word problem woes

[musicianmom]

So, what do you do when a kid's word-problem-solving ability lags way behind their computation ability?  Dd can handle most of Singapore 5A, but the word problems are killing us both.

[mysticmomma]

Go back. Get the cwp and start at 1 if needed.

[musicianmom]

Well, I have CWP for 3 and 4 (obviously I should have USED them), so I'll start with 3 and see if she can handle it or if I need to go back further. Thanks.

[crazyforlatin]

If you need a more incremental, direct approach, this series by Singapore is excellent. You don't need to drop CWP even if you use the books in the link, but it may help a child get over a temporary word problem slump.

 

http://www.singaporemath.com/Heuristic_and_Model_Approach_s/151.htm

[Tanikit]

I would suspect that there was a language issue that needed working on then, not a math issue - it usually means they are battling to understand what is being asked - this is why they often teach drawing pictures and later the bar method it is more so they can clearly see what is being asked than how to solve it. I agree go back to CWP, but work on reading and understanding the question without doing any math at all - take the equations out of it and just get him to reword the question without solving it at all - some kids are so concentrated on using the figures in an equation that they can't see anything but figures and they miss the words.

 

This article gives other reasons for problems and what was done to help and also identify the problems: http://www.bsrlm.org.uk/IPs/ip29-3/BSRLM-IP-29-3-06.pdf

 

[geodob]

A major confusion with word problems, is that they use a different thinking process than basic math.

With basic math, it uses a beginning to end calculation process.

But with word problems, they often involve thinking back and forward, to work them out.

Where you might be given the answer, and then have to work out how to arrive at the answer?

 

So you might find that the problem is that your DD is trying to do the word problems, in a 'beginning to end' process?

 

 

 

[Dana]

CWP is challenging.

The bar model approach is really powerful but it takes a lot of practice. Going back to 3 should be a good starting point. The Process Skills books that LatinTeach linked are excellent as well for setting up the bar models.

[kiwik]

When I did exams I used to constantly remind myself that most of the stuff in word problems is completely irrelevant. I used to make 3 lists, what I know, what I need to know and any formulae that link the first two.

 

I short cut way of doing this is to use highlighters to show the relevant numbers and phrases. It doesn't matter what their names are or whether or not they like candy but numbers, less, more, share evenly etc are important.

[musicianmom]

We went back to 3. She's doing the practice problems, we haven't hit the challenging ones yet. She's furious that I'm making her waste so much time drawing bar diagrams for such easy problems.

 

Basically she resents having to do math at all, ever, and she's going to punish me with her behavior. :(

[Chrysalis Academy]

Hands-on Equations, Zaccaro, and Math for Real Kids have been really good here.  I've decided 6th grade is going to be "the year of problem solving" here.  So instead of doing informal logic as I had planned, we're going to do a second session each day that focuses on problem solving, in math, science, etc.  Besides the above, I have Zaccaro's Ten Things . . . book, and I'm drooling over his "Becoming a Problem Solving Genius."

[mathnerd]

We use CWP, Zaccaro and MEP for word problems. Word problems are tricky because you need to pay attention to the way the words are structured in the sentences to convey the meaning. For example, a simple "NOT" or "together" thrown into the question would make the meaning of the question totally different. So, in our house, we do the word problems when I have the time to sit with my child. I make him walk through the problems explaining his thinking process to me. I also ask that he circle the "tricky words" in each problem so that he can spot the phrase that determines the key logic of the question. After this, the solution becomes easy. I believe solving word problems have many more benefits than in mathematics. It strengthens logical reasoning, critical thinking as well as reading comprehension. So, even though DS is mad at me for making him go through the solution step by step, I insist that he walk through the solutions until he makes no mistakes.

[Dana]

We went back to 3. She's doing the practice problems, we haven't hit the challenging ones yet. She's furious that I'm making her waste so much time drawing bar diagrams for such easy problems.

