Students & Word Problems

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  • #1
I have been struggling with word problems all of my life. Ironically, I am not alone. Students around the globe fear and struggle with word problems. In your opinion, why is this the case?
 

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  • #2
berkeman
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I think there are two main reasons:
  1. Not having a good strategy
  2. Not having enough practice

#1: The "strategy" involves defining some quantities (values and variables) that will work to solve the problem. Given the word definition of the problem, figure out what you want to call various lengths, positions, speeds, accelerations, etc., and whether they are constant values or variables. Then set up the equations describing their relationships and proceed to solve them.

#2: And once you have the strategy sort of figured out, you can do more word problems and refine the #1 part.

Then rinse and repeat... :smile:
 
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  • #3
I think there are two main reasons:
  1. Not having a good strategy
  2. Not having enough practice

#1: The "strategy" involves defining some quantities (values and variables) that will work to solve the problem. Given the word definition of the problem, figure out what you want to call various lengths, positions, speeds, accelerations, etc., and whether they are constant values or variables. Then set up the equations describing their relationships and proceed to solve them.

#2: And once you have the strategy sort of figured out, you can do more word problems and refine the #1 part.

Then rinse and repeat... :smile:
I see it this way:

1. Word problems are typically worded poorly.

2. Forming an equation(s) leading to the right answer(s) IS THE MAIN PROBLEM I am having. Students around the globe will agree.

3. Practice sometimes leads to more confusion or nothing. For example, I can go to singing school and practice vocal chord range and harmony. I can learn to sing the shape notes, you know, the DO,RE, MIs and NEVER, EVER sing like Dave Boyer, Frank Sinatra, Elvis Presley and so many other famous singers. I think practice is overrated.

4. Since 2006, I must have answered at least 1,000 word problems and still struggle greatly.

You say?
 
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  • #4
berkeman
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1. Word problems are typically worded poorly.
Then find a better learning resource. We see good word problems and confusing/bad word problems here at PF all the time. I understand that encountering badly posed word problems can be frustrating, but if your sources are consistently presenting badly worded problems, ditch that learning resource.
2. Forming an equation(s) leading to the right answer(s) IS THE MAIN PROBLEM I am having. Students around the globe will agree.
Sure, that's one of the key skills that you need to build.

One of the reasons that our PF Homework Help Template has a section for the "Relevant Equations" is that understanding how to identify them is a key to solving Physics/Math/Engineering problems.

If you can post an example word problem that you've seen lately that was hard for you, that would help.

In the mean time, can you post the Relevant Equations for this word problem? Solving it would be extra credit...

"A 5kg mass is thrown upward with an initial velocity of 5m/s and an initial height of 2m. How long does it take to hit the ground?"

Bonus Question -- "What role does the mass = 5kg play in this question?"
 
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  • #5
Then find a better learning resource. We see good word problems and confusing/bad word problems here at PF all the time. I understand that encountering badly posed word problems can be frustrating, but if your sources are consistently presenting badly worded problems, ditch that learning resource.

Sure, that's one of the key skills that you need to build.

One of the reasons that our PF Homework Help Template has a section for the "Relevant Equations" is that understanding how to identify them is a key to solving Physics/Math/Engineering problems.

If you can post an example word problem that you've seen lately that was hard for you, that would help.

In the mean time, can you post the Relevant Equations for this word problem? Solving it would be extra credit...

"A 5kg mass is thrown upward with an initial velocity of 5m/s and an initial height of 2m. How long does it take to hit the ground?"

Bonus Question -- "What role does the mass = 5kg play in this question?"

This is my fault. I should have been clear from day one. I know ABSOLUTELY NOTHING about physics and/or applications of physics. To answer your word problem, I need to form a formula. This is the problem I am having. I am not leaning toward physics. I am more interested in algebra word problems, geometry and trigonometry word problems and later on related rates.
 
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  • #6
berkeman
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I am not leaning toward physics. I am more interested in algebra word problems
What's an algebra word problem? Can you give an example?
 
  • #7
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What's an algebra word problem? Can you give an example?
Here's one...

Mary is 4 years older than her brother John. Eight years ago Mary was twice as old as John. What are Mary's and John's ages now?

The key to this problem is to set up variables for the current ages of the two siblings, and write an equation that represents their age relationship eight years ago. It's important to distinguish between their ages now and eight years ago.
 
