these capabilities is not an overnight affair but rather a continuous journey of personal and professional development to become a good problem solver. As you advance these essential problem-solving skills, you’ll find yourself becoming a go-to source for solutions in your workplace, deepening your value and effectiveness in your role.

Strategies to Enhance Problem Solving Skills

Developing effective problem-solving skills is a dynamic and continuous process. To better navigate the complexities of the workplace and personal challenges, it’s beneficial to adopt certain strategies that can enhance these skills over time. Below are some effective strategies to consider incorporating into your personal development plan :

Continuous Learning

Keeping abreast of industry trends, technological advancements, and professional knowledge is essential. Engaging in continuous learning through courses, workshops, and reading can expose you to new ideas and methodologies that enhance your problem-solving skills.

Practice Critical Analysis

Like any other skill, problem-solving abilities improve with practice. Try to tackle diverse problems, even if they’re hypothetical. Games and puzzles that require strategic thinking can also sharpen your problem-solving skills.

Reflect on Past Experiences

Maintaining a journal where you document thechallenges you’ve faced, the approaches you took, and the outcomes can help you analyze your growth. This reflection can provide insights into how your approaches can be improved or adapted for future issues.

Foster Creativity

Regular brainstorming sessions, either solo or in a group, can help you think outside the box and generate creative solutions. Don’t judge ideas as they come; the goal is to open up as many possibilities as you can, and then evaluate them later for viability.

Seek Diverse Perspectives

Different perspectives can lead to unique solutions. By networking with others and collaborating, you can experience different problem-solving styles and learn new techniques. This can be particularly useful in complex scenarios where interdisciplinary approaches might be beneficial.

Develop Emotional Intelligence

Since problem-solving often involves other people, understanding emotional dynamics can lead to better outcomes. Work on emotional intelligence by practicing empathy and self-awareness. Knowing how your emotions influence your decisions can help you manage them more effectively.

Implement Structured Problem-Solving Methods

Familiarize yourself with structured problem-solving techniques such as SWOT Analysis, Root Cause Analysis, or the Five Whys. These frameworks can provide a systematic approach to dissecting and addressing problems more effectively.

Embrace Mistakes as Learning Opportunities

Every problem-solving process offers a lesson. Embrace mistakes and analyze them to understand what went wrong and why. This analysis can turn failures into valuable learning opportunities, preventing similar mistakes in the future.

Prioritize Problems

Not all problems need to be solved immediately, and not all require the same amount of resources. Learning to prioritize problems based on their impact and urgency can enhance your effectiveness.

By incorporating these strategies into your regular practices, you can sharpen your problem-solving skills and become more adept at navigating the challenges of both your professional and personal life. Enhancing these skills not only makes you a more competent individual but also a valuable team player and leader in any organizational setting.

Training and Resources for Skill Enhancement

Developing and enhancing problem-solving skills is a journey that involves continual learning and growth. Thankfully, in today’s digital world, there are abundant resources and training opportunities available that cater to varying levels of expertise and professional fields. Utilizing these resources can significantly boost your ability to tackle complex problems effectively. Here’s a guide to some of the most valuable types and sources of training and resources available:

Online Courses and Workshops

Platforms like Coursera, edX, and LinkedIn Learning offer courses taught by industry professionals and university professors. These platforms cover a wide range of topics from analytical thinking, critical reasoning, and creative problem-solving, to specialized courses tailored to specific industries. Interactive workshops can also simulate real-life problem-solving scenarios, offering hands-on experience.

Books and eBooks

A wealth of knowledge exists in books focused on enhancing problem-solving skills. Titles such as “Thinking, Fast and Slow” by Daniel Kahneman, and “The Art of Problem Solving” by Russell L. Ackoff provide insights into human cognition and practical strategies for effective problem-solving. eBooks available on platforms like Amazon Kindle allow easy access to the latest titles as well as classic texts.

Professional Development Seminars

Industry-specific seminars hosted by professional bodies or trade associations can be invaluable. These seminars often address current challenges in the field and offer problem-solving techniques that are immediately applicable to your work. Attending these events also provides networking opportunities with peers who may have faced similar challenges.

Mentorship Programs

Finding a mentor in your field can provide personalized guidance on navigating professional challenges. Mentors can share their experiences, offer advice on developing problem-solving strategies, and provide feedback on your approach to different situations.

Group Discussion Forums and Online Communities

Platforms like Reddit, Quora, and specific professional networks (e.g., Stack Overflow for tech professionals) can be excellent resources for sharing and receiving advice on problem-solving. Engaging with these communities allows you to discuss real-world problems, explore multiple perspectives, and learn from the experiences of others.

Simulation Games

Strategic and simulation games (e.g., chess, SimCity, or even escape rooms) can be fun and effective ways to sharpen your strategic thinking and decision-making skills. These games challenge you to think ahead, anticipate problems, and devise solutions within constraints, mirroring real-life problem-solving situations.

YouTube Channels and TED Talks

Educational YouTube channels (such as TED-Ed or CrashCourse) and TED Talks offer free access to engaging content that can broaden your perspective and inspire innovative thinking. They cover a vast range of subjects, including psychology, business strategies, and science—all of which can enhance your problem-solving skills.

E-learning Apps

Mobile apps designed for learning new skills can be highly convenient. Apps like Lumosity, which offers brain-training exercises, or Brilliant.org , which focuses on problem-solving and critical thinking, allow you to practice and improve your skills on the go.

By leveraging these diverse training and resources, you can effectively enhance your problem-solving skills and apply them to your professional and personal life. Remember, the key to improvement is consistency and the willingness to step out of your comfort zone to tackle new challenges.

Practical Ways to Apply Problem Solving in Everyday Work

Incorporating problem-solving techniques into daily work routines can transform the way challenges are approached, making processes more efficient and outcomes more effective. Here are practical ways to apply problem-solving skills in everyday work:

Start with Clear Problem Definition

The first step in solving any problem is accurately defining it. Spend time understanding the issue at hand. Ask questions like, “What exactly is the problem?”, “Why is it a problem?”, and “What are the consequences of this problem?” A clear, concise problem statement paves the way for focused and effective solutions.

Break Down the Problem

Large or complex problems can seem daunting at first. Break them down into smaller, more manageable components. This approach makes it easier to tackle each part of the problem systematically, without feeling overwhelmed. Analyzing smaller pieces of the puzzle often reveals insights that apply to the problem at large.

Implement the 5 Whys Technique

Originating from lean manufacturing practices, the 5 Whys technique is about asking “Why?” a minimum of five times to drill down into the root cause of a problem. This method encourages deeper investigation beyond surface-level issues and can uncover underlying problems that, once solved, prevent future occurrences.

Leverage Diverse Perspectives

Collaboration can bring diverse perspectives to the table, shedding new light on the problem. Encourage team members to share their insights, experiences, and potential solutions. Sometimes, a fresh pair of eyes can see a solution that may not be apparent from a single viewpoint.

Apply Critical Thinking

Critical thinking involves analyzing facts to understand a problem or topic objectively. It requires distancing yourself from emotional responses to evaluate data and evidence logically. In the context of problem-solving, this means looking at all angles of a problem, questioning assumptions, and considering various outcomes before deciding on a course of action.

Experiment with Brainstorming and Mind Mapping

Brainstorming sessions can generate a multitude of solutions in a short amount of time, making them invaluable for problem-solving. Mind mapping, on the other hand, can help visually organize thoughts, ideas, and potential solutions, making the relationships between different aspects of the problem and its possible solutions clearer.

Prioritize Solutions

Once potential solutions have been identified, evaluate and prioritize them based on criteria like feasibility, impact, and resource requirements. This step ensures that effort is invested in implementing solutions that are most likely to resolve the problem effectively.

Develop an Action Plan

An actionable plan outlines the steps needed to implement the chosen solution. This plan should include tasks, timelines, responsible individuals, and resources needed. Breaking the solution down into manageable steps ensures progress can be tracked, and adjustments can be made as needed.

Reflect and Learn from Outcomes

After implementing a solution, it’s crucial to assess its effectiveness. Did it solve the problem? What worked well, and what didn’t? Reflecting on these questions and learning from the outcomes is a critical part of the problem-solving process. It not only helps in refining current solutions but also enhances problem-solving skills for future challenges.

By integrating these practical strategies into everyday work, individuals and teams can foster a proactive problem-solving culture. This approach not only addresses issues more efficiently but also contributes to continuous improvement and innovation within the workplace.

Incorporating Problem Solving into Team Collaboration

Bringing problem-solving to the forefront of team collaboration not only enhances productivity but also drives innovation and team cohesion. Here are several strategies for effectively incorporating problem-solving into the fabric of team collaboration :

Foster Open Communication

Establish a communication-rich environment where team members feel comfortable sharing their thoughts and ideas. Encourage active listening and ensure that all voices are heard without judgment. This openness facilitates the free flow of information, which is critical for identifying issues and brainstorming solutions collaboratively.

Define Roles Clearly

Clearly defining roles within the team helps in streamlining the problem-solving process. Assign a facilitator to guide discussions, a scribe to document the process, and various roles based on team members’ unique skills and expertise. When everyone understands their responsibilities, the team can tackle problems more efficiently.

Utilize Group Problem-Solving Models

Adopt structured problem-solving models such as the PDCA cycle (Plan-Do-Check-Act) or the Six Thinking Hats technique to give a clear framework to the collaborative process. These models help organize thoughts, manage the flow of ideas, and assess solutions systematically.

Create a Safe Space for Creativity

Innovative solutions often arise from creative thinking. Create a team culture where creativity is valued and nurtured. Establish an environment where it’s safe to take risks and where unconventional ideas are explored, not immediately dismissed.

Encourage Collaborative Tools

Leverage technology to facilitate collaboration. Use project management tools, shared documents, and digital whiteboards to allow team members to contribute ideas, organize thoughts, and track progress in real-time, even when working remotely.

Value Diverse Perspectives

Diversity within teams brings a range of perspectives to problem-solving, which can lead to more comprehensive and robust solutions. Encourage team members with different backgrounds, skills, and experiences to contribute their viewpoints. Recognize the value of diversity as a strength in the problem-solving process.

