I'm from Italy and I'm 13 years old. I'm good in Math and I'm good in languages (I know Italian, English and Russian and I think I'm good at them). I'm a programmer and I know HTML, CSS, JS and Python. I've created some program (like webapp), but unfortunately my problem solving and logical thinking isn't good. I've read on the web that when you're younger, it is possible to improve problem solving abilities and logical thinking. What are some steps that I can take to improve problem solving and logical thinking ?
First of all I want to laud you on your knowledge of programming. You know a lot more than I did when I was your age. I tried to learn Italian after watching The Godfather but lost interest after a while because there's no one to talk in it with.
There are two types of mentalities about intelligence and success in life. Studies have shown that children who's parents praised them for being hard working do better in the long run than children who were praised for being intelligent. This is because the second group develop the mentality that they understand things because they are smart and when they have difficulty feel it's beyond their capabilities and give up, while the former group persevere. Fortunately, it's possible to change this mentality. From now on, I want you to think about problem solving skills and logical thinking as skills that can be improved with hard work, much like playing an instrument. Then, you will no longer say, "I am not good at problem solving." You'll say, "I haven't spent enough time working on improving my problem solving abilities." It's actually a massive difference in thinking and produces dramatically different results.
Now that I've gotten the mental aspect out of the way, let me tell you some of the things you can do. I too, liked programming but I soon became so impressed with problem solving that I ended up liking Mathematics much more. My advice to you will be simple and uncomplicated - Spend time solving puzzles and problems.
Now, mathematics is a wonderful platform to develop these skills. You need to work on problems which require elementary knowledge but deep thinking. Problems that appear in mathematical contest are perfect for this ! Here are some recommendations to get you started off :
Puzzles : Aha! Insight - Martin Gardner
Lady or the Tiger - Raymond Smullyan
Both of these authors have a wide body of work in recreational mathematics. If you like these books, explore their other books.
Puzzling Adventures of Dr. Ecco - Dennis Shasha
Puzzle Math - George Gamow
Problem Solving : Mathematical Circles
There's also a journal called Parabola (by UNSW) which has a problem section every issue. Try working through it. Their issues are available for free on the Internet. Bookmark that website on your Browser.
There's an interesting YouTube channel called Mind Your Decisions, which deals with tricky problems and game theory. That will be useful for you too. Subscribe to it.
If you'd like, I could recommend more books, journals, YouTube channels and podcasts about mathematics but I don't want you to get overwhelmed. Often, it's better to be concise to know exactly where to start. I have the problem of not finishing books I start because I simply have too many of them. I'm working on choosing one at a time so I can finish some of them off !
You could also try learning some strategic game like chess and Go. Try playing Sudoku. However, don't get addicted. After you've played Sudoku for about two months, it can be tempting to continue solving them but they will not continue to increase your problem solving abilities as dramatically. It's important to move on after that period. I got addicted to playing Sudoku on the bus ride and got pretty good at it. After a while, it is no longer a challenge and you hit a plateau. This doesn't happen with games like chess and Go though.
I've just happened to come across this free online course on logical and critical thinking.
Excerpt from the site's "About the course":
We are constantly being given reasons to do and believe things: to believe that we should buy a product, support a cause, accept a job, judge someone innocent or guilty, that fairness requires us to do some household chore, and so on. Assessing the reasons we are given to do or believe these things calls upon us to think critically and logically. Improve your logical and critical thinking skills
Even though we’re called upon to use our critical and logical thinking skills all the time, most of us are not that good at it. This free online course aims to help you develop and improve these skills.
You’ll learn how to:
- identify and avoid common thinking mistakes that lead to the formation of bad beliefs;
- recognise, reconstruct and evaluate arguments;
- use basic logical tools to analyse arguments;
- and apply those tools in areas including science, moral theories and law.
Associate Professor Tim Dare and Dr Patrick Girard from the University of Auckland take us on an informative and engaging eight week journey through the worlds of logical and critical thinking helping us to avoid these common obstacles and fallacies and improve our logical and critical thinking skills.
Throughout the course, Tim and Patrick provide videos, articles, and assignments to lead us through the thickets of logical and critical thinking.
The Math Stack Exchange has some great ideas for math habits that improve your mathematical practice.
Some of the ideas mentioned:
- Know the items in your toolkit.
- When learning about a new concept, visualize examples of the concept, and visualize examples of things that are not-quite-the-concept.
- When learning about theorems, try to come up with counter-examples -- and understand which piece of the theorem's assumptions disqualifies each counter-example.
- Simplify a problem until you can solve the simplified problem, then modify your solution to deal with the complication(s) you removed.
- Make notes about what is confusing.
- It is better to make an obvious mistake -- especially if you label it obviously -- than to rely on a concept you do not understand.
Some other questions on this Stack Exchange have ideas that can help, as well:
As was pointed out, you have millions of way of improving problem solving and logical thinking skills. No answer could be comprehensive. Thus I insert my 5 cents.
There is a course “Effective Thinking Through Mathematics” by Michael Starbird from the University of Texas at Austin. It offers several rather easy puzzles. A special feature of this course is that it demonstrates more general problem solving methods using these puzzles as examples. Students are told to observe their process of thinking and solving so they notice which strategy turned out useful. As a result, they can even invent their own strategies tailored to their way of thinking.