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  • #8
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1. Word problems are typically worded poorly.
Some word problems are worded poorly, but I doubt this is generally true. As @berkeman said, if you're using a resource with many poorly-worded problems of this type, get another source.
2. Forming an equation(s) leading to the right answer(s) IS THE MAIN PROBLEM I am having. Students around the globe will agree.
Well, yes, that is the crux of the problem. You need to define variables that represent the unknown quantities, and then translate from the text of the problem to mathematical statements: equations or inequalities.
3. Practice sometimes leads to more confusion or nothing. For example, I can go to singing school and practice vocal chord range and harmony. I can learn to sing the shape notes, you know, the DO,RE, MIs and NEVER, EVER sing like Dave Boyer, Frank Sinatra, Elvis Presley and so many other famous singers. I think practice is overrated.
I disagree, at least partly. Innate talent plays a significant role, but I'd bet that many famous signers started at an early age, which implies lots of practice. One singer who comes to mind is Aretha Franklin, who got her chops very early on, singing in church. Elvis also started early on, as well. Obviously, both had some inborn talent, but talent alone won't always get you very far.

If you find that practicing solving word problems leads to confusion, you're probably doing something wrong. As already said, post some examples here and we'll steer you in the right direction.
 
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  • #9
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In your opinion
I see it this way

Boy, this really really sounds like you don't want other people's opinions. You were just looking for an excuse to tell us yours.

Word problems are typically worded poorly
As others have said, it is true for some problems, sure. The majority? If it's that's the case, again as they said, you need another source of problems. But by blaming the problems, you let yourself off the hook. No need to get better, because it's all the problems' fault.

FWIW, I have seen a correlation between students who struggle with word problems and students who struggle with problems that require them to put two or more facts together.
 
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  • #10
symbolipoint
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Boy, this really really sounds like you don't want other people's opinions. You were just looking for an excuse to tell us yours.


As others have said, it is true for some problems, sure. The majority? If it's that's the case, again as they said, you need another source of problems. But by blaming the problems, you let yourself off the hook. No need to get better, because it's all the problems' fault.

FWIW, I have seen a correlation between students who struggle with word problems and students who struggle with problems that require them to put two or more facts together.
MAYBE. What @nycmathguy should do, is actually give two DIFFERENT kinds of examples which he finds difficult or confusing, which should come from his assigned textbook/s. Then someone or more can help to analyze the word problems.
 
  • #11
What's an algebra word problem? Can you give an example?
Two numbers add up to 72. One number is twice the other. Find the numbers.
 
  • #12
Here's one...

Mary is 4 years older than her brother John. Eight years ago Mary was twice as old as John. What are Mary's and John's ages now?

The key to this problem is to set up variables for the current ages of the two siblings, and write an equation that represents their age relationship eight years ago. It's important to distinguish between their ages now and eight years ago.
Current age:

Mary = x + 4
John = x

Eight years ago:

(x + 4) - 8 = 2(x - 4)

x + 4 - 8 = 2x - 8

x - 4 = 2x - 8

x - 2x = - 8 + 4

-x = -4

x = -4/-1

x = 4

John is 4 years old.

Mary is x + 4 or 8 years old.

Is this right?
 
  • #13
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Current age:

Mary = x + 4
John = x

Eight years ago:

(x + 4) - 8 = 2(x - 4)
The equation above is incorrect.
nycmathguy said:
x + 4 - 8 = 2x - 8

x - 4 = 2x - 8

x - 2x = - 8 + 4

-x = -4

x = -4/-1

x = 4

John is 4 years old.

Mary is x + 4 or 8 years old.

Is this right?
So 8 years ago, John would have been -4 and Marry would have been 0. Does that make any sense?
These kinds of problems are easy to check, which is something you should always do.
 
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  • #14
Borek
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4. Since 2006, I must have answered at least 1,000 word problems and still struggle greatly.

So there were semesters I did more word problems than you did in 15 years.
 
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  • #15
symbolipoint
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Current age:

Mary = x + 4
John = x

Eight years ago:

(x + 4) - 8 = 2(x - 4)

x + 4 - 8 = 2x - 8

x - 4 = 2x - 8

x - 2x = - 8 + 4

-x = -4

x = -4/-1

x = 4

John is 4 years old.

Mary is x + 4 or 8 years old.

Is this right?
These kind are absolutely literal. They tell exactly what the situation is, and transferring into symbols or symbols and numerals is exactly as the written description.

Mark44's example: "Mary is 4 years older than her brother John. Eight years ago Mary was twice as old as John. What are Mary's and John's ages now?"

Mary, x
John, y
Mary, also according to description, x=y+4
The eight years ago, Mary x-8; John y-8;
Then the last sentence means, x-8=2(y-8).

Your system of equations, if you wish to continue using the two variables:
x=y+4
x-8=2(y-8)
.


Now you can just solve the system. You have an easy substitution, ready to make to begin.
 