 

Basically she resents having to do math at all, ever, and she's going to punish me with her behavior. :(

 

:grouphug:

 

Couple ideas...

(1) I let my son use the calculator for many of the word problems in the "challenging" section. He has to show more work when using the calculator (set up must be correct and written out clearly). Then I'm focusing on him setting up the word problem and not on arithmetic.

 

(2) By going back a couple levels, maybe skip the basic problems and just have her do the challenging ones.

 

(3) Sometimes I'll require my son show a bar model for one of the three problems of the page. If he gets it right, no need to do bar models for the other problems, but I say I want to be sure he can demonstrate the set up to me.

 

We did have some major battles over showing work and set up of problems. It was a long haul, but I think it's paid off. Good luck!!

[mathwonk]

Even as a retired teacher, I appreciate all the effort you guys are doing to teach kids to use words in math. No matter how many times I myself illustrated problems in class with words and explanations written out every step of the way, or handed out notes with problems explained and solved in both words and symbols, my students just gave me back numbers and formulas with no words at all to explain what they were doing or why.

 

I never understood how they expected me to understand what they were doing when they made no attempt at all to set up the problem or explain what needed to be done before just doing it, and often doing it wrong. it is really hard to give partial credit or to give guidance when there is no description of ones thinking at all.

 

A math assignment should be written up more or less like an English assignment. It is an essay, with an introduction, a body, and a conclusion. Maybe workbooks with fill in the blank choices of numerical answers are to blame for this? Or SAT type tests with multiple choice answers?

 

What puzzled me was why my elaborate examples of how to do it were universally ignored. I.e. "you see what I am giving you as explanation? Please give me something similar." There were maybe one or two students in a class of 30 who would even attempt this.

 

 

I recall some data we were once shown, that there was no correlation between SAT math scores

 

and performance on our entry level college math courses, but a good correlation with SAT verbal scores.

 

I am not sure this was correct, but I believed it, since in college math is more about reasoning.

[musicianmom]

Ok, I give up.

 

The problem is not the math. It's not dd's language abilities. It's that even after she draws the bars and figures out what the problem is asking for, at some point there is a small leap that your brain has to make, using logic skills, to find how to get to the answer. I know this because I, with my adult brain, have to do this when *I* work the problems.

 

She is very bright, just under the IQ cutoff for gifted. When the problem calls for those little logical leaps, her brain doesn't do it.

 

I don't know what to do for her math. We've stopped Singapore temporarily and gone back to BA, finishing up 3B. I may just keep her in BA until we run out of levels. She likes it and is succeeding with it. I so wish she could just go all the way through with BA, but she would be in 8th grade by the time it's finished.

 

I'm not willing to consign her to being a mediocre math student yet and just give her an easy, get-it-done math program. But we can't keep fighting about math.

[Chrysalis Academy]

But she does ok with BA problems?  Some of those require even my brain to make "little" logical leaps that can be challenging!   If she does ok with the challenging problems in BA but not with Singapore, maybe it isn't logic.  Maybe it's the way Singapore problems are set up, and the bar model.  I have a hard time with those myself, and my dd, who does well with word problems, tends to have a hard time with the bar-model setup, not having been trained that way from the beginning.  I wonder if a more algebraic approach might make solving word problems easier?  You might try using HOE with her.  There are really tough & interesting word problems, but kids are taught to approach them algebraically (without even realizing they are doing so) and that approach really works so much better for us here.  I know I"m not the only one, I've ready other discussions about this here as well.

 

Just trying to offer some hope - maybe it isn't her, maybe it's Singapore.  And maybe it is her, but that logic, connection-making thing just hasn't clicked yet.  But if she's using BA as an 8 yo, I don't think you have to consign her to being a mediocre math student just yet!  Her brain will change and mature a lot over the next couple of years.   