Implement Regular Group Reflection Sessions

After completing a project or resolving an issue, reconvene the team for reflection sessions. What was learned? What could have been done better? Reviewing the problem-solving process and the outcomes can offer valuable learning experiences that improve the teams’ ability to handle future issues collectively.

Establish a Clear Process for Decision Making

While consensus may be ideal, it’s not always practical. Establish a decision-making process that is transparent and fair, such as voting or taking turns to make final decisions. Having a process in place can help avoid conflict and ensure that decisions are made in a timely manner.

Empower Team Members

Empower individuals within the team to take initiative and make decisions within their scope. This empowerment can lead to faster problem resolution and encourages a sense of ownership and accountability within the team.

Celebrate Successes and Learn from Failures

Acknowledge when the team successfully solves a problem and celebrate the achievement, no matter how small. This positive reinforcement motivates team members for future problem-solving endeavors. Similarly, view failures not as setbacks but as learning opportunities, providing valuable insights for improvement.

Incorporating problem-solving into team collaboration isn’t just about fixing issues; it’s about building a dynamic, resilient, and innovative team capable of confronting any challenge that comes their way with confidence and collective expertise.

Measuring the Impact of Improved Problem-Solving Skills

As organizations and teams focus on enhancing problem-solving abilities, it becomes essential to measure the impact of these improvements. Evaluating the outcomes not only validates the effort invested in developing these skills but also guides future training and development initiatives. Here are approaches to quantitatively and qualitatively measure the impact of enhanced problem-solving skills within a team or organization:

Benchmarking Performance Metrics

Before and after implementing problem-solving training or initiatives, benchmark key performance indicators (KPIs) relevant to the organization’s goals. Metrics such as customer satisfaction scores, product defect rates, service delivery times, and employee efficiency can provide tangible evidence of the impact of improved problem-solving skills. Monitoring these metrics over time helps in assessing the long-term effects on operational efficiency and productivity.

Employee Feedback and Self-Assessment

Gather feedback from team members about their confidence and competence in solving problems before and after training or initiatives. Surveys, interviews, and self-assessment tools can be used to measure perceived improvements in problem-solving abilities. Employees’ reflections on their growth and challenges provide invaluable insights into the effectiveness of development efforts and areas for further improvement.

Case Studies and Success Stories

Document specific instances where enhanced problem-solving skills led to significant positive outcomes—for example, a complex project delivered successfully, a critical issue resolved efficiently, or a notable innovation developed. These case studies serve as qualitative evidence of the impact and can be incredibly motivating for individuals and teams, illustrating the real-world applications and benefits of effective problem-solving.

Turnaround Time for Issue Resolution

Measure the time taken to identify, address, and resolve issues before and after applying focused problem-solving strategies. A reduction in the turnaround time indicates a more efficient problem-solving process. This metric can be particularly revealing in high-pressure environments where rapid response to challenges is crucial.

Innovation and Idea Implementation

Track the number of new ideas, innovations, and continuous improvement projects generated and implemented within a specific timeframe. Improved problem-solving skills often lead to a more innovative mindset and a higher rate of actionable ideas that can drive the organization forward.

Return on Investment (ROI)

Calculate the return on investment for training and development initiatives aimed at enhancing problem-solving skills. This can involve comparing the costs associated with these initiatives against the tangible benefits obtained, such as cost savings from efficiencies, increased sales from innovative products, or reduced waste and rework. Demonstrating a strong ROI is compelling evidence of the value of investing in problem-solving capabilities.

Employee Retention and Engagement

Examine trends in employee retention and engagement levels. Organizations that focus on developing problem-solving skills often see improvements in these areas because employees feel more empowered, valued, and capable. Higher engagement and lower turnover rates indirectly reflect the positive impact of a problem-solving culture.

Customer Feedback and Retention

Monitor changes in customer feedback and retention rates. Improvements in problem-solving can enhance product quality, customer service, and overall satisfaction, leading to positive feedback and higher retention. Changes in these metrics can provide insight into how enhanced problem-solving skills are perceived from the customer’s perspective.

By employing a combination of these quantitative and qualitative measures, organizations can gain a comprehensive understanding of the impact of improved problem-solving skills. This evaluative approach enables continuous improvement, helping to cultivate a culture of problem-solving that drives success and innovation.

Improving problem-solving skills in the workplace is crucial for any organization aiming to enhance efficiency, foster innovation, and maintain competitiveness. By encouraging a collaborative environment, providing ongoing training, implementing structured problem-solving frameworks, and promoting a culture of continuous improvement, teams can develop stronger analytical and creative thinking capabilities.

It’s essential for these efforts to be supported by managers and integrated into the core values of the organization to ensure their effectiveness and sustainability. As businesses work on refining these skills among their employees, they not only solve immediate challenges more effectively but also equip their workforce with the tools needed for future success. Thus, investing in and nurturing problem-solving skills becomes a pivotal strategy for organizational growth and resilience.

• Product overview
• All features
• Latest feature release
• App integrations

CAPABILITIES

• project icon Project management
• Project views
• Custom fields
• Status updates
• goal icon Goals and reporting
• Reporting dashboards
• workflow icon Workflows and automation
• portfolio icon Resource management
• Capacity planning
• Time tracking
• my-task icon Admin and security
• Admin console
• asana-intelligence icon Asana AI
• list icon Personal
• premium icon Starter
• briefcase icon Advanced
• Goal management
• Organizational planning
• Campaign management
• Creative production
• Content calendars
• Marketing strategic planning
• Resource planning
• Project intake
• Product launches
• Employee onboarding
• View all uses arrow-right icon
• Project plans
• Team goals & objectives
• Team continuity
• Meeting agenda
• View all templates arrow-right icon
• Work management resources Discover best practices, watch webinars, get insights
• Customer stories See how the world's best organizations drive work innovation with Asana
• Help Center Get lots of tips, tricks, and advice to get the most from Asana
• Asana Academy Sign up for interactive courses and webinars to learn Asana
• Developers Learn more about building apps on the Asana platform
• Community programs Connect with and learn from Asana customers around the world
• Events Find out about upcoming events near you
• Partners Learn more about our partner programs
• Asana for nonprofits Get more information on our nonprofit discount program, and apply.

Featured Reads

• Collaboration |
• How to build your critical thinking ski ...

How to build your critical thinking skills in 7 steps (with examples)

Critical thinking is, well, critical. By building these skills, you improve your ability to analyze information and come to the best decision possible. In this article, we cover the basics of critical thinking, as well as the seven steps you can use to implement the full critical thinking process.

Critical thinking comes from asking the right questions to come to the best conclusion possible. Strong critical thinkers analyze information from a variety of viewpoints in order to identify the best course of action.

Don’t worry if you don’t think you have strong critical thinking abilities. In this article, we’ll help you build a foundation for critical thinking so you can absorb, analyze, and make informed decisions. 

What is critical thinking? 

Critical thinking is the ability to collect and analyze information to come to a conclusion. Being able to think critically is important in virtually every industry and applicable across a wide range of positions. That’s because critical thinking isn’t subject-specific—rather, it’s your ability to parse through information, data, statistics, and other details in order to identify a satisfactory solution. 

Definitions of critical thinking

Various scholars have provided definitions of critical thinking, each emphasizing different aspects of this complex cognitive process:

Michael Scriven , an American philosopher, defines critical thinking as "the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication as a guide to belief and action."

Robert Ennis , professor emeritus at the University of Illinois, describes critical thinking as "reasonable, reflective thinking focused on deciding what to believe or do."

Diane Halpern , a cognitive psychologist and former president of the American Psychological Association, defines it as "the use of cognitive skills or strategies that increase the probability of a desirable outcome."

Decision-making tools for agile businesses

In this ebook, learn how to equip employees to make better decisions—so your business can pivot, adapt, and tackle challenges more effectively than your competition.

Top 8 critical thinking skills

Critical thinking is essential for success in everyday life, higher education, and professional settings. The handbook "Foundation for Critical Thinking" defines it as a process of conceptualization, analysis, synthesis, and evaluation of information.

In no particular order, here are eight key critical thinking abilities that can help you excel in any situation:

1. Analytical thinking

Analytical thinking involves evaluating data from multiple sources in order to come to the best conclusions. Analytical thinking allows people to reject cognitive biases and strive to gather and analyze intricate subject matter while solving complex problems. Analytical thinkers who thrive at critical thinking can:

Identify patterns and trends in the data

Break down complex issues into manageable components

Recognize cause-and-effect relationships

Evaluate the strength of arguments and evidence

Example: A data analyst breaks down complex sales figures to identify trends and patterns that inform the company's marketing strategy.

2. Open-mindedness

Open-mindedness is the willingness to consider new ideas, arguments, and information without prejudice. This critical thinking skill helps you analyze and process information to come to an unbiased conclusion. Part of the critical thinking process is letting your personal biases go, taking information at face value and coming to a conclusion based on multiple points of view .

Open-minded critical thinkers demonstrate:

Willingness to consider alternative viewpoints

Ability to suspend judgment until sufficient evidence is gathered

Receptiveness to constructive criticism and feedback

Flexibility in updating beliefs based on new information

Example: During a product development meeting, a team leader actively considers unconventional ideas from junior members, leading to an innovative solution.

3. Problem-solving

Effective problem solving is a cornerstone of critical thinking. It requires the ability to identify issues, generate possible solutions, evaluate alternatives, and implement the best course of action. This critical thinking skill is particularly valuable in fields like project management and entrepreneurship.

Key aspects of problem-solving include:

Clearly defining the problem

Gathering relevant information

Brainstorming potential solutions

Evaluating the pros and cons of each option

Implementing and monitoring the chosen solution

Reflecting on the outcome and adjusting as necessary

Example: A high school principal uses problem-solving skills to address declining student engagement by surveying learners, consulting with higher education experts, and implementing a new curriculum that balances academic rigor with practical, real-world applications.