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  • #16
Here's one...

Mary is 4 years older than her brother John. Eight years ago Mary was twice as old as John. What are Mary's and John's ages now?

The key to this problem is to set up variables for the current ages of the two siblings, and write an equation that represents their age relationship eight years ago. It's important to distinguish between their ages now and eight years ago.
Current age:

Mary = x + 4
John = x

Eight years ago
The equation above is incorrect.
So 8 years ago, John would have been -4 and Marry would have been 0. Does that make any sense?
These kinds of problems are easy to check, which is something you should millennial
At least I gave it a go, right? Saying the problem is easy does not help in any way.
 
  • #17
Some word problems are worded poorly, but I doubt this is generally true. As @berkeman said, if you're using a resource with many poorly-worded problems of this type, get another source.

Well, yes, that is the crux of the problem. You need to define variables that represent the unknown quantities, and then translate from the text of the problem to mathematical statements: equations or inequalities.

I disagree, at least partly. Innate talent plays a significant role, but I'd bet that many famous signers started at an early age, which implies lots of practice. One singer who comes to mind is Aretha Franklin, who got her chops very early on, singing in church. Elvis also started early on, as well. Obviously, both had some inborn talent, but talent alone won't always get you very far.

If you find that practicing solving word problems leads to confusion, you're probably doing something wrong. As already said, post some examples here and we'll steer you in the right direction.

I don't know much about Aretha Franklin's musical background. I know who she was in the music business. Great voice. Did you know that Elvis did not attend singing school? Did you also know that Elvis did not know how to read and write music? He was naturally gifted. In terms of word problems, I will post hundreds of applications as I travel through my textbooks. This cannot be done in one day.
 
  • #18
Boy, this really really sounds like you don't want other people's opinions. You were just looking for an excuse to tell us yours.


As others have said, it is true for some problems, sure. The majority? If it's that's the case, again as they said, you need another source of problems. But by blaming the problems, you let yourself off the hook. No need to get better, because it's all the problems' fault.

FWIW, I have seen a correlation between students who struggle with word problems and students who struggle with problems that require them to put two or more facts together.
1. I am not blaming the word problems.

2. I blame the people hired to write word problems and exams. Most of the time, the people hired to write exams or HOW TO SOLVE WORD PROBLEMS books never taught mathematics or even have a math degree.

3. The Yankees did the same thing. They hired Marcus Thames who was a horrible baseball player in his era to be the hitting coach. Result: Yankees are falling deeper and deeper into last place. Apply this analogy to DISQUALIFIED individuals writing math books and word problems.
 
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  • #19
MAYBE. What @nycmathguy should do, is actually give two DIFFERENT kinds of examples which he finds difficult or confusing, which should come from his assigned textbook/s. Then someone or more can help to analyze the word problems.
Word problems will be posted as I travel through the textbooks. Also, no more than 5 or 6 weekly questions will be posted. Too many questions at the same time leads to more confusion.
 
  • #20
So there were semesters I did more word problems than you did in 15 years.
Good for you. I still say that too much practice is overrated. I will post hundreds of word problems here in the coming months. One day at a time is the best way to learn.
 
  • #21
These kind are absolutely literal. They tell exactly what the situation is, and transferring into symbols or symbols and numerals is exactly as the written description.

Mark44's example: "Mary is 4 years older than her brother John. Eight years ago Mary was twice as old as John. What are Mary's and John's ages now?"

Mary, x
John, y
Mary, also according to description, x=y+4
The eight years ago, Mary x-8; John y-8;
Then the last sentence means, x-8=2(y-8).

Your system of equations, if you wish to continue using the two variables:
x=y+4
x-8=2(y-8)
.


Now you can just solve the system. You have an easy substitution, ready to make to begin.
Nicely done.
 
  • #22
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2. I blame the people hired to write word problems and exams. Most of the time, the people hired to write exams or HOW TO SOLVE WORD PROBLEMS books never taught mathematics or even have a math degree.
What's your evidence for your claim that most people hired to write word problems have never taught math or even have a degree in math? Do you suppose that someone can waltz in the door of, say Addison-Wesley and say, "I'm here to write word problems for Precalc textbooks."

While it's true that some elementary and high school math teachers don't have degrees in mathematics, this is not the case in colleges and universities.
 
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  • #23
berkeman
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I will post hundreds of word problems here in the coming months.
Rhut-rho...
 
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  • #24
symbolipoint
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Current age:

Mary = x + 4
John = x

Eight years ago

At least I gave it a go, right? Saying the problem is easy does not help in any way.
You are correct. That is a mistake that some teachers at times, impulsively make. (But the current age-description example here, really is easy.)
 
