10 Ways to Think Like a Mathematician

Please do not think that being a good mathematician is easy. It takes years of dedication, practice, and hard work to become a really great mathematician. If you are serious about becoming one of the greatest mathematicians in the world then this guide will help you get there!

This list is not my own, it’s actually from a poster I used to have hanging in my classroom. But I did not hang this poster simply because it was cute and took up a lot of space on my otherwise bare walls (I was a high school math teacher…not the most creative type…). I hung it because I really and truly believe that these are some of the most helpful things one can do when trying to solve a problem.

Step 1: Before anything else, start with basic arithmetic… addition, subtraction, multiplication and division.

Step 2: As you begin to master these skills, learn the higher level math of algebra… exponentiation, polynomials, etc.

Step 3: Now that you have a firm grasp of basic math and algebra it is time to move on to trigonometry. This includes everything from sine, cosine, tangent, cotangents and so on.

Step 4: Once trigonometry is mastered you will learn about calculus. This includes derivatives and integrals.

Step 5: After all of this math has been learned it is time to do some real world applications with statistics! You’ll be using all the material you have learned to solve real world problems.

Step 6: Now that you have learned all of these necessary skills it is time to take your knowledge and put it to the test. Solve every math problem you can get your hands on! The more practice, the better!

Step 7: If you want to be a great mathematician then solving problems is not enough. You have to SHOW everyone how good you are at solving problems! Enter math contests and win every one of them!

Step 8: This step is vital if you want to be a truly great mathematician… leave your comfort zone. Do things that are totally outside of your skill set. At first this will be difficult, but if you keep trying you will get better.

Step 9: Be sure to work on your attitude too! Every great mathematician has a positive, can-do attitude. It is no accident that the world always needs more mathematicians… because it is so difficult to become one!

Step 10: You are almost there! If you follow these ten steps and put the work in, you will become a great mathematician. You will be respected by everyone and most importantly… you will be good at it!

Thinking Like a Mathematician:

Question everything. When looking at something that is said to be true, see if you can prove it. If someone tells you something is true, ask them to prove it to you. Trying to prove something to yourself will help you exercise your math brain and start thinking about all math problems in this way

Study logic . Being able to spot faulty logic is a skill that mathematicians need. We are surrounded by claims about the world, which need to be scrutinized and evaluated carefully. Critical thinking skills will help you make sure nothing gets past your sharp math brain.

Be precise. Math problems are not meant to be vague. If you are given an equation or a definition, make sure to ask what the symbols in them mean and how they should be used. Math is defined very precisely. Make sure you use it that way.

Think abstractly . It does not matter what kind of problem you are looking at, if you can describe it in terms of numbers and variables, then math could probably help you solve it. There is a way of thinking about the world that will help you solve any problem – math!

Learn to look at your problems from many angles . Part of this stems from looking at the problems more abstractly. Look at a problem from different perspectives and see if one can be solved using methods that are altogether unrelated to the ones you had been using.

Every mathematician is a genius. We all have that potential inside us, and with the right mindset, anyone can learn to think like a mathematician.

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