Longtime PickTheBrain reader Marc recently contacted me with the following request:

Hi John. Just wondering if you’re going to post any articles on the importance of quantitative reasoning or perhaps tips on studying math – much like your articles on reading and writing. I think it would be a great idea.

I completely agree. Actually, I’m surprised that we’ve never covered this area before. As a former engineering student, I’ve been through my share of difficult quantitative courses. Although they require many of the same skills as qualitative learning, there are few strategies that don’t overlap.

## Get Comfortable With Your Formulas

The surest path to failure on a math or science exam is not knowing the important formulas. If you don’t have these relationships memorized, you can’t solve basic problems or understand the big picture.

For higher level math, physics, and finance courses, the number of formulas you need to know can be overwhelming. The key to excelling in these situations is putting in the time and effort from the very beginning. If you start memorizing formulas from day one, you’ll barely need to study come exam time.

Start off by keeping a special section of your notebook specifically for formulas. As you learn new ones, write them down. Review your formula list as often as possible, at least a few times a week. You don’t need to spend a lot of time — it’s more important to review frequently. The idea is to build familiarity.

## Problems, Problems, Problems

Success in most math and science courses comes down to your ability to do problems. The first key to success is knowing all the important formulas. The second is knowing the different tricks and wrinkles used in different types of problems.

They only way to get this knowledge is experience. You need to do as many problems as possible so you know what to expect on the exam and don’t get fooled. Try not to slack on problem sets during the year by “collaborating” too much or taking shortcuts. If you run into a problem you can’t solve, reach out to your TA’s, professors, or fellow students.

You’ll also find that memorizing important formulas and working through problems will improve your understanding of the broader concepts and how they fit together.

Although the examples in this post focus on academic success, the same concepts apply to all quantitative learning. By recording important formulas into one file or notebook, thoroughly memorizing them, and applying this knowledge to problem solving, you’ll be able to understand extremely difficult concepts — provided you put in the time.

See also: Raise Your GPA

Great post, John! Thanks. I’d also like to note that somewhere on this site, or perhaps a link to another one, it is said that dedicating an hour or so a day to a particular craft will help you master it in just a few years. I think the same applies to math. Unlike some other areas of learning, math is something that must be done. Practical math and solving problems sets are a good way to retain what is learn.

Marc,

I agree that working on something daily is crucial to learning. That was my big point with learning formulas. It’s much easier to do in 5-10 min a day for 2 months than by cramming for 12 hours straight!

Well I didn’t do engineering, but as a finance student I certainly had to deal with some complex formulas. Often, though, they look harder than they actually are. As you say John, the key is to practice using them to solve problems consistently throughout the term, so that you are not having to cram in the last week before exams!

From my experience as a math tutor for 18 years, I would also add a #3 to this list:

3. Learn the “vocabulary” of your math class!

Many students struggle on tests and homework because they learn to just look at the “math part” of the question and go on instinct. They do not actually read the question, often because they wouldn’t really understand the words in the question anyway. When studying, pay particular attention to the wording of questions. Learn what is of expected of you when the question says, “Simplify” or “Factor Fully” or “Evaluate.” Most students don’t realize that sometimes half the questions actually tell you exactly what to do, if you just understood what the instructions said!

For more tips on “doing well in math class” (which isn’t always the same as “learning math”), see http://www.mostly-math.com/feat_10tips.shtml

One of the things that really helped me was understanding how the formulas were created, so to speak. Knowing why there’s a plus here and a minus there is the reason I was able to memorize formulas for a derivatives class last year and ultimately do well.

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Eugene is right, but didn’t put it strongly enough. You should never memorise maths formulae, and you shouldn’t ever have to memorise science formulae. If you’re memorising it, that means you don’t understand why the formula is what it is. Take the time to understand why, even if it means reading books that aren’t on your syllabus; it’ll still be much quicker and easier, not to mention miles more interesting, than memorising. You still need to be able to keep the formulae within easy mental reach, but practicing problems should do that nicely.

