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**GRAMMARLY REPORT**

## How to Get Better at Math

For most people, math seems like one of the most challenging subjects out there. It’s abstract, it’s complex. And unfortunately, for those reasons, many people adopt the belief that they’re not math people, which is patently untrue because math is a skill that can be learned just like any other. The obvious question is, how do you get better at math? Well, fortunately, this is one of those questions that has a pretty simple answer. If you want to get better at math, you have to do lots and lots of math. And the tougher the problems are, the better because challenging problems will stretch your understanding and lead you to breakthroughs. But in studying math and working through these complex problems, you will eventually come to problems that stump you that you could be completely stuck with. And when you get to these points, it’s important to know how to ultimately solve these problems because these are the ones that are going to stretch and build your skillset.

So that is what I want to focus on in this post. I want to give you some practical techniques for working through and eventually solving those problems that seem impossible at first. 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. It Goes. “If you can’t solve a problem, then there is an easier problem that you can solve, Find it”. This is, in my opinion, the most important technique to understand and put into practice. When you’re trying to solve tough math problems because math builds upon itself, more complex concepts are built upon simple concepts. And if you don’t have a strong grasp of the fundamental principles, then a more complex problem will likely stump you. So if you come across a problem that you can’t solve, first identify the components or operations, it wants you to carry out.

A lot of times, complex problems will have multiple. What you can do in this case is split the problem into multiple problems that isolate just one of those components or operations. I want to show you this concept in action. So let’s work through a quick example now. So this is a summation problem, which is the Greek symbol, Sigma, and it essentially says that we’re going to add up a series of expressions that use a variable starting at one and ending at four as shown.

But if you notice, this summation problem also has a fractional exponent in it. So when you’re working on a problem that combines the two of them, you might get stuck. So assuming that’s the case, let’s break this problem into two more straightforward problems that each focus on, just one of the underlying concepts. First, let’s create a more straightforward summation problem that gets rid of that fractional exponent all together. Now, all we have to do is evaluate that expression four times and then add up the answers, which gets us to a final answer of 66.

And now, let’s move on to the fractional exponent. You can rewrite this as four to the power of three times the power of one half, and then you can rewrite that again to the square root of four, to the power of three. And once you evaluate that, you get an answer of 8.

Now, the whole point of working on these more straightforward, single concept problems is to master the underlying concept or operation that you’re working on here. So if you solve a few and still don’t feel confident about that concept, keep working on it until you do. Remember, Mastery means not being able to get it wrong, not just getting it right once. Once you’ve mastered those underlying components in an isolated setting now, you can come back to the more complicated problem that combines them. At this point, you should be able to work those isolated concepts in your sleep, which means that all of your mental processing power can go towards the new and novel problem of how they work in tandem.

There is one additional way of simplifying tough problems that I want to talk about, and you might have already guessed it if you paid close attention to the examples. I didn’t use complex numbers, long numbers, decimal points, significant fractions. And I stuck to a low limit on my summation problem. Complex big numbers with lots of decimal points can distract your attention from the concepts and operations you’re supposed to practice. So if you’re stuck on a tough problem with these kinds of numbers, go work a similar problem with minimal hole numbers that are easy to add or operate in your head. That way, you can zero in on the actual concepts. Of course, sometimes you have to shake even understanding the concepts and operations themselves to work with them and solve that problem.

And in that case, it’s time to do some learning, dig into your book, look through your notes or find example problems online. You can follow along step by step to 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’re working on as well.

### Tools

There are several tools out there that you can use to do this. But the two that I want to focus on in this post, which are the best ones I’ve been able to find, are Wolfram Alpha and Symbolab. Both of these websites will allow you to type in an equation and get an answer. The difference between these two is that Wolfram Alpha, while being much more powerful and capable, does require you to be part of their paid plan if you want to get those step by step solutions. By contrast, I found that typing in equations in the symbolab was a little bit slower and less intuitive than it is with Wolfram Alpha. There, step by step, solutions are free, regardless of the tool you choose to use here. The underlying point is that sometimes it can be helpful to see a step by step solution for a problem you’re stuck on.

But there are two crucial 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, expanding the mental effort required to solve the problem yourself is going to stretch your capabilities. It will make you a better mathematician in a way that is 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 you understand how the answer was arrived at. But once you’ve done that, challenge yourself to go back and rework the problem without looking at that reference. It is vital to stay vigilant about this because if you want to get better at math, the whole point is to master the concepts that you’re working with. The danger that comes with looking at solutions is that with math, it’s straightforward to follow along with a step by step solution and comprehend what’s going on. But that is very different from 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 math class working through assigned homework. Don’t rush when you work through math problems. I know it’s tempting to try to work through the assignment as fast as you can. But with math and science and any complex subject, especially brushing, you will only hurt yourself down the road because you don’t master the concepts when you rush. You brute force your way to answers, or you look things up, or you otherwise kind of face your way to a completed homework assignment. And later on, when you’re sitting in a testing room, or you have to apply what you’ve learned in the real world, you are going to get a harsh lesson about precisely what it is you don’t know.

If you want to get better at math 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, isolate them, work more straightforward problems that use just one, and then master each concept.

- 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 explainer article online lookup sample problems.

- Use tools like Wolfram Alpha or Symbolab to get step by step solutions to the problem you’re working on.

- Finally, don’t rush through your homework assignments. Make sure you’re focusing intently on mastering the concepts, not just finishing.

Hopefully, these tips will give you the confidence to tackle some tough math problems and expand your math skill set. I want to leave you with a quote from the great physicist Richard Feynman, who said, “I don’t believe in the idea that there are a few peculiar people capable of understanding math and the rest of the world is normal. Math is a human discovery, and it’s no more complicated than humans can understand”.

The bottom line is this. Ultimately, your ability to get good at math 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 increase naturally. It becomes a self-sustaining cycle.