[Crimson Wife]

Many of the Singapore problems in the CWP & IP books for levels 4 through 6 remind me of the type of problems on the SAT. The Kumon word problems series is more straightforward and I had my DD work through the relevant sections of those books before tackling the ones in CWP & IP.

[acurtis75]

I had to go back and start with CWP 2 with my dd who is gifted. It wasn't because she was incapable of the math it was the different approach that Singapore uses for problems. I've always been good in math but struggled with the Singapore way of presenting information. We tried to start in level 3 because she was well beyond 3rd grads math but had to step down a level to get a foundation in the singapore way of wording and solving problems. We don't use Singapore as our spine but because a lot of schools and tests use similar methods I felt we should at least do CWP. We are just starting level 3 at the same time dd is completing beast academy 3c, life of Fred fractions and starting mus pre-algebra.

[jennynd]

Even as a retired teacher, I appreciate all the effort you guys are doing to teach kids to use words in math. No matter how many times I myself illustrated problems in class with words and explanations written out every step of the way, or handed out notes with problems explained and solved in both words and symbols, my students just gave me back numbers and formulas with no words at all to explain what they were doing or why.

 

I never understood how they expected me to understand what they were doing when they made no attempt at all to set up the problem or explain what needed to be done before just doing it, and often doing it wrong. it is really hard to give partial credit or to give guidance when there is no description of ones thinking at all.

 

A math assignment should be written up more or less like an English assignment. It is an essay, with an introduction, a body, and a conclusion. Maybe workbooks with fill in the blank choices of numerical answers are to blame for this? Or SAT type tests with multiple choice answers?

 

What puzzled me was why my elaborate examples of how to do it were universally ignored. I.e. "you see what I am giving you as explanation? Please give me something similar." There were maybe one or two students in a class of 30 who would even attempt this.

 

 

I recall some data we were once shown, that there was no correlation between SAT math scores

 

and performance on our entry level college math courses, but a good correlation with SAT verbal scores.

 

I am not sure this was correct, but I believed it, since in college math is more about reasoning.

DS is one of those kid do not like to show process. In his eyes, multiple steps is just one step, there is nothing to explain. It is just the way it is. The NY standard test result just came back and he is one point shy of perfect score and I highly suspect that 1 point is from one of those explaining why type question. He tend to simplify the explanation. He just don't see it. Not lack of trying. He really tried. It is like asking how you get up in the morning. He will say I just getup. And the teacher expecting," I open my eyes, I move my left leg and I move my right legs, I puts my legs on the ground.....on and on... "

How do you help a kid like that and make him to write the explanation that him think is absolutely unnecessary.

 

He does gets a lot better when we did algebra this past year.. But for the 3rd grade math. He simply do not see there is anything to explain

[ebunny]

 

The problem is not the math. It's not dd's language abilities. It's that even after she draws the bars and figures out what the problem is asking for, at some point there is a small leap that your brain has to make, using logic skills, to find how to get to the answer.

 

 

On the face of it, (since I don't know her personally), it would seem like she struggles with reasoning skills.

 

My suggestion is that you let her continue with BA and instead of using Singapore Math (or any other curricula), get her to solve Sudoku or Kakuro or play games that promote strategy such as Connect 4, Rush hour, Master Mind, Scotland Yard.

 

I've used the above ideas with great success while tutoring children who had trouble with logical reasoning. My theory is that using Math to teach reasoning skills (as is usually done) may not be the best approach for some children.

 

HTH

[Arcadia]

It is like asking how you get up in the morning. He will say I just getup. And the teacher expecting," I open my eyes, I move my left leg and I move my right legs, I puts my legs on the ground.....on and on... "

How do you help a kid like that and make him to write the explanation that him think is absolutely unnecessary.

Has he done proofs kind of questions? Maybe show him the marking scheme for proofs questions. Not writing the steps down means not getting full credit for the question.

For my boy's K12 math tests, out of 5 marks for a question, only 1 mark may be for the correct answer. No working means sure fail.

