數(shù)學(xué)英語 10 How to Understand the Language of Math
by Jason Marshall
This is our very first Math Dude article, and in honor of that we’re going all the way back to basics to answer some fundamental questions about math that should help you evaluate the status of your relationship with numbers. But let me start by saying I understand that math might be a painful subject for many of you. Sure, some people love it—and they’re lucky that math comes naturally to them. If that person is you—great! But if you’re like many people I know, just hearing the word ‘math’ is enough to induce waves of nausea. If that’s you, then rest assured you can do math. It will take a bit of work and dedication, but becoming mathematically literate is a challenge you can meet.
Why is Math Important?
It is highly likely that at some point you’ll need to take a standardized test with math on it—perhaps the SAT, or use math in a current or future job. If you squander the opportunity to correct your mathematical deficiencies now, you may regret it in the future when friends and colleagues start throwing around statistics that leave you feeling clueless. Worrying that your innumeracy will be discovered isn’t much fun, so why not take the time to learn a bit of math now, instead? I won’t sugar-coat it; this won’t always be easy. But it will certainly be worth your while. And if I do my job right, it should even be fun. No, that was not a joke...I did indeed say fun.
How to Understand the Language of Math
Okay, let’s get back to talking about your relationship with math. Do you speak math? Not sure what I mean? Well, math is a foreign language. And, like any language, you have to speak it proficiently before you can use it efficiently. But besides needing to know it for tests or work, why should you want to speak math? What’s it useful for?
Think of math as a very large box of tools all intent on helping you get your stuff done. Stuff like calculating your tax refund; making a budget; building a paper airplane, or a computer, or even the industrious robotic explorers that orbit and rove around Mars. Sure, some of these applications are more sophisticated than others, but they’re all built on the same foundation of knowledge expressed with the language of math. And by developing your ability to speak and understand this language, you too can use your mathematical tools to get your stuff done.
You Might Know More Than You think
And I have some good news for you: it’s likely that you’re already a far more proficient math speaker than you give yourself credit for. Don’t believe me? Here’s a simple example to demonstrate what I mean. First, I need you to stop and check how much money you have in your wallet. Really, go ahead and check. Got it? Okay, now that you have that number in your head, here’s the scenario: You and I are throwing a party tonight, and I desperately need you to pick up some things at the store. You’ve been aching to try barbecuing a pizza, so we’re gonna give it a shot. But, there’s one little problem—I’m really bad at planning ahead, so my refrigerator is completely empty. We need everything—pizza dough, tomato sauce, cheese, pepperoni, charcoal—everything. So here’s my question for you: Given what’s in your wallet, if you had to go to the store right now to make these purchases, would you have enough money?
Well, presuming you’re older than ten and have done a bit of grocery shopping in your time, I’m guessing you could figure this out without too much trouble. In fact, I’d wager that you tackle little problems like this every day, and you rarely—if ever—think twice about them. Most of the time you solve them intuitively, and you certainly don’t need to resort to any kind of systematic solution method like the one I’m about to describe. But humor me for a few minutes while I go through this in detail. There’s a payoff, I promise.
How to Solve Everyday Math Problems
Whether or not you’ve realized it before, there are basically three steps you need to take to answer this type of question.
First, you need to draw upon your past experiences to estimate how much each item on your shopping list is going to cost. You don’t have to be super precise here; we’re just looking for a ballpark figure—say, to the nearest dollar. In this case, I’d guess the charcoal will cost about $5, the cheese and pepperoni about $3 each, and the dough and tomato sauce roughly $2 apiece.
The second step is to add these individual amounts together to figure out the total cost of the shopping trip. In this case it’s pretty simple: $5 plus $3 is $8, plus another $3 is $11, plus $2 is $13, and finally plus another $2 is a total of $15.
Okay, the third and final step you need to do to figure out whether or not you need to go to the bank before the grocery store is to compare your total estimated cost to the amount of money you have in your wallet. If you found $10 in your wallet earlier—well $10 < $15—so you definitely need to go to the bank first. On the other hand, if you currently have $20—then since $20 > $15—you’ll have plenty of money for the groceries.
