How to get better in maths: How to solve it?
How to study maths on your own? To get better in maths? Best maths tips for studying maths? If I asked you to think of a tough problem what is the first thing that comes to mind? Well, if you are anything like me you probably thought of some big complex maths equation, right? You will think about how to solve it? For most people, maths seems like one of the most difficult subjects out there.
It’s complex, and unfortunately a lot of people adopt the belief that they are just not maths people. They even do not know how to solve a simple problem. Which is patently untrue because maths is a skill that can be learned just like any other. But since you clicked on this article hopefully you are not one of those people. Hopefully you have at least some degree of belief that you can become better at maths. And if you do, the obvious questions are how do you get better at maths, to study maths on your own?. How to study maths in college? and how to study maths? So, here I will provide you the best tips to study maths.
How to solve a maths problem?
Well, fortunately, these questions have a pretty simple answer. If you want to get better at maths, you must do lots and lots of maths. This is the best way to study maths. Practice, practice and practice. And the tougher the problems are, the better. Because tough problems will stretch your understanding and lead you to new break through. Once you know how to solve it then you are a master. But, working through these tough problems you are eventually going to come to problems that you get completely stuck on.
When you get to these points, it’s important to know how to solve these problems. Because these are the ones that are really going to stretch and build your skill set. So that is what I want to focus on in this article. I want to give you practical techniques for working through, and eventually solving those problems that seem insurmountable at first.
How to solve it?
To start, I want to focus on a piece of advice. The Hungarian mathematician George Polya shared in his 1945 book “How to Solve It”. This is the important technique to understand and put into practice when you are trying to solve maths problems. Because maths builds upon itself. More complex concepts are built upon simpler concepts. And if you don’t have grasp on the fundamental principles, then a complex problem will be hard. So, if you come across a problem that you can’t solve, Try to solve it. First, identify the components or the operations that it wants you to carry out.
Understanding the concepts
Of course, sometimes you have too shaky of an understanding of the concepts and operations themselves for you to work with them and solve that problem. And in that case, it’s time to go do some learning. Go dig into your book, look through your notes, or find example problems online that you can follow along with step-by-step so you can see how people are getting to the solutions, using these concepts. And, if you need to, you can get a step-by-step solution to the exact problem you are working on as well.
There are several tools out there that you can use to do this. The two that I want to focus on in this article which are the best ones I have been able to find are Wolfram Alpha and Symbolab . Both websites will allow you to type in an equation and get an answer and also gypha and Symbolab that you can follow along with. The difference between the two is that WolframAlpha , while being much more power and capable, does require you to be part of their paid plan if you want to get those step-by-step solutions. By contrast, while I found that typing in equations into Symbolab was a little bit slower and less intuitive than it is with WolframAlpha their step-by-step solutions are free.
Online maths tools
Regardless of the online maths tool that you choose to use here the underlying point is that, sometimes it can be useful to see a step-by-step solution for a problem. But, there are two very important caveats here. First and foremost, before you go running off to find a solution, ask yourself Honestly, have I pushed my brain to the limit trying to solve this problem first? Expending the mental effort required to solve the problem yourself is going to stretch your capabilities. It’s going to make you a better mathematician in a way that just looking through solutions won’t.
Now, if you do need to look up a solution, that’s fine. Look it up, follow the steps and make sure that you understand how the answer was arrived at. But, once you have done that, challenge yourself to go back and rework the problem without looking at that reference. It is important to stay vigilant about this. Because if you want to get better at maths the whole point is to master the concepts that you are working with.
Step by step maths solution
The danger that comes with looking up solutions is that, with maths it’s easy to follow along with a step-by-step solution and comprehend what’s going on. But that is very different than being able to do it on your own. And that brings me to my final tip for you. And this is especially important for anybody in a maths class working through assigned homework. Don’t rush when you work through maths problems. I know it’s really tempting to try to work through homework as fast as you can and heck, I even made an article about it recently.
With maths and science and any sort of complex subject especially rushing is only going to hurt you down the road. Because when you rush, you don’t master the concepts. You just brute force your way to answers or you look things up, or you otherwise kind of cheaty-face your way to a completed homework assignment. And later, when you are sitting in a testing room, or you have to apply what you have learned in the real world you are going to get a harsh lesson about exactly what it is you don’t know. So, let’s recap here. If you want to get better at maths and you want to improve your ability to solve those tough problems first, identify the combination of concepts or operations being used in a problem and then isolate them. Work simpler problems that use just one and then master each concept.
Practice on Concepts
You can also simplify the problem by leaving the combination of concepts intact but swapping in smaller, easier to handle numbers. If you need help with the concepts themselves go to your book or an explained article online look up sample problems, or use a tool like WolframAlpha or Symbolab to get step-by-step solutions to the problem you are working on. And finally, don’t rush through your homework assignments. Make sure that you are focusing intently on mastering the concepts, not just finishing.
Hopefully these tips will give you the confidence to tackle some tough maths problems. To expand your maths skill set, I want to leave you with a quote from the great physicist, Richard Feynman.
“The bottom line is this: Ultimately, your ability to get good at maths and anything else for that matter starts with having the confidence to approach it. And as you solve problems and make mental breakthroughs your confidence is going to naturally increase. It becomes a self-sustaining cycle.”
Here is my another article about the history of maths