4. Reasoned judgment

Reasoned judgment is a key component of higher order thinking that involves making thoughtful decisions based on logical analysis of evidence and thorough consideration of alternatives. This critical thinking skill is important in both academic and professional settings. Key aspects reasoned judgment include:

Objectively gathering and analyzing information

Evaluating the credibility and relevance of evidence

Considering multiple perspectives before drawing conclusions

Making decisions based on logical inference and sound reasoning

Example: A high school science teacher uses reasoned judgment to design an experiment, carefully observing and analyzing results before drawing conclusions about the hypothesis.

5. Reflective thinking

Reflective thinking is the process of analyzing one's own thought processes, actions, and outcomes to gain deeper understanding and improve future performance. Good critical thinking requires analyzing and synthesizing information to form a coherent understanding of a problem. It's an essential critical thinking skill for continuous learning and improvement.

Key aspects of reflective thinking include:

Critically examining one's own assumptions and cognitive biases

Considering diverse viewpoints and perspectives

Synthesizing information from various experiences and sources

Applying insights to improve future decision-making and actions

Continuously evaluating and adjusting one's thinking processes

Example: A community organizer reflects on the outcomes of a recent public event, considering what worked well and what could be improved for future initiatives.

6. Communication

Strong communication skills help critical thinkers articulate ideas clearly and persuasively. Communication in the workplace is crucial for effective teamwork, leadership, and knowledge dissemination. Key aspects of communication in critical thinking include:

Clearly expressing complex ideas

Active listening and comprehension

Adapting communication styles to different audiences

Constructing and delivering persuasive arguments

Example: A manager effectively explains a new company policy to her team, addressing their concerns and ensuring everyone understands its implications.

7. Research

Critical thinkers with strong research skills gather, evaluate, and synthesize information from various sources of information. This is particularly important in academic settings and in professional fields that require continuous learning. Effective research involves:

Identifying reliable and relevant sources of information

Evaluating the credibility and bias of sources

Synthesizing information from multiple sources

Recognizing gaps in existing knowledge

Example: A journalist verifies information from multiple credible sources before publishing an article on a controversial topic.

8. Decision-making

Effective decision making is the culmination of various critical thinking skills that allow an individual to draw logical conclusions and generalizations. It involves weighing options, considering consequences, and choosing the best course of action. Key aspects of decision-making include:

Defining clear criteria for evaluation

Gathering and analyzing relevant information

Considering short-term and long-term consequences

Managing uncertainty and risk

Balancing logic and intuition

Example: A homeowner weighs the costs, benefits, and long-term implications before deciding to invest in solar panels for their house.

7 steps to improve critical thinking

Critical thinking is a skill that you can build by following these seven steps. The seven steps to critical thinking help you ensure you’re approaching a problem from the right angle, considering every alternative, and coming to an unbiased conclusion.

First things first: When to use the 7 step critical thinking process

There’s a lot that goes into the full critical thinking process, and not every decision needs to be this thought out. Sometimes, it’s enough to put aside bias and approach a process logically. In other, more complex cases, the best way to identify the ideal outcome is to go through the entire critical thinking process. 

The seven-step critical thinking process is useful for complex decisions in areas you are less familiar with. Alternatively, the seven critical thinking steps can help you look at a problem you’re familiar with from a different angle, without any bias. 

If you need to make a less complex decision, consider another problem solving strategy instead. Decision matrices are a great way to identify the best option between different choices. Check out our article on 7 steps to creating a decision matrix .

1. Identify the problem or question

Before you put those critical thinking skills to work, you first need to identify the problem you’re solving. This step includes taking a look at the problem from a few different perspectives and asking questions like: 

What’s happening? 

Why is this happening? 

What assumptions am I making? 

At first glance, how do I think we can solve this problem? 

A big part of developing your critical thinking skills is learning how to come to unbiased conclusions. In order to do that, you first need to acknowledge the biases that you currently have. Does someone on your team think they know the answer? Are you making assumptions that aren’t necessarily true? Identifying these details helps you later on in the process. 

2. Gather relevant information

At this point, you likely have a general idea of the problem—but in order to come up with the best solution, you need to dig deeper. 

During the research process, collect information relating to the problem, including data, statistics, historical project information, team input, and more. Make sure you gather information from a variety of sources, especially if those sources go against your personal ideas about what the problem is or how to solve it.

Gathering varied information is essential for your ability to apply the critical thinking process. If you don’t get enough information, your ability to make a final decision will be skewed. Remember that critical thinking is about helping you identify the objective best conclusion. You aren’t going with your gut—you’re doing research to find the best option

3. Analyze and evaluate data

Just as it’s important to gather a variety of information, it is also important to determine how relevant the different information sources are. After all, just because there is data doesn’t mean it’s relevant. 

Once you’ve gathered all of the information, sift through the noise and identify what information is relevant and what information isn’t. Synthesizing all of this information and establishing significance helps you weigh different data sources and come to the best conclusion later on in the critical thinking process. 

To determine data relevance, ask yourself:

How reliable is this information? 

How significant is this information? 

Is this information outdated? Is it specialized in a specific field? 

4. Consider alternative points of view

One of the most useful parts of the critical thinking process is coming to a decision without bias. In order to do so, you need to take a step back from the process and challenge the assumptions you’re making. 

We all have bias—and that isn’t necessarily a bad thing. Unconscious biases (also known as cognitive biases) often serve as mental shortcuts to simplify problem solving and aid decision making. But even when biases aren’t inherently bad, you must be aware of your biases in order to put them aside when necessary. 

Before coming to a solution, ask yourself:

Am I making any assumptions about this information? 

Are there additional variables I haven’t considered? 

Have I evaluated the information from every perspective? 

Are there any viewpoints I missed?

5. Draw logical conclusions

Finally, you’re ready to come to a conclusion. To identify the best solution, draw connections between causes and effects. Use the facts you’ve gathered to evaluate the most objective conclusion. 

Keep in mind that there may be more than one solution. Often, the problems you’re facing are complex and intricate. The critical thinking process doesn’t necessarily lead to a cut-and-dry solution—instead, the process helps you understand the different variables at play so you can make an informed decision. 

6. Develop and communication solutions

Communication is a key skill for critical thinkers. It isn’t enough to think for yourself—you also need to share your conclusion with other project stakeholders. If there are multiple solutions, present them all. There may be a case where you implement one solution, then test to see if it works before implementing another solution. 

This process of communicating and sharing ideas is key in promoting critical thinking within a team or organization. By encouraging open dialogue and collaborative problem-solving, you create an environment that fosters the development of critical thinking skills in others.

7. Reflect and learn from the process

The seven-step critical thinking process yields a result—and you then need to put that solution into place. After you’ve implemented your decision, evaluate whether or not it was effective. Did it solve the initial problem? What lessons—whether positive or negative—can you learn from this experience to improve your critical thinking for next time? 

By engaging in this metacognitive reflective thinking process, you're essentially teaching critical thinking to yourself, refining your methodology with each iteration. This reflective practice is fundamental in developing a more robust and adaptable approach to problem-solving.

Depending on how your team shares information, consider documenting lessons learned in a central source of truth. That way, team members that are making similar or related decisions in the future can understand why you made the decision you made and what the outcome was.

Example of critical thinking in the workplace

Imagine you work in user experience design (UX). Your team is focused on pricing and packaging and ensuring customers have a clear understanding of the different services your company offers. Here’s how to apply the critical thinking process in the workplace in seven steps: 

Step 1: Start by identifying the problem

Your current pricing page isn’t performing as well as you want. You’ve heard from customers that your services aren’t clear, and that the page doesn’t answer the questions they have. This page is really important for your company, since it’s where your customers sign up for your service. You and your team have a few theories about why your current page isn’t performing well, but you decide to apply the critical thinking process to ensure you come to the best decision for the page. 

Gather information about how the problem started

Part of identifying the problem includes understanding how the problem started. The pricing and packaging page is important—so when your team initially designed the page, they certainly put a lot of thought into it. Before you begin researching how to improve the page, ask yourself: 

Why did you design the pricing page the way you did? 

Which stakeholders need to be involved in the decision making process? 

Where are users getting stuck on the page?

Are any features currently working?

Step 2: Then gather information and research

In addition to understanding the history of the pricing and packaging page, it’s important to understand what works well. Part of this research means taking a look at what your competitor’s pricing pages look like. 

Ask yourself: 

How have our competitors set up their pricing pages?

Are there any pricing page best practices? 

How does color, positioning, and animation impact navigation? 

Are there any standard page layouts customers expect to see? 

Step 3: Organize and analyze information

You’ve gathered all of the information you need—now you need to organize and analyze it. What trends, if any, are you noticing? Is there any particularly relevant or important information that you have to consider? 

Step 4: Consider alternative viewpoints to reduce bias

In the case of critical thinking, it’s important to address and set bias aside as much as possible. Ask yourself: 

Is there anything I’m missing? 

Have I connected with the right stakeholders? 

Are there any other viewpoints I should consider? 

Step 5: Determine the most logical solution for your team

You now have all of the information you need to design the best pricing page. Depending on the complexity of the design, you may want to design a few options to present to a small group of customers or A/B test on the live website.

Step 6: Communicate your solution to stakeholders

Critical thinking can help you in every element of your life, but in the workplace, you must also involve key project stakeholders . Stakeholders help you determine next steps, like whether you’ll A/B test the page first. Depending on the complexity of the issue, consider hosting a meeting or sharing a status report to get everyone on the same page. 

Step 7: Reflect on the results

No process is complete without evaluating the results. Once the new page has been live for some time, evaluate whether it did better than the previous page. What worked? What didn’t? This also helps you make better critical decisions later on.

Tools and techniques to improve critical thinking skills

As the importance of critical thinking continues to grow in academic and professional settings, numerous tools and resources have been developed to help individuals enhance their critical thinking skills. Here are some notable contributions from experts and institutions in the field:

Mind mapping for better analysis

Mind mapping is a visual technique that helps organize and structure information. It's particularly useful for synthesizing complex ideas and identifying connections between different concepts. The benefits of mind mapping include:

Enhancing creativity by encouraging non-linear thinking

Improving memory and retention of information

Facilitating brainstorming and idea generation

Providing a clear overview of complex topics

To create a mind map:

Start with a central idea or concept.

Branch out with related sub topics or ideas.

Use colors, symbols, and images to enhance visual appeal and memorability.