You Already Do Real Math Stuff Every Day
Perhaps you’re thinking: “Okay, all of that, and I can now solve one little problem…that I already knew how to solve anyway!” Well, not exactly. Remember how I said that going into detail on this simple problem would be worth your while? Here’s the payoff. The truth is that the mathematical part of this exercise had absolutely nothing to do with pizza or the contents of your wallet. Yes, in practice we were adding quantities of money and seeing if we had sufficient funds to cover a transaction. But mathematically we were estimating unknown values, assigning them to variables, performing integer arithmetic, and solving inequalities. In other words, we were doing real math stuff. Surprised? Well maybe, but hopefully it’s now apparent that math really does apply to things you do every day. And, perhaps more importantly, that you already know how to do a lot of it.
Here’s another thing. Instead of purchasing ingredients for a pizza, we could just as easily have been talking about buying coconuts with coffee beans—or absolutely anything else for that matter. In fact, we didn’t actually have to be talking about buying anything. Abstractly adding the numbers 5–3–3–2–and–2 for kicks, then checking to see if the sum is less than 20? Sure, that would’ve worked too because math is quite happy to work without any real-world references at all—the principles and methods are exactly the same in either case. And this is very powerful stuff. It means that once you know how to solve a problem based on one set of ideas, you don’t just know how to solve that problem. But rather, since you now know the underlying general principles, you can also solve every other problem in existence that’s based upon those principles.
Why Math can be Confusing
While powerful, that potential to use math to solve abstract problems is also one of the things that can make it confusing to learn. Often a problem will appear fairly straight-forward when it’s put in everyday terms. But when the same type of problem is put in purely abstract mathematical terms, it can seem like a totally different beast. So here’s a quick and dirty tip for you: When learning new math, if you’re confronted by an abstract beast of a problem, remember that it’s okay to turn it back into something you’re more comfortable with. In other words, feel free to turn that confusing problem asking you to compare the size of one number to the sum of a list of other numbers—or whatever else it is—back into a question about affording the ingredients for a pizza. Because underneath the hood, they’re really the same thing.
Alright, I hope everyone is eager to start speaking math fluently. Please check out the next article where we’ll start right in on learning some math fundamentals at math basic training.
Please email your questions and comments to。。。。。。the Math Dude on Twitter at。。。。。。and become a fan on Facebook. You can also follow me, your humble host, on Twitter at。。。。。
This is our very first Math Dude article, and in honor of that we’re going all the way back to basics to answer some fundamental questions about math that should help you evaluate the status of your relationship with numbers. But let me start by saying I understand that math might be a painful subject for many of you. Sure, some people love it—and they’re lucky that math comes naturally to them. If that person is you—great! But if you’re like many people I know, just hearing the word ‘math’ is enough to induce waves of nausea. If that’s you, then rest assured you can do math. It will take a bit of work and dedication, but becoming mathematically literate is a challenge you can meet.
Why is Math Important?
It is highly likely that at some point you’ll need to take a standardized test with math on it—perhaps the SAT, or use math in a current or future job. If you squander the opportunity to correct your mathematical deficiencies now, you may regret it in the future when friends and colleagues start throwing around statistics that leave you feeling clueless. Worrying that your innumeracy will be discovered isn’t much fun, so why not take the time to learn a bit of math now, instead? I won’t sugar-coat it; this won’t always be easy. But it will certainly be worth your while. And if I do my job right, it should even be fun. No, that was not a joke...I did indeed say fun.
How to Understand the Language of Math
Okay, let’s get back to talking about your relationship with math. Do you speak math? Not sure what I mean? Well, math is a foreign language. And, like any language, you have to speak it proficiently before you can use it efficiently. But besides needing to know it for tests or work, why should you want to speak math? What’s it useful for?
Think of math as a very large box of tools all intent on helping you get your stuff done. Stuff like calculating your tax refund; making a budget; building a paper airplane, or a computer, or even the industrious robotic explorers that orbit and rove around Mars. Sure, some of these applications are more sophisticated than others, but they’re all built on the same foundation of knowledge expressed with the language of math. And by developing your ability to speak and understand this language, you too can use your mathematical tools to get your stuff done.