  • #25
symbolipoint
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1. I am not blaming the word problems.

2. I blame the people hired to write word problems and exams. Most of the time, the people hired to write exams or HOW TO SOLVE WORD PROBLEMS books never taught mathematics or even have a math degree.

3. The Yankees did the same thing. They hired Marcus Thames who was a horrible baseball player in his era to be the hitting coach. Result: Yankees are falling deeper and deeper into last place. Apply this analogy to DISQUALIFIED individuals writing math books and word problems.
Be aware, many Mathematics books are written by people who do have some Mathematics or equivalent degree. Revisions are often made to correct mistakes and to add more or better information to the editions. Also teachers often write or create many or some of their own quizes and tests, and even without any Mathematics degree, they write these instructional things very well.
 
  • #26
symbolipoint
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Good for you. I still say that too much practice is overrated. I will post hundreds of word problems here in the coming months. One day at a time is the best way to learn.
The idea would be over-using the physicsforums. Post fewer! Post one or two exercises which represent your problem-solving difficulties, and spend much of your time studying and practicing.
 
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  • #27
symbolipoint
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What's your evidence for your claim that most people hired to write word problems have never taught math or even have a degree in math? Do you suppose that someone can waltz in the door of, say Addison-Wesley and say, "I'm here to write word problems for Precalc textbooks."

While it's true that some elementary and high school math teachers don't have degrees in mathematics, this is not the case in colleges and universities.
To be honest, teaching Algebra1 or Algebra 2, or Geometry in high school does not require a Mathematics undergraduate-or-higher degree. ANYONE with an engineering or physical science degree can review and re-build and increase his/her knowledge in these courses more than well enough to teach them for high school students; and in fact these teachers did learn at least through college level Calculus (and often a few other Mathematicses) while earning their degrees. Teachers of Mathematics DO AND WILL review what they have already studied - more than once.
 
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  • #28
Be aware, many Mathematics books are written by people who do have some Mathematics or equivalent degree. Revisions are often made to correct mistakes and to add more or better information to the editions. Also teachers often write or create many or some of their own quizes and tests, and even without any Mathematics degree, they write these instructional things very well.
So, if that's the case, how does this help me?
 
  • #29
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I think with word problems, it helps to write out each sentence separately. Ask yourself what each sentence means. What info is it giving you. What is it asking you to find.

Many of my classmates struggled with word problems. I found it came down to lack of cold hard practice.
 
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  • #30
symbolipoint
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Be aware, many Mathematics books are written by people who do have some Mathematics or equivalent degree. Revisions are often made to correct mistakes and to add more or better information to the editions. Also teachers often write or create many or some of their own quizes and tests, and even without any Mathematics degree, they write these instructional things very well.

So, if that's the case, how does this help me?
To re-state differently, using a teacher or the works of a document author, who do not have a degree IN MATHEMATICS is not an insured obstacle in your handling of the subject matter nor your learning the subject matter.
 
  • #31
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So, if that's the case, how does this help me?
You should stop blaming the problems (or the problem-writers) and look inward,
 
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  • #32
You should stop blaming the problems (or the problem-writers) and look inward,
So, I'm the problem and not illiterate writers that cannot put together a structured set of sentences. Have you ever read a probability word problem? Talk about fuzzy language.
 
  • #33
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So, I'm the problem and not illiterate writers that cannot put together a structured set of sentences. Have you ever read a probability word problem? Talk about fuzzy language.
You have not reached that level yet. Most important is learn basic Algebra 1, and common 'Basic Mathematics' such as what most people are expected to learn in grades 6, 7, 8, 9. Any Probability instruction and exercises at that level would generally be less complicated; and would not be in large enough portion of the coursework to strongly affect your course grade.
 
  • #34
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So, I'm the problem and not illiterate writers that cannot put together a structured set of sentences. Have you ever read a probability word problem? Talk about fuzzy language.

Before you continue your tirade against poorly written word problems, you should pause and strongly reflect upon the example tendered above by Mark44 in Post #7.

Mary is 4 years older than her brother John. Eight years ago Mary was twice as old as John. What are Mary's and John's ages now?

It is a rudimentary word problem containing only three short sentences. It is clearly written. No ambiguities. No red herrings; i.e., extraneous information intentionally strewn to test whether you can extract the relevant information from background noise.

Yet, in your Reply #12, you got it dead wrong. So, what is a reasonable conclusion that we should draw?
 
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  • #35
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So, I'm the problem and not illiterate writers that cannot put together a structured set of sentences. Have you ever read a probability word problem? Talk about fuzzy language.
So, there's this game show hosted by someone called Monty Hall ...
 
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