Draw connections between related ideas across different branches.

Mind mapping can be particularly effective in project planning , content creation, and studying complex subjects.

The Socratic Method for deeper understanding

The Socratic Method, named after the ancient Greek philosopher Socrates, involves asking probing questions to stimulate critical thinking and illuminate ideas. This technique is widely used in higher education to teach critical thinking. Key aspects of the Socratic Method include:

Asking open-ended questions that encourage deeper reflection

Challenging assumptions and preconceived notions

Exploring the implications and consequences of ideas

Fostering intellectual curiosity and continuous inquiry

The Socratic Method can be applied in various settings:

In education, to encourage students to think deeply about subject matter

In business, it is important to challenge team members to consider multiple points of view.

In personal development, to examine one's own beliefs and decisions

Example: A high school teacher might use the Socratic Method to guide students through a complex ethical dilemma, asking questions like "What principles are at stake here?" and "How might this decision affect different stakeholders?"

SWOT analysis for comprehensive evaluation

SWOT (Strengths, Weaknesses, Opportunities, Threats) analysis is a strategic planning tool that can be applied to critical thinking. It helps in evaluating situations from multiple angles, promoting a more thorough understanding of complex issues. The components of SWOT analysis are:

Strengths: internal positive attributes or assets

Weaknesses: internal negative attributes or limitations

Opportunities: External factors that could be beneficial

Threats: External factors that could be harmful

To conduct a SWOT analysis:

Clearly define the subject of analysis (e.g., a project, organization, or decision).

Brainstorm and list items for each category.

Analyze the interactions between different factors.

Use the analysis to inform strategy or decision-making.

Example: A startup might use SWOT analysis to evaluate its position before seeking investment, identifying its innovative technology as a strength, limited capital as a weakness, growing market demand as an opportunity, and established competitors as a threat.

Critical thinking resources

The Foundation for Critical Thinking : Based in California, this organization offers a wide range of resources, including books, articles, and workshops on critical thinking.

The National Council for Excellence in Critical Thinking : This council provides guidelines and standards for critical thinking instruction and assessment.

University of Louisville : Their Critical Thinking Initiative offers various resources and tools for developing critical thinking skills.

The New York Times Learning Network provides lesson plans and activities to help develop critical thinking skills through current events and news analysis.

Critical thinking frameworks and tools

Paul-Elder Critical Thinking Framework : Developed by Dr. Richard Paul and Dr. Linda Elder, this framework provides a comprehensive approach to developing critical thinking skills.

Bloom's Taxonomy : While not exclusively for critical thinking, this classification system is widely used in education to promote higher-order thinking skills.

The California Critical Thinking Disposition Inventory (CCTDI) : This assessment tool measures the disposition to engage in problems and make decisions using critical thinking.

The Ennis-Weir Critical Thinking Essay Test : Developed by Robert Ennis, this test assesses a person's ability to appraise an argument and to formulate a written argument.

By incorporating these tools and techniques into regular practice, individuals can significantly enhance their critical thinking capabilities, leading to more effective problem-solving, decision-making, and overall cognitive performance.

Critically successful 

Critical thinking takes time to build, but with effort and patience you can apply an unbiased, analytical mind to any situation. Critical thinking makes up one of many soft skills that makes you an effective team member, manager, and worker. If you’re looking to hone your skills further, read our article on the 25 project management skills you need to succeed .

Related resources

10 tips to improve nonverbal communication

Scaling clinical trial management software with PM solutions

4 ways to establish roles and responsibilities for team success

6 ways to develop adaptability in the workplace and embrace change

Stack Exchange Network

Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

How to Improve Mathematical Thinking and General Problem Solving Skills?

I'm a sophomore in university and seriously feel that I'm bad at solving mathematical and algorithmic problems (be it discrete math, calculus or just puzzles). I noticed that I'm only good at solving questions that are similar to the ones that have been taught to us.

Here's how I generally approach it:

• What is the problem? What do I need to do here?
• Does it look like I've encountered this before?
• Can I think of a smaller problem to solve instead?

If the answer is no to all the above then I sort of blank out. I stare at it and force my brain to run through a wide variety of stuff, almost like a brute force attempt of solving it. Obviously that leads me to nowhere everytime. I simply can't think "outside the box."

What can I do to improve my situation?

• soft-question
• problem-solving
• $\begingroup$ What kinds of questions are you talking about? I think a lot of it does come down to recognizing certain tricks and patterns, and you build up this ability with experience. How often do people truly think outside of the box? $\endgroup$ –  wj32 Commented Nov 1, 2012 at 20:57
• 3 $\begingroup$ "What can I do to improve my situation?" (1) Do A LOT of problems. (2) Read George Polya's "How To Solve It" $\endgroup$ –  BobaFret Commented Nov 1, 2012 at 21:05
• $\begingroup$ Hmm not exactly sure how to answer this. Just questions in general on any topic say textbook practice problems or questions in: projecteuler.net/problems although these are more math puzzle types. $\endgroup$ –  Charles Khunt Commented Nov 1, 2012 at 21:06
• 1 $\begingroup$ I think that how we perceive ourselves, specifically how we perceive ourselves in terms of "what I'm good at" or "what I'm bad at" can be self-fulfilling. I think one's attitude when encountering novel situations, in general, like new problems, has a lot to do with how successful one is in handling the situation: if one develops confidence in one's competence, one is more likely to persevere . One can be fearful, intimidated (retreat); one can feel challenged and stimulated; etc... $\endgroup$ –  amWhy Commented Nov 1, 2012 at 21:07
• 1 $\begingroup$ I added a couple tags; hopefully, these tags will counter the "not constructive" close vote. $\endgroup$ –  Emily Commented Nov 1, 2012 at 21:08

6 Answers 6

You might want to read Thinking Mathematically . (I read it and it's excellent. It will teach you exactly what you're looking for.)

• 2 $\begingroup$ Hear hear! A terrific book: we've based part of a course on reading and doing maths for our first year undergrads on it. It helps them not just with problem solving, but also with understanding what it is we do when we do maths. $\endgroup$ –  user12477 Commented Nov 1, 2012 at 21:15
• 1 $\begingroup$ @amWhy That's a different book. See this instead. $\endgroup$ –  Michael Greinecker Commented Nov 1, 2012 at 21:24
• $\begingroup$ @Michael: thanks for checking that out and pointing it out!...oops, seems I've posted an incorrect link! I'll delete it at once! $\endgroup$ –  amWhy Commented Nov 1, 2012 at 21:38
• $\begingroup$ Dear @amWhy, I read your now deleted comment as an alternative recommendation. $\endgroup$ –  Rudy the Reindeer Commented Nov 2, 2012 at 7:34
• $\begingroup$ @MattN Thanks for your comment; I'll "repost" the link here as a different book, perhaps worth looking into. $\endgroup$ –  amWhy Commented Nov 2, 2012 at 13:19

I belonged to a school education system where we were made to do lots of different problems, but we were never told to try and understand the underlying theory behind the problems. This made me scared of math. What I basically had was a cookbook of a variety of wonderful recipes without realizing why I needed to add salt or sugar to a dish. May be you are facing the same problem? May be you are learning all these different techniques to solve problems without really understanding the theory behind why the problems can be solved using those techniques? Hence, because you don't understand the theory behind the techniques, once you get a problem that cannot be solved using the techniques you are familiar with, you get stuck.

While I agree with glebovg that trying to develop an intuition for how to write proofs is essential, I feel that you should make the effort to start reading proofs first. For instance, a book that really helped me understand Calculus was Spivak's Calculus. Try going through the proofs there, and learn the underlying theory. This is coming from someone who was in your position not too long ago.

I encourage you to read books that emphasize problem solving, but at some point you will just have muster the courage to open a book with proofs, and read through it.

Also, the issue of memorization is kind of a slippery slope. You will find that often even when you are trying to understand the theory, you will just have to memorize some computational techniques here and there. I think Terry Tao has a good post where he addresses the issue of memorization. I agree with him that certain basic things have to be memorized. For instance, you will have to memorize what the axioms of a group or a field are. I think memorization and understanding go hand in hand. Certainly your goal should not be to only memorize techniques to solve problems.

Here is more advice from a master:

http://terrytao.wordpress.com/career-advice/solving-mathematical-problems/

http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/

http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-grades-and-exams-and-methods/

http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

All the best!

• $\begingroup$ A very insightful answer and suggested readings! $\endgroup$ –  user1007190 Commented Dec 30, 2023 at 5:25

I think proving theorems really develops your thinking. Try to prove a few important theorems from calculus as well as discrete math, or try to understand someone's proof. Of course, the more you know the better, so that is why we say math is not a spectator sport. You need to do more than just the homework if you want to improve. Sometimes many results that you learn in, say discrete math, might seem confusing, but once you see why they are important in a different context, for example in number theory or algebra, you should remember them. To be honest, I think understanding and being able to prove theorems is actually relevant to math, whereas puzzles are just for fun. The best advice I can give is: Do not try to memorize math and simply remember everything for an exam because that way you might get a good grade, but you will forget everything a few days after the exam, instead try to understand why something is true. This way you will remember something practically forever, because you will be able to derive it when you forget.

I don't know about puzzles, so I write only about solving mathematics problems. In my experiences in this site, I find it far easier to solve problems in a field(like abstract algebra) I know well than in a field(like analysis) I know less. I think it's like walking in a town. If the town is where you live, you know every corner and you think you can almost walk with blindfold. On the other hand, if you are new in the town, you lose your way easily.

So the question is how we know a field well. Read textbooks, understand proofs, try to prove a theorem before reading the proof of a textbook. Reconstruct a proof without seeing a textbook. do exercises, try to find examples and counterexamples, try to find problems by yourself and solve them, etc.

I got a PhD and a postdoc in pure mathematics and I just can talk from my experience. I think that mathematical thinking can be improved with your experience solving problems and reading. For me, there are 2 options.