It’s interesting to note that no matter what the subject area, outright practice in it from Day 1 to memorize the basics and build up from there is crucial for later success. (Now, if only I actually took that advice in high school algebra…)

So true…it took me a few terms of mediocre performance to understand the importance of this as well.

Guys… What are you talking about? How can one REMEMBER all of these formulas? Even if you remember them, it wouldn’t help you understanding what they mean.

Remembering without understanding is a big mistake.

Deriving and understanding the links is a key to succeeding with quantitative reasoning and math.

And after all, ablity to derive all the formulas from each other helps correct forgotten formula. And some simple formulas you even do not need to remember, it is easier to derive them from already known ones.

“Remembering without understanding is a big mistake.”

YES!

This article was written by somebody who has only achieved the second level of the proverb:

I hear…I forget

I see…and I remember

I do…and I understand

Did you stop reading before the part where it recommends DOING as many problems as possible?

No I didn’t stop reading. If the essay title was instead “How to master Math and Science in School”, I might agree with the following:

“Success in most math and science courses comes down to your ability to do problems. The first key to success is knowing all the important formulas. The second is knowing the different tricks and wrinkles used in different types of problems.”

As somebody with a career in Math and Science, did you think “knowing the different tricks and wrinkles” belongs to the 2nd level or the 3rd level of the proverb?

Or perhaps your main vocation is that of being a writer: Does writing practice essays to questions contrived by god-knows-who cause “Mastery” of writing?

In retrospect, perhaps is was the use of the word “Master” in the title that set my expectations in the wrong place.

So many of you are critical of the memorization. Guess what? You can’t effectively memorize what you don’t thoroughly understand. Remembering the formulas and equations are a natural consequence of understanding them.

Great tips,

To your Success

Tracy ho

wisdomgettingloaded

This article will help me a whole lot, I’m just getting back to school after understanding the importance of it. Any tips on overall success in university?

I’ve been failing my maths and science from day one, I failed my matric aswel. I am about to rewrite my matric and i might need your help this time around.

anyone who feel that can help me please send me all helpfull info to

pha2chedzo@gmail.com

or invite me on facebook my name is Phathutshedzo Evidence Mudau

good people please help me because from where I live I am nothing without a matric certificate.

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hi there

lavra ka baal

hi im ennocent an i have problems of solvaing maths problems………………..so i need more tip of doin this guys……………….i know that they say hter many way of killing a cat,,but this one is so hard for me to kill………..so plzzzzzzzzzz HELP ME!!!!!!!!!!!!!

madarchod teri maa ki chooooooooooooot

i am master in maths but in 9th class i am lose in maths i dont no why

My age is 14 and I am thorough with my School Maths and I want to study further Maths at this age but there’s no one to teach me.I hope I may get someone here to teach me Intermediate maths so that it would be easy for me when i go to intermediate

Thank You.

well fatima i can suggest u onething never be over confident never think urself as master of maths and done u will perform well

this tips are all good… but the most important thing to remember in studying math is just to relax and think about the concepts that can be linked to the math problem that you are trying to solve for …..focusing is not enough but if you try to combine focusing and critical thinking then, you could be now like Rene Descartes……….and solve any math problem even those harder one.

these r very good tips

Being a Master in any form requires 10,000 hours of practice. Everyone that has left a message on this blog needs to learn English before they can utilize their skills in Math. When it comes to studying Mathematics, one must become one with math. Also one must not only want to do math because it is a requirement, one must study math intuitively and passionately. Becoming passionate about math brings a sense of ease to the mind when being stressed during times of struggle with computation. So find a way to be most comfortable with the desire to love math for all its infinite correlations between nature and in return, you will accept the struggles you face. Then, you will be able to overcome any problem you face (that has been proved). In order to one day Master Math, you must complete each level of math with a near 100% grade in order to prove to your peers, entrepreneurs and yourself that you are knowledgeable and credible at solving and recalling math. So if at first you fail or do not receive a 90%, keep trying, and make sure to effectively utilize your resources e.g. tutors, peers, teachers. Be repetitive with your practice while moving forward, do not do a problem once and never look back. Be sure to “Master” every step of the infinite pyramid the math lies upon.