California standardized tests is only multiple choice so he knows he can get away with no working for that :P

 

ETA:

For example something like question 14 or 15 on page 49 http://highered.mcgraw-hill.com/sites/dl/free/0072532947/78545/chapter1.pdf

Each step listed for those questions would get like 1 mark for his tests.

[jennynd]

Has he done proofs kind of questions? Maybe show him the marking scheme for proofs questions. Not writing the steps down means not getting full credit for the question.

For my boy's K12 math tests, out of 5 marks for a question, only 1 mark may be for the correct answer. No working means sure fail.

California standardized tests is only multiple choice so he knows he can get away with no working for that :p

 

ETA:

For example something like question 14 or 15 on page 49 http://highered.mcgraw-hill.com/sites/dl/free/0072532947/78545/chapter1.pdf

Each step listed for those questions would get like 1 mark for his tests.

 

He did fine with Algebra writting down process with few skipping steps on the calculation. But in general.. acceptable. we had not try any proof. I am hesitated to go AOPS geometry for this very reason. I don't think he will be able to do it. He did NEM1 and 2 with geometry part and was fine with it but there is no proof in there, at least I did not see any yet.

 

And I did see him get A LOT better this past year with the teacher really pushing it. Without her affort, I think DS will not be 1 point away from perfect score. You should see his work starting of the year last year. Everything will be just a number,

[mathwonk]

Well one thing every kid should learn is that they need to tell what their symbols mean. Just starting out writing X without saying that X is the number that satisfies the given properties leaves the reader completely at a loss. Even using A without saying it stands for area is a bad habit. Or always using b for the coefficient of X in a quadratic is a bad habit. Using formulas like X = (1/2a)(-b ± sqrt(b^2-4ac)) without saying what a,b,c, and X stand for is really meaningless. Equally sloppy is using formulas like a^2 _+ b^2 = c^2, without saying what the letters mean is poor form.

 

It is sufficient just to write aX^2+bX+c = 0 usually, or to label a right triangle with c on the hypotenuse, but one should also put a little square corner in the right angle to convey that it is a right triangle, not just expect that if it looks like about 90degrees it is right. It is also good practice to actually say in words "we want to find a number X such that aX^2 + bX+c = 0, where...."

 

It is like writing short story, you have to introduce the characters: who is A? who is B? You have to set the stage. Any child who can write or tell a story can understand this. It is about learning communication skills.

 

Basic rule: anytime one uses letters in a calculation, one should explain to the clueless reader what those letters are chosen to represent. Of course if they are used in the same way over and over one can shortcut the process after the first time or so.

 

The student should adopt the mindset of a teacher, they are explaining what they are doing, not just doing it. Every homework should be written up almost as if it were a lesson for ones younger sibling.

 

it should also be written in stages. First drafts can be more crude and leave out more. After the solution is complete, then the writeup begins, and the explanation is expanded. Ideally it should include what method is being used and how it was thought of.

 

Have you looked at the epsilon camp algebra problem set on my webpage? or the geometry notes with proof exercises?

 

http://www.math.uga.edu/~roy/epsilon13.pdf

 

http://www.math.uga.edu/~roy/camp2011/10.pdf

[Pen]

Well one thing every kid should learn is that they need to tell what their symbols mean. Just starting out writing X without saying that X is the number that satisfies the given properties leaves the reader completely at a loss. Even using A without saying it stands for area is a bad habit. Or always using b for the coefficient of X in a quadratic is a bad habit. Using formulas like X = (1/2a)(-b ± sqrt(b^2-4ac)) without saying what a,b,c, and X stand for is really meaningless. Equally sloppy is using formulas like a^2 _+ b^2 = c^2, without saying what the letters mean is poor form.