Option 1: improve your mathematical thinking by yourself. This means trying to approach the problem from all the possible points of view that you can imagine. Organize them, try to apply them one by one and draw a lot. Try to improvise and start solving similar problems in simpler versions. This is very hard to do, especially when you learn in a systematic way because this requires creativity but if you spend time doing this even if you don't solve it you can grow a lot and develop intuition. Warning! Do not spend more than 1 week with the same problem. Not all people solve problems quickly and that is just fine. If you cannot solve a problem after your hard work is a good idea to ask for help (books, mentors, the internet, etc) or just leave it in a special list and move forward. You will be able to solve that list in the future. Reading some comments reminds me that teaching to others the exercises that you can solve is a very powerful way to improve your mathematical thinking, it helps to organize your knowledge and discipline your mind. Please be patient with others. Some day someone will be patient with you and you will need it!!!

Option 2: improve your mathematical thinking using help. Some people may think that asking for help from others or books destroys your creativity and limit your mathematical thinking to the creativity of others. But only a few gifted can afford that. I think that there is nothing wrong with gathering some strategies of others to enrich your own bunch of tools. Consult a friend, professor, books or forums like this. When you ask for help the method to solve a problem is something that you haven't thought of, however, the new experience can help you to solve new problems in the future. When you are facing a new kind of problem and you do not have a clue where to start, look for examples and solved exercises. If you are in high school most likely there is a lot of reading material, examples and solved exercises for the topics that you are interested in.

In the end, your experience solving problems and your background will develop your mathematical thinking, and you can do it using options 1 and 2.

Old thread, but I came across this and wanted to pitch in my 2 cents.

I remember when I first got to college and was studying mechanical engineering. My high school education taught me the plug-n-chug method of thinking, so topics like differential equations, physics, let alone, linear algebra, dynamics, thermo, mechanics, etc. were really really difficult for me.

Somehow I struggled through it though, and graduated, but I always felt uneasy about having as solid of problem-solving skills in my educational foundation as I wanted on it. Especially since I was now working (tho my day-to-day work didn't require those specific skills). I ended up making a hack solution and practiced one math or physics problem a day on my own. I felt like I really came to understand those things since now I took the time to go through them myself, and see where all the formulas were derived from. Knowing that, I knew better when I could apply an equation, and in what manner.

I actually came across this site later: www.learnerds.com which pretty much was what I was looking for. An interesting (semi-realistic) math/engineering/science question a day with a good solution, and the authors are great at responding back to your comments, regardless of your level.

You must log in to answer this question.

Not the answer you're looking for browse other questions tagged soft-question problem-solving learning ..

• Featured on Meta
• We've made changes to our Terms of Service & Privacy Policy - July 2024
• Bringing clarity to status tag usage on meta sites
• 2024 Community Moderator Election
• 2024 Election Results: Congratulations to our new moderator!

Hot Network Questions

• Is it possible to add custom Social Media accounts to contacts in the Contacts app?
• In Moon, why does Sam ask GERTY to activate a third clone before the rescue team arrives?
• How does a closed-cycle rocket engine keep the chamber pressure from stalling the pump turbine?
• Chord definition misunderstanding
• Adverb of Place vs. Predicate nominative
• How to completely change the `f` key to a `/` and the `F` key to a `?`
• Can objective morality be derived as a corollary from the assumption of God's existence?
• "Show single Polygon" Atlas Filter Expression
• Why did Worf respond when Picard ordered the Enterprise out of the asteroid in TNG: The Pegasus?
• Should I be worried about this giant crack?
• Which BASIC dialect first featured a single-character comment introducer?
• Is there anything that stops the majority shareholder(s) from destroying company value?
• What (if any) pre-breathes were "attempted" on the ISS, and why?
• Does the overall mAh of the battery add up when batteries are parallel?
• Are there any virtues in virtue ethics that cannot be plausibly grounded in more fundamental utilitarian principles?
• How to display 3 horizontal nested tabs on mobile device
• What other goals could a space project with the primary goal of experience building with heavy lift rockets perform?
• What might cause these striations in this solder joint?
• How would Earth's plants change in this speculated Earth-like planet?
• Explaining Arithmetic Progression
• Retroactively specifying `-only` or `-or-later` for GPLv2 in an adopted project
• Home water pressure higher than city water pressure?
• Fast circular buffer
• C - mini string lib

How to think like a programmer — lessons in problem solving

By Richard Reis

If you’re interested in programming, you may well have seen this quote before:

“Everyone in this country should learn to program a computer, because it teaches you to think.” — Steve Jobs

You probably also wondered what does it mean, exactly, to think like a programmer? And how do you do it??

Essentially, it’s all about a more effective way for problem solving .

In this post, my goal is to teach you that way.

By the end of it, you’ll know exactly what steps to take to be a better problem-solver.

Why is this important?

Problem solving is the meta-skill.

We all have problems. Big and small. How we deal with them is sometimes, well…pretty random.

Unless you have a system, this is probably how you “solve” problems (which is what I did when I started coding):

• Try a solution.
• If that doesn’t work, try another one.
• If that doesn’t work, repeat step 2 until you luck out.

Look, sometimes you luck out. But that is the worst way to solve problems! And it’s a huge, huge waste of time.

The best way involves a) having a framework and b) practicing it.

“Almost all employers prioritize problem-solving skills first. Problem-solving skills are almost unanimously the most important qualification that employers look for….more than programming languages proficiency, debugging, and system design. Demonstrating computational thinking or the ability to break down large, complex problems is just as valuable (if not more so) than the baseline technical skills required for a job.” — Hacker Rank ( 2018 Developer Skills Report )

Have a framework

To find the right framework, I followed the advice in Tim Ferriss’ book on learning, “ The 4-Hour Chef ”.

It led me to interview two really impressive people: C. Jordan Ball (ranked 1st or 2nd out of 65,000+ users on Coderbyte ), and V. Anton Spraul (author of the book “ Think Like a Programmer: An Introduction to Creative Problem Solving ”).

I asked them the same questions, and guess what? Their answers were pretty similar!

Soon, you too will know them.

Sidenote: this doesn’t mean they did everything the same way. Everyone is different. You’ll be different. But if you start with principles we all agree are good, you’ll get a lot further a lot quicker.

“The biggest mistake I see new programmers make is focusing on learning syntax instead of learning how to solve problems.” — V. Anton Spraul

So, what should you do when you encounter a new problem?

Here are the steps:

1. Understand

Know exactly what is being asked. Most hard problems are hard because you don’t understand them (hence why this is the first step).

How to know when you understand a problem? When you can explain it in plain English.

Do you remember being stuck on a problem, you start explaining it, and you instantly see holes in the logic you didn’t see before?

Most programmers know this feeling.

This is why you should write down your problem, doodle a diagram, or tell someone else about it (or thing… some people use a rubber duck ).

“If you can’t explain something in simple terms, you don’t understand it.” — Richard Feynman

Don’t dive right into solving without a plan (and somehow hope you can muddle your way through). Plan your solution!

Nothing can help you if you can’t write down the exact steps.

In programming, this means don’t start hacking straight away. Give your brain time to analyze the problem and process the information.

To get a good plan, answer this question:

“Given input X, what are the steps necessary to return output Y?”

Sidenote: Programmers have a great tool to help them with this… Comments!

Pay attention. This is the most important step of all.

Do not try to solve one big problem. You will cry.

Instead, break it into sub-problems. These sub-problems are much easier to solve.

Then, solve each sub-problem one by one. Begin with the simplest. Simplest means you know the answer (or are closer to that answer).

After that, simplest means this sub-problem being solved doesn’t depend on others being solved.

Once you solved every sub-problem, connect the dots.

Connecting all your “sub-solutions” will give you the solution to the original problem. Congratulations!

This technique is a cornerstone of problem-solving. Remember it (read this step again, if you must).

“If I could teach every beginning programmer one problem-solving skill, it would be the ‘reduce the problem technique.’ For example, suppose you’re a new programmer and you’re asked to write a program that reads ten numbers and figures out which number is the third highest. For a brand-new programmer, that can be a tough assignment, even though it only requires basic programming syntax. If you’re stuck, you should reduce the problem to something simpler. Instead of the third-highest number, what about finding the highest overall? Still too tough? What about finding the largest of just three numbers? Or the larger of two? Reduce the problem to the point where you know how to solve it and write the solution. Then expand the problem slightly and rewrite the solution to match, and keep going until you are back where you started.” — V. Anton Spraul

By now, you’re probably sitting there thinking “Hey Richard... That’s cool and all, but what if I’m stuck and can’t even solve a sub-problem??”

First off, take a deep breath. Second, that’s fair.

Don’t worry though, friend. This happens to everyone!

The difference is the best programmers/problem-solvers are more curious about bugs/errors than irritated.

In fact, here are three things to try when facing a whammy:

• Debug: Go step by step through your solution trying to find where you went wrong. Programmers call this debugging (in fact, this is all a debugger does).

“The art of debugging is figuring out what you really told your program to do rather than what you thought you told it to do.”” — Andrew Singer

• Reassess: Take a step back. Look at the problem from another perspective. Is there anything that can be abstracted to a more general approach?

“Sometimes we get so lost in the details of a problem that we overlook general principles that would solve the problem at a more general level. […] The classic example of this, of course, is the summation of a long list of consecutive integers, 1 + 2 + 3 + … + n, which a very young Gauss quickly recognized was simply n(n+1)/2, thus avoiding the effort of having to do the addition.” — C. Jordan Ball

Sidenote: Another way of reassessing is starting anew. Delete everything and begin again with fresh eyes. I’m serious. You’ll be dumbfounded at how effective this is.

• Research: Ahh, good ol’ Google. You read that right. No matter what problem you have, someone has probably solved it. Find that person/ solution. In fact, do this even if you solved the problem! (You can learn a lot from other people’s solutions).

Caveat: Don’t look for a solution to the big problem. Only look for solutions to sub-problems. Why? Because unless you struggle (even a little bit), you won’t learn anything. If you don’t learn anything, you wasted your time.

Don’t expect to be great after just one week. If you want to be a good problem-solver, solve a lot of problems!

Practice. Practice. Practice. It’ll only be a matter of time before you recognize that “this problem could easily be solved with .”

How to practice? There are options out the wazoo!

Chess puzzles, math problems, Sudoku, Go, Monopoly, video-games, cryptokitties, bla… bla… bla….