You Might Know More Than You think
And I have some good news for you: it’s likely that you’re already a far more proficient math speaker than you give yourself credit for. Don’t believe me? Here’s a simple example to demonstrate what I mean. First, I need you to stop and check how much money you have in your wallet. Really, go ahead and check. Got it? Okay, now that you have that number in your head, here’s the scenario: You and I are throwing a party tonight, and I desperately need you to pick up some things at the store. You’ve been aching to try barbecuing a pizza, so we’re gonna give it a shot. But, there’s one little problem—I’m really bad at planning ahead, so my refrigerator is completely empty. We need everything—pizza dough, tomato sauce, cheese, pepperoni, charcoal—everything. So here’s my question for you: Given what’s in your wallet, if you had to go to the store right now to make these purchases, would you have enough money?
Well, presuming you’re older than ten and have done a bit of grocery shopping in your time, I’m guessing you could figure this out without too much trouble. In fact, I’d wager that you tackle little problems like this every day, and you rarely—if ever—think twice about them. Most of the time you solve them intuitively, and you certainly don’t need to resort to any kind of systematic solution method like the one I’m about to describe. But humor me for a few minutes while I go through this in detail. There’s a payoff, I promise.
How to Solve Everyday Math Problems
Whether or not you’ve realized it before, there are basically three steps you need to take to answer this type of question.
First, you need to draw upon your past experiences to estimate how much each item on your shopping list is going to cost. You don’t have to be super precise here; we’re just looking for a ballpark figure—say, to the nearest dollar. In this case, I’d guess the charcoal will cost about $5, the cheese and pepperoni about $3 each, and the dough and tomato sauce roughly $2 apiece.
The second step is to add these individual amounts together to figure out the total cost of the shopping trip. In this case it’s pretty simple: $5 plus $3 is $8, plus another $3 is $11, plus $2 is $13, and finally plus another $2 is a total of $15.
Okay, the third and final step you need to do to figure out whether or not you need to go to the bank before the grocery store is to compare your total estimated cost to the amount of money you have in your wallet. If you found $10 in your wallet earlier—well $10 < $15—so you definitely need to go to the bank first. On the other hand, if you currently have $20—then since $20 > $15—you’ll have plenty of money for the groceries.
You Already Do Real Math Stuff Every Day
Perhaps you’re thinking: “Okay, all of that, and I can now solve one little problem…that I already knew how to solve anyway!” Well, not exactly. Remember how I said that going into detail on this simple problem would be worth your while? Here’s the payoff. The truth is that the mathematical part of this exercise had absolutely nothing to do with pizza or the contents of your wallet. Yes, in practice we were adding quantities of money and seeing if we had sufficient funds to cover a transaction. But mathematically we were estimating unknown values, assigning them to variables, performing integer arithmetic, and solving inequalities. In other words, we were doing real math stuff. Surprised? Well maybe, but hopefully it’s now apparent that math really does apply to things you do every day. And, perhaps more importantly, that you already know how to do a lot of it.
Here’s another thing. Instead of purchasing ingredients for a pizza, we could just as easily have been talking about buying coconuts with coffee beans—or absolutely anything else for that matter. In fact, we didn’t actually have to be talking about buying anything. Abstractly adding the numbers 5–3–3–2–and–2 for kicks, then checking to see if the sum is less than 20? Sure, that would’ve worked too because math is quite happy to work without any real-world references at all—the principles and methods are exactly the same in either case. And this is very powerful stuff. It means that once you know how to solve a problem based on one set of ideas, you don’t just know how to solve that problem. But rather, since you now know the underlying general principles, you can also solve every other problem in existence that’s based upon those principles.
Why Math can be Confusing
While powerful, that potential to use math to solve abstract problems is also one of the things that can make it confusing to learn. Often a problem will appear fairly straight-forward when it’s put in everyday terms. But when the same type of problem is put in purely abstract mathematical terms, it can seem like a totally different beast. So here’s a quick and dirty tip for you: When learning new math, if you’re confronted by an abstract beast of a problem, remember that it’s okay to turn it back into something you’re more comfortable with. In other words, feel free to turn that confusing problem asking you to compare the size of one number to the sum of a list of other numbers—or whatever else it is—back into a question about affording the ingredients for a pizza. Because underneath the hood, they’re really the same thing.
Alright, I hope everyone is eager to start speaking math fluently. Please check out the next article where we’ll start right in on learning some math fundamentals at math basic training.
Please email your questions and comments to。。。。。。the Math Dude on Twitter at。。。。。。and become a fan on Facebook. You can also follow me, your humble host, on Twitter at。。。。。
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