Understands How Formulas Are Used

In a recent IntMath Poll, many readers reported that they find math difficult considering they have trouble learning math formulas and an almost equal number accept trouble agreement math formulas.

I wrote some tips on learning math formulas hither: How to larn math formulas.

Now for some suggestions on how to understand math formulas. These should be read together with the "learning" tips considering they are closely related.

a. Agreement math is like understanding a foreign language: Say you lot are a native English language speaker and you come across a Japanese newspaper for the kickoff time. All the squiggles look very strange and you find you don't understand anything.

If you want to learn to read Japanese, you demand to acquire new symbols, new words and new grammer. You volition only start to sympathise Japanese newspapers (or manga comics ^_^) once yous have committed to memory a few hundred symbols & several hundred words, and you accept a reasonable agreement of Japanese grammar.

When it comes to math, you lot also need to learn new symbols (similar π, θ, Σ), new words (math formulas & math terms like "role" and "derivative") and new grammer (writing equations in a logical and consistent manner).

And so before you can empathize math formulas you lot demand to learn what each of the symbols are and what they mean (including the letters). You likewise need to concentrate on the new vocabulary (look it up in a math lexicon for a 2d opinion). Also take annotation of the "math grammar" — the way that it is written and how 1 step follows some other.

A little bit of endeavor on learning the nuts will produce huge benefits.

b. Learn the formulas yous already sympathize: All math requires earlier math. That is, all the new things you are learning now depend on what yous learned terminal week, last semester, last yr and all the way back to the numbers y'all learned as a piffling kid.

If you learn formulas every bit you go, information technology will help you to understand what'south going on in the new stuff you are studying. You volition better recognize formulas, especially when the messages or the notation are inverse in small means.

Don't always rely on formula sheets. Commit every bit many formulas as you lot tin to memory — you'll be amazed how much more confident you become and how much better you'll understand each new concept.

c. Always learn what the formula will give you and the conditions: I notice that a lot of students write the quadratic formula every bit

$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Just this is Non the quadratic formula! Well, it's not the whole story. A lot of important stuff is missing — the bits which help you to sympathize it and apply it. We need to have all of the following when writing the quadratic formula:

The solution for the quadratic equation

ax ² + bx + c = 0

is given past

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

A lot of students miss out the "x =" and have no idea what the formula is doing for them. Also, if you miss out the following chip, you won't know how and when to apply the formula:

ax ² + bx + c = 0

Learning the full state of affairs (the complete formula and its conditions) is vital for understanding.

d. Keep a chart of the formulas you need to know: Repetition is fundamental to learning. If the simply time you come across your math formulas is when you open your textbook, there is a skilful chance they volition exist unfamiliar and you will need to beginning from scratch each time.

Write the formulas down and write them frequently. Apply Post-Information technology notes or a big piece of paper and put the formulas around your sleeping accommodation, the kitchen and the bathroom. Include the weather for each formula and a description (in words, or a graph, or a picture).

The more than familiar they are, the more than chance yous will recognize them and the meliorate yous volition understand them as you are using them.

e. Math is ofttimes written in different means — only with the same significant: A lot of confusion occurs in math because of the way it is written. It often happens that you think yous know and sympathise a formula and and so you'll encounter information technology written in another way — and panic.

A simple example is the fraction "one-half". It can be written every bit ane/2, and also diagonally, as ½ and in a vertical arrangement like a normal fraction. We can even have it as a ratio, where the ratio of the 2 (equal) parts would be written 1:1.

Some other instance where the aforementioned concept can be written in different means is angles, which tin exist written every bit uppercase messages (A), or maybe in the form ∠BAC, as Greek letters (similar θ) or as lower instance letters (ten). When you are familiar with all the dissimilar ways of writing formulas and concepts, y'all will exist able to empathise them ameliorate.

Every time your teacher starts a new topic, take item annotation of the manner the formula is presented and the alternatives that are possible.

Do you have whatever tips to add? How do you figure out your math formulas? Which formulas are hardest to understand?

Adept luck with understanding math formulas!