In fact, a common pattern amongst successful people is their habit of practicing “micro problem-solving.” For example, Peter Thiel plays chess, and Elon Musk plays video-games.

“Byron Reeves said ‘If you want to see what business leadership may look like in three to five years, look at what’s happening in online games.’ Fast-forward to today. Elon [Musk], Reid [Hoffman], Mark Zuckerberg and many others say that games have been foundational to their success in building their companies.” — Mary Meeker ( 2017 internet trends report )

Does this mean you should just play video-games? Not at all.

But what are video-games all about? That’s right, problem-solving!

So, what you should do is find an outlet to practice. Something that allows you to solve many micro-problems (ideally, something you enjoy).

For example, I enjoy coding challenges. Every day, I try to solve at least one challenge (usually on Coderbyte ).

Like I said, all problems share similar patterns.

That’s all folks!

Now, you know better what it means to “think like a programmer.”

You also know that problem-solving is an incredible skill to cultivate (the meta-skill).

As if that wasn’t enough, notice how you also know what to do to practice your problem-solving skills!

Phew… Pretty cool right?

Finally, I wish you encounter many problems.

You read that right. At least now you know how to solve them! (also, you’ll learn that with every solution, you improve).

“Just when you think you’ve successfully navigated one obstacle, another emerges. But that’s what keeps life interesting.[…] Life is a process of breaking through these impediments — a series of fortified lines that we must break through. Each time, you’ll learn something. Each time, you’ll develop strength, wisdom, and perspective. Each time, a little more of the competition falls away. Until all that is left is you: the best version of you.” — Ryan Holiday ( The Obstacle is the Way )

Now, go solve some problems!

And best of luck ?

Special thanks to C. Jordan Ball and V. Anton Spraul . All the good advice here came from them.

Thanks for reading! If you enjoyed it, test how many times can you hit in 5 seconds. It’s great cardio for your fingers AND will help other people see the story.

freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More

If you read this far, thank the author to show them you care. Say Thanks

Learn to code for free. freeCodeCamp's open source curriculum has helped more than 40,000 people get jobs as developers. Get started

More From Forbes

What is the best way to teach problem solving.

• Share to Facebook
• Share to Twitter
• Share to Linkedin

What's the best way to teach problem solving? originally appeared on Quora : the place to gain and share knowledge, empowering people to learn from others and better understand the world .

Answer by Kreg Moccia , Director of Academics at Yup, on Quora :

Teachers should know the difference between “a process for solving   this   problem” and “a process for solving   any   problem”. The former is a procedure to apply in a specific situation, and the latter is a transferable way of thinking about math problems.

There are a number of frameworks for this, but the most effective ones develop a student’s   executive function skills   while doing math.

In particular, I like George Polya’s process described in his book How to Solve It (easily remembered with the acronym UPSC):

• Understand: Determine what is given in a problem and what you are being asked to find. Find relevant concepts that apply and define any technical vocabulary that you’re unsure of.
• Plan: Decide on a strategy in advance for solving a problem. Write it down so that you can come back to it if you get lost in the process of solving.
• Solve: Execute your strategy and attend to precision. Be careful to check your work as you go along, and don’t be afraid to go back to the Plan step to find another strategy if this one doesn’t seem to be working.
• Check: Is your answer reasonable in the context of the situation? Is it the only possible answer? How can I ensure that it’s accurate?

In my experience as a teacher, school leader, and now as Director of Academics here at Yup, students tend to neglect the U, P, and C parts of this, opting instead to glean basic information from the problem and rushing to put pencil to paper. Once they have an answer, they move on, relieved to be finished and sometimes even afraid of what it would mean to check and find out that they were wrong.

As teachers, it’s our responsibility to ensure that a process like this is made explicit for students and that they are constantly self-reflecting on which parts of it they are strong with and which parts are areas where they need to improve.

Here are some examples of questions and feedback that will be more useful for a student and develop executive function skills:

• Slow down when you read each sentence. Go back and reread if necessary.
• Annotate the question with definitions of terms you’re unfamiliar with.
• Compare your strategy with a classmate’s strategy - whose is better, and why?
• Check back on your plan as you solve to make sure you’re on the right track.
• How do you know that your answer makes sense?
• What steps can you take to make sure that result is accurate?

Less transferable feedback:

• You missed a negative sign here.
• Remember to factor after grouping your terms.
• Don’t forget that the exponent becomes the coefficient of the term when you differentiate.
• I see a mistake in the second line.

As teachers, the latter feedback is often necessary for the sake of expediency, but it is ultimately less empowering for the student in the long-run.

This question originally appeared on Quora - the place to gain and share knowledge, empowering people to learn from others and better understand the world. You can follow Quora on Twitter and Facebook . More questions:

• Mathematics Education : Why isn’t memorizing steps and processes the best way to teach math?
• Education : Why is math important?
• Tutoring : What are some good ways to help kids who are struggling to learn math?

• Editorial Standards
• Reprints & Permissions

• Trending Now
• Foundational Courses
• Data Science
• Practice Problem
• Machine Learning
• System Design
• DevOps Tutorial

15 Tips to Improve Logic Building Skills in Programming

“In some ways, programming is like a painting. You start with a blank canvas and certain basic raw materials. You use a combination of science, art, and craft to determine what to do with them.” – Andrew Hunt

Yes, programming in itself is a very beautiful art. Sometimes we may face some problems while trying to program, but we can definitely overcome them. So, in this article, we will be sharing the top 15 tips and techniques that can help you to make your programming skills more strong, and rectify some common programming problems and this will also help you in the logic-building process.

How to Improve Your Logic-Building Skills in Programming?

Here are the ways in which you can improve your logic-building skills in programming. So let’s get started!!!

1. Concepts are Building Blocks for Programming

While trying to crack the logic of any coding problem, many of us think that we never came across such algorithms or theorems while studying and therefore are not able to solve the problem. In order to solve any problem, we should know the concepts of that topic, then only we would be able to apply them and solve the problem. Theoretical knowledge and concepts can be gained by reading articles, blogs, documentation, and watching videos based on that topic. You can also refer to the articles on GeeksforGeeks for building your concepts. We should also know the application of concepts and practice some important problems based on that topic.

2. Be Consistent

Many times it happens that we take up a challenge to solve a question for some number of days and then discontinue in the middle after some days!! It is a popular saying that practice makes a man perfect!! The same is the case with building programming logic. Make it a point to revise, or read an article or solve a question daily despite being very busy with remaining activities. Practicing consistently will help a lot in the overall logic-building process. In order to motivate yourself, you should always contemplate the reason why you started, reward yourself, and make programming fun by solving some quizzes and experimenting with the programs to see different outputs.

3. Pen and Paper Approach

After seeing any problem, we generally start coding the same on our IDE. So, when we are asked to write code on paper in interviews, we fail to do so. Always try to write the pseudo code or algorithm of the code before implementing them. It will help you in writing the code and the next time whenever you approach a similar problem you will be able to recollect more easily. It will also help you in getting syntactically strong.

4. Revision is Very Important

Many of you might be facing this issue that you learn a particular concept but after a few days or months when another question with the same logic or concept appears, you are unable to solve it. This is because you haven’t revised the concepts. Always make it a point to write down the important concepts and logic of questions that are important and keep them revised again and again. This will help you in recollecting the concepts easily.

5. Do as Many Questions as You Can 

It happens with most of us that there comes a single question and most of us get stuck there for 4 to 5 days and still are not able to crack it. Always try to practice lots of questions in order to develop your programming logic skills. This will help you in improving your logic building. If you are stuck on a single question, don’t spend a lot of time after a single question instead look for the concepts hidden behind the question.

6. Puzzle Solving

In many coding competitions, problems are not directly asked based on a concept. Instead, it generally involves a story woven around it, and we have to figure out the logic for solving the program. In such cases, sometimes we are unable to solve the problem. Try solving puzzles such as Sudoku to develop your logic and thinking ability because programming is nothing but solving complex problems with the help of good logic. 

7. Follow Step-by-Step Approach

We don’t start running since the day we are born. Similar logic applies to coding also. We should not directly jump to difficult questions. We should go from Basic to Advance questions. You can take the ratio of questions such while choosing 10 questions you can divide them into 5 easy, 3 medium, and 2 hard questions. You can find these questions on many good websites. Sometimes, people solve a lot of easy questions from all the sites, but they are not able to solve medium-level questions. Instead, make a balance of all the levels. This will help in clearing the coding tests while placements as most of the questions are from easy to medium level.

8. Find a Programmer’s Community

Sometimes we get bored while solving problems by ourselves with no one to teach or guide us. In such cases, you can always try discussing solutions or complex questions with fellow programmers and friends. This will always help you in finding new logic for the same problem and will help you in optimizing your code. This will also improve your confidence and communication skills!!

9. Go through the Editorials

It happens a lot of times that we are not able to solve some questions, so we just leave the question or understand the editorial and move forward without implementing it. After programming any question, go through the editorial section and the top submissions of the code. Here you will be able to find optimized and different logic for the same code. Try to implement the solutions in the editorial section after understanding them, so that the next time you find such a question you will be able to solve it.

10. Take Part in Coding Challenges

Most people are aware of coding challenges and if you want to build your logical skills then you must keep taking part in the same. Taking part regularly in coding challenges is very useful as it makes you familiar with the logical mindset. In a coding challenge, there are numerous types of questions that provide you with a lot of exposure. Also, taking part in such challenges allows you to see solutions of various codes provided by different coders and helps you if stuck at some point. 

11. Learn New Things Regularly

Programmers should never stop learning or being stuck on one topic. They must keep on solving multiple topics as it will help them to expand their area of knowledge by building technical skills. The aim should be solving new problems daily and not being stuck to the old pattern or algorithm in order to achieve success. However, at times some topics are a bit tough and take numerous attempts to solve, in that case, stop solving that and go on to the next one as sometimes new problems are helpful in solving the old ones. 

12. Understand Mathematical Concepts

Mathematics is an important aspect of programming and understanding properly will help you in making numerous visuals or graphs, coding in applications, simulation, problem-solving applications, design of algorithms, etc.

13. Build Projects

Project building is another task that will enhance your logical building skills in programming. It challenges your ability to tackling with new things by using different methods and tactics. It is recommended that you must build one project in order to get a proper clarity of the subject and assess yourself in order to work ahead efficiently.

14. Notes Preparation

Notes are saviors and if one does that regularly then nothing can beat them from achieving their goal. While making notes you must write down every trick, concept, and algorithm so that if you need it again it is easily available. So if you are solving any problem then make sure to note down the library functions it will also be helpful for your future interviews. Noting down basic algorithms such as merge sort, binary search, etc. will help you if you are stuck somewhere. 

15. Patience is the Key

Most of the time we leave programming after some days just because we are unable to solve the questions. Let’s always motivate ourselves by saying let’s just try one more time differently, before we decide to quit!!!

If you’ll patiently work on your programming logic skills and follow the tips which we have shared with you, no one can stop you from being a good programmer and you will surely crack all the coding tests and interviews!!!

Please Login to comment...

Similar reads.

• Technical Scripter
• Technical Scripter 2020

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Get the Reddit app

Discuss interview prep strategies and leetcode questions

Does leetcode really improve your problem solving skills

I have been solving problems on leetcode for over a month now. and I can say I have improved a little bit after learning more about data structures and using them and I can probably solve easy problems now in the O(n) time complexity.

However, I still am not able to solve a lot of easy and medium problems and I feel like nothing has improved at the same time, I am good at graphs , 2d array problems and trees , but I still get stuck on most of the array problems and string problems of easy and medium level, and I feel like my problem solving skills has not grown significantly.

Just wanted to know if it's just me or anyone else feels like this? how much time and effort does it take to grow your problem solving skills? What is the best exercise that can help you?

By continuing, you agree to our User Agreement and acknowledge that you understand the Privacy Policy .

Enter the 6-digit code from your authenticator app

You’ve set up two-factor authentication for this account.

Enter a 6-digit backup code

Create your username and password.

Reddit is anonymous, so your username is what you’ll go by here. Choose wisely—because once you get a name, you can’t change it.

Reset your password

Enter your email address or username and we’ll send you a link to reset your password

Check your inbox

An email with a link to reset your password was sent to the email address associated with your account

Choose a Reddit account to continue

• PRO Courses Guides New Tech Help Pro Expert Videos About wikiHow Pro Upgrade Sign In
• EDIT Edit this Article
• EXPLORE Tech Help Pro About Us Random Article Quizzes Request a New Article Community Dashboard This Or That Game Happiness Hub Popular Categories Arts and Entertainment Artwork Books Movies Computers and Electronics Computers Phone Skills Technology Hacks Health Men's Health Mental Health Women's Health Relationships Dating Love Relationship Issues Hobbies and Crafts Crafts Drawing Games Education & Communication Communication Skills Personal Development Studying Personal Care and Style Fashion Hair Care Personal Hygiene Youth Personal Care School Stuff Dating All Categories Arts and Entertainment Finance and Business Home and Garden Relationship Quizzes Cars & Other Vehicles Food and Entertaining Personal Care and Style Sports and Fitness Computers and Electronics Health Pets and Animals Travel Education & Communication Hobbies and Crafts Philosophy and Religion Work World Family Life Holidays and Traditions Relationships Youth
• Browse Articles
• Learn Something New
• Quizzes Hot
• Happiness Hub
• This Or That Game
• Train Your Brain
• Explore More
• Support wikiHow
• About wikiHow
• Log in / Sign up
• Education and Communications
• Mathematics

How to Improve Mental Math Skills

Last Updated: August 2, 2024 Approved

This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. There are 8 references cited in this article, which can be found at the bottom of the page. wikiHow marks an article as reader-approved once it receives enough positive feedback. In this case, 83% of readers who voted found the article helpful, earning it our reader-approved status. This article has been viewed 326,826 times.

Eventually, you'll find yourself in a situation where you'll have to solve a math problem without a calculator. Trying to imagine a pen and paper in your head often doesn't help much. Fortunately there are faster and easier ways to do calculations in your head—and they often break down a problem in a way that makes more sense than what you learned in school. Whether you're a stressed-out student or a math wizard looking for even faster tricks, there's something for everyone to learn.

Break addition and subtraction problems into parts.

• 712 + 281 → "700 + 200," "10 + 80," and "2 + 1"
• 700 + 200 = 9 00, then 10 + 80 = 9 0, then 2 + 1 = 3
• 900 + 90 + 3 = 993 .
• Thinking in "hundreds" or "tens" instead of single digits will make it easier to keep track when digits sum to more than ten. For example, for 37 + 45, think "30 + 40 = 70" and "7 + 5 = 12". Then add 70 + 12 to get 82.

Change the problem to make round numbers.

• Addition : For 596 + 380 , realize that you can add 4 to 596 to round it to 600, then add 600 + 380 to get 980. Undo the rounding by subtracting 4 from 980 to get 976 .
• Subtraction : For 815 - 521 , break it up into 800 - 500, 10 - 20, and 5 - 1. To turn the awkward "10 - 20" into "20 - 20", add 10 to 815 to get 825. Now solve to get 304, then undo the rounding by subtracting 10 to get 294 .
• Multiplication : For 38 x 3 , you can add 2 to 38 to make the problem 40 x 3, which is 120. Since the 2 you added got multiplied by three, you need to undo the rounding by subtracting 2 x 3 = 6 at the end to get 120 - 6 = 114 .

Learn to add many numbers at once.

• For example, 7 + 4 + 9 + 13 + 6 + 51 can be reorganized to (7 + 13) + (9 + 51) + (6 + 4) = 20 + 60 + 10 = 90.

Multiply from left to right.

• For 453 x 4 , start with 400 x 4 = 1600, then 50 x 4 = 200, then 3 x 4 = 12. Add them all together to get 1812 .
• If both numbers have more than one digit, you can break it into parts. Each digit has to multiply with each other digit, so it can be tough to keep track of it all. 34 x 12 = (34 x 10) + (34 x 2) , which you can break down further into (30 x 10) + (4 x 10) + (30 x 2) + (4 x 2) = 300 + 40 + 60 + 8 = 408 .

Try a fast multiplication trick best for numbers 11 through 19.

• Let's look at numbers close to 10, like 13 x 15 . Subtract 10 from the second number, then add your answer to the first: 15 - 10 = 5, and 13 + 5 = 18.
• Multiply your answer by ten: 18 x 10 = 180.
• Next, subtract ten from both sides and multiply the results: 3 x 5 = 15.
• Add your two answers together to get the final answer: 180 + 15 = 195 .
• Careful with smaller numbers! For 13 x 8, you start with "8 - 10 = -2", then "13 + -2 = 11". If it's hard to work with negative numbers in your head, try a different method for problems like this.
• For larger numbers, it will be easier to use a "base number" like 20 or 30 instead of 10. If you try this, make sure you use that number everywhere that 10 is used above. [3] X Research source For example, for 21 x 24, you start by adding 21 + 4 to get 25. Now multiply 25 by 20 (instead of ten) to get 500, and add 1 x 4 = 4 to get 504.

Simplify problems with numbers ending in zero.

• Addition : If all numbers have zeroes at the end, you can ignore the zeroes they have in common and restore them at the end. 85 0 + 12 0 → 85 + 12 = 97, then restore the shared zero: 97 0 .
• Subtraction works the same way: 10 00 - 7 00 → 10 - 7 = 3, then restore the two shared zeroes to get 3 00 . Notice that you can only remove the two zeroes the numbers have in common, and must keep the third zero in 1000.
• Multiplication : ignore all the zeroes, then restore each one individually. 3 000 x 5 0 → 3 x 5 = 15, then restore all four zeroes to get 15 0 , 00 0 .
• Division : you can remove all shared zeroes and the answer will be the same. 60, 000 ÷ 12, 000 = 60 ÷ 12 = 5 . Don't add any zeroes back on.

Easily multiply by 4, 5, 8, or 16.

• To multiply by 5, instead multiply by 10, then divide by 2.
• To multiply by 4, instead double the number, then double it again.
• For 8, 16, 32, or even higher powers of two, just keep doubling. For example, 13 x 8 = 13 x 2 x 2 x 2, so double 13 three times: 13 → 26 → 52 → 104 .

Memorize the 11s trick.

• What is 7 2 x 11?
• Add the two digits together: 7 + 2 = 9.
• Put the answer in between the original digits: 7 2 x 11 = 7 9 2 .
• If the sum is more than 10, place only the final digit and carry the one: 5 7 x 11 = 6 2 7 , because 5 + 7 = 12. The 2 goes in the middle and the 1 gets added to the 5 to make 6.

Turn percentages into easier problems.

• 79% of 10 is the same as 10% of 79. This is true of any two numbers. If you can't find the answer to a percentage problem, try switching it around.
• To find 10% of a number, move the decimal one place to the left (10% of 65 is 6.5). To find 1% of a number, move the decimal two places to the left (1% of 65 is 0.65).
• Use these rules for 10% and 1% to help you with more difficult percentages. For example, 5% is ½ of 10%, so 5% of 80 = (10% of 80) x ½ = 8 x ½ = 4 .
• Break percentages into easier parts: 30% of 900 = (10% of 900) x 3 = 90 x 3 = 270 .

Memorize advanced multiplication shortcuts for specific problems.

• For problems like 84 x 86 , where the tens place is the same and the ones place digits sum to exactly 10, the first digits of the answer are (8 + 1) x 8 = 72 and the last digits are 4 x 6 = 24, for an answer of 7224 . That is, for a problem AB x AC, if B + C = 10, the answer starts with A(A+1) and ends with BC. This also works for larger numbers if all digits besides the ones place are identical. [6] X Research source
• You can rewrite the powers of five (5, 25, 125, 625, ...) as powers of 10 divided by an integer (10 / 2, 100 / 4, 1000 / 8, 10000 / 16, ...). [7] X Research source So 88 x 125 becomes 88 x 1000 ÷ 8 = 88000 ÷ 8 = 11000 .

Memorize squares charts.

• Memorize the squares from 1 to 20 (or higher, if you're ambitious). (That is, 1 x 1 = 1; 2 x 2 = 4; 3 x 3 = 9, and so on.)
• To multiply two numbers, first find their average (the number exactly between them). For example, the average of 18 and 14 is 16.
• Square this answer. Once you've memorized the squares chart, you'll know that 16 x 16 is 256.
• Next, look at the difference between the original numbers and their average: 18 - 16 = 2. (Always use a positive number here.)
• Square this number as well: 2 x 2 = 4.
• To get your final answer, take the first square and subtract the second: 256 - 4 = 252 .

Find useful ways to practice your mental math.

• Flashcards are great for memorizing multiplication and division tables, or for getting used to tricks for specific kinds of problems. Write the problem on one side and the answer on the other, and quiz yourself daily until you get them all right.
• Online math quizzes are another way to test your ability. Look for a well-reviewed app or website made by an educational program.
• Practice in everyday situations. You could add together the total of items you buy as you shop, or multiply the gas cost per volume by your car's tank size to find the total cost. The more of a habit this becomes, the easier it will be.

Joseph Meyer

Exercise your mental math muscles. Improve your math skills by solving daily math problems without using calculators, paper, or counting aids. By solely using your mind and getting into math discussions with your classmates, you will refine your skills and discover new approaches to problem-solving.

Practice Problems and Answers

Community Q&A

• In the real world, you don't always need to know the exact answer. If you're at the grocery store and trying to add 7.07 + 8.95 + 10.09, you could round to the closest whole numbers and estimate that the total is roughly 7 + 9 + 10 = 26. Thanks Helpful 12 Not Helpful 3
• Some people find it easier to think in money than abstract numbers. Instead of 100 - 55, try thinking of a dollar minus a 50¢ coin and a 5¢ coin. Thanks Helpful 6 Not Helpful 9

You Might Also Like

• ↑ http://gizmodo.com/10-tips-to-improve-your-mental-math-ability-1792597814
• ↑ https://www.youtube.com/watch?v=Rgw9Ik5ZGaY
• ↑ https://www.youtube.com/watch?v=SV1dC1KAl_U
• ↑ https://www.youtube.com/watch?v=1JW9BA57aR8
• ↑ http://www.wired.co.uk/article/master-mental-maths
• ↑ https://www.youtube.com/watch?v=YCBTw8KAqkw
• ↑ https://www.scientificamerican.com/article/5-tips-faster-mental-multiplication/
• ↑ Daron Cam. Academic Tutor. Expert Interview. 29 May 2020.

About This Article

One way to improve your mental math skills is to memorize your multiplication and division tables, so you always have the answer to those problems instantly. If you have trouble memorizing the numbers, try creating your own flash cards with blank notecards and asking a friend to help you practice. Another good way to practice your mental math skills is to add up the prices of your items when you’re at the store, and check to make sure you added correctly once the cashier rings you up. You can also try downloading a mental math app like Luminosity to keep your math skills sharp. To learn how to visualize an equation in your head, read on! Did this summary help you? Yes No

• Send fan mail to authors

Reader Success Stories

May 23, 2022

Did this article help you?

Feb 12, 2023

Apr 11, 2023

Ariel Arnaiz

Nov 22, 2022

Deborah Yeary

Jun 8, 2018

Featured Articles

Trending Articles

Watch Articles

• Terms of Use
• Privacy Policy
• Do Not Sell or Share My Info
• Not Selling Info

wikiHow Tech Help Pro:

Level up your tech skills and stay ahead of the curve

Talk to our experts

1800-120-456-456

How to Improve Your Problem-Solving Skills for JEE?

The key to succeeding in the JEE examination is a fast-paced and accurate problem-solving ability. Well, there is no rocket science that needs to be mastered for this, and all you need to do is practice problem-solving rigorously on a daily basis. You have to develop your own strategies that will be effective for solving the problems of Mathematics, Physics, and Chemistry in JEE, accurately. There may be multiple approaches to solving a particular problem, but for JEE preparation you have to choose the most time-saving approach. Below-given tips will help you to cultivate the best problem-solving skills for JEE.

Tips for Effective Problem-Solving Skills

1. Look for the Data Given When you Read a Problem

The key to improving problem-solving skills for JEE is to analyse a problem when you read it and make a note of all the data given in the problem. Initially, you may need to re-read a problem twice or thrice to understand what all data is given and how to use it. With practice, you will be able to make a note of the given data mentally as soon as you read a problem. For example, when you will read a Physics problem, you will be automatically looking for the numerical data given in it and try to register it as parts of the formulas you know.

2. Practice Mental Maths Skills

Practising mental maths skills is one of the most helpful ways to enhance your problem-solving skills for JEE. There are various tricks in mental maths that will help you arrive at a numerical answer with fewer steps. There are tricks for three-digit multiplications, subtraction without a carry, and so on, which will help you calculate faster in the JEE exam. It will cost you a lot of time in the exam if you follow the traditional long methods for calculating.

3. Make Mind Maps to Solve Problems

When you read a question try to develop mind maps with the data and values given in it before solving it. Mind maps will help you think of various problem-solving techniques by visualising them, thereby cutting down the time of the trial and error method. This way you can make a good habit of solving most problems mentally, as you will know how to zero down on the correct problem-solving technique when you read it. For beginners, you can draw flowcharts of various problem-solving techniques and analyse which one will take the shortest time.

4. Think About the Problems From Simple Perspectives

It is of utmost importance that you do not judge a problem by its length or by the terms used in it before you begin to solve the problem. Often, when a question is being asked from your problem area, you tend to jump to the conclusion that it is a difficult problem. If you do not work on this mindset, it is very likely that you will skip the easy problems as well. So, when you read a problem, think of it from a simple perspective, without getting intimidated by the topic it is from. 

5. Have All the Theorems and Formulas at Your Fingertips

To enhance your problem-solving skills for JEE, the foremost thing that you need to work on is learning the formulas and theorems from Physics, Chemistry, and Mathematics. You must spend the least amount of time remembering any formula or theorem during the examination. Note down all the formulas on a separate sheet of paper and paste them on your study table, so that you can revise them every day. You may highlight the formulas that you find difficult to remember and practice regularly. When you spend the least amount of time to rummage up the right formula to solve a problem, you can dedicate a greater amount of time to calculate the answer. This way your accuracy will also be enhanced.

6. Prefer Quality to Quantity When you Practice

Often JEE aspirants set a daily goal of solving a particular number of sums, to improve their problem-solving speed. For example, you can set a goal to solve 50 sums every day, when you begin with the syllabus and increase the total number of sums every week. But the one thing that you need to remember here, is to pay attention to the difficulty level of the sums that you solve. Solving 100 easy sums in a day may be the same thing as solving 50 difficult sums in a day. Practice solving sums of standard difficulty levels, so that you can be well versed with the required problem-solving techniques before the exam.

7. Use a Stopwatch 

Recording the time taken to solve a problem on a stopwatch, during practice, will be of great help for JEE aspirants. For example, it will take less time for you to solve a sum on day 10 of practice, as compared to that on day 1. When you begin with your revisions, record the time you take to solve 10 sums on a stopwatch and try to solve the same number of sums in a shorter time the next day. It will help you to achieve your best problem-solving speed and attempt the maximum number of questions in the JEE examination.

8. Make a Habit of Reading Graphs and Charts

Most students take a longer time to solve the problems that require graph-reading or chart reading. Some students tend to forget the parameters represented on the graph and keep checking it over and over again for noting down the graph readings. Another mistake that students commonly make when solving graph-reading problems is with the scale of the graphs. They forget to convert the graph readings according to the scale of the graphs. Hence, practising sums of graph-reading and chart-readings is very important for improving the problem-solving skills of JEE aspirants. 

9. Kow How to Build Confidence 

We don't always practise in the most effective way. Students frequently select difficult books or questions, attempt to solve them, and then check the solution and consider the question completed. However, such practice will be useless if you do not attempt those questions again in the future, because you will remember the question as soon as you see it, but will be unable to get the final answer. So, begin sorting questions into different groups. You can single-tick the questions that are simple and that you will be able to answer correctly the first time. Second, double tick the good questions, which you should be able to answer on the first attempt. Finally, triple-check the questions that seem difficult to you and for which you need to look for answers. So, you'll have a lot of ticked questions after a while. You can also prepare for the exam by answering a few selected questions the day before. As a result, you will get more confidence and a deeper understanding of the subject. 

10. Try to Backtrace with Answers

You need not solve all the problems with detailed steps in the JEE examination, instead, for some sums try to backtrace with the given answers. For example, if you know the correct formula for a particular sum, you can substitute the given answer choices in it to see which one satisfies the formula along with the other given values. This method of backtracking is very time-saving as you do not need to calculate all the steps to find the correct answer.

You can take various crash courses and tutorials on popular study portals such as Vedantu, to learn tricks to pace up your problem-solving skills. Group study sessions are also helpful when it comes to enhancing your problem-solving skills, as your fellow aspirants may come up with new time-saving strategies for JEE.

Problem-solving is not a natural talent. It must be developed over time with effort and experience. Improving your problem-solving skills is an important part of your JEE or NEET 2022 preparation. 

FAQs on How to Improve Your Problem-Solving Skills for JEE?

1. How can I make my skills stronger for the JEE Exam?

If you are more confident, you will solve problems faster; otherwise, if you are doubtful, you will check simple calculations multiple times. And self-assurance can only be gained through practice. It is a well-known fact that practice makes perfect. Irrespective of how many practice papers are given, speed and accuracy are always the top priorities for everyone. Finishing a paper on time needs not just a lot of practice but also a thorough understanding of the subject. Always remember that no matter what happens, you can always improve. 

2. How can I get confidence in the JEE Examination?

You must be determined and self-motivated if you truly want to clear your exam. If you have great willpower, you can easily pass the JEE exam. Nothing is impossible if you think positively. Here are a few tips to gain confidence for the JEE Exam.

Make no comparisons to others. Be confident in yourself.

Prepare for the JEE Exam with a clear focus.

Make a schedule for yourself and stick to it.

Every day, solve one previous year's question paper.

Evaluate and revise your performance; this is only a mock test.