 

It is sufficient just to write aX^2+bX+c = 0 usually, or to label a right triangle with c on the hypotenuse, but one should also put a little square corner in the right angle to convey that it is a right triangle, not just expect that if it looks like about 90degrees it is right. It is also good practice to actually say in words "we want to find a number X such that aX^2 + bX+c = 0, where...."

 

It is like writing short story, you have to introduce the characters: who is A? who is B? You have to set the stage. Any child who can write or tell a story can understand this. It is about learning communication skills.

...

 

I love that analogy.  I may try it on my ds.

 

 

 

For OP, if your sig is up to date and your dd is 8, she does not seem to be doing so badly if 5th grade word problems are a struggle.  I think figuring out word problems frequently lags behind.

 

I found the Critical Thinking Press books by Anita Harnadek (? not sure if that is quite right name) helpful because they start with around 60 problems where the numbers are all the same, but you have to pay attention to what to do with them based on the words...if that is part of the difficulty.  It is a very different sort of thing than CWP problems.  Otherwise, if the SM 5 word problems are too hard, but others you tried are too easy, why not just accelerate to where you find ones that are at the current challenge level for her?

 

For the person asking about writing steps, this does not help for writing them out, but I have found asking my ds to walk me through something he has done (orally) can be helpful in articulating the steps.

 

 

 

 

 

Mathwonk, your post also reminds me of  the Billy Collins poem, Forgetfulness,  because of a phrase about the quadratic:

 

 

"...Long ago you kissed the names of the nine Muses goodbye

and watched the quadratic equation pack its bag,

..."   It is funny, for those of us old enough to appreciate it.

 

[Uff Da!]

 

 

For OP, if your sig is up to date and your dd is 8, she does not seem to be doing so badly if 5th grade word problems are a struggle.  I think figuring out word problems frequently lags behind.

 

 

I agree with this.  I was thinking about this thread yesterday when my DD turned a simple word problem into a three page drawing extravaganza and still couldn't get close to the answer.  It was as if she was juggling too many balls and refused to put some down to move to the next step.

[Chrysalis Academy]

I just got Zaccaro's book Becoming a Problem Solving Genius.  I really like it!  We're going to go through this and his 10 things book for "logic" this year, in lieu of Art of Argument.  It takes a kid through steps and strategies for solving problems in a really systematic way.  Maybe you and your dd could work through a book like this together?  

[Woodland Mist Academy]

I just got Zaccaro's book Becoming a Problem Solving Genius.  I really like it!  We're going to go through this and his 10 things book for "logic" this year, in lieu of Art of Argument.  It takes a kid through steps and strategies for solving problems in a really systematic way.  Maybe you and your dd could work through a book like this together?  

 

 

Would you mind sharing how you plan to use it?

 

Then will you rework my schedule to fit it in? Pretty please? ;)

[Chrysalis Academy]

Ummm, yeah, I'll be glad to share how I use it. . . as soon as I figure it out!  :huh:

[Arcadia]

 

And I did see him get A LOT better this past year with the teacher really pushing it. Without her affort, I think DS will not be 1 point away from perfect score. You should see his work starting of the year last year. Everything will be just a number,

 

My older needs the teacher's nagging for writing more than he need her nagging for math.  His everything for math was a number most of the time until using the AoPS book to afterschool. Some questions he need to write it out.

 

A math assignment should be written up more or less like an English assignment. It is an essay, with an introduction, a body, and a conclusion.

 

 

I chance on this today and thought it is relevant in a way to this thread. I'll read Polya's "How to solve it" when I am less sleepy.  I like his steps, even a elementary school kid can follow the thought process.

"George Polya's Four basic principles of problem solving." (page 3 and 4 of 4  pages, summary by UCB)

[mathwonk]

Winter I loved reading your description of your daughter's ball juggling production. i don't care what someone produces, I can deal with anything, just so they produce!

[jennynd]

The student should adopt the mindset of a teacher, they are explaining what they are doing, not just doing it. Every homework should be written up almost as if it were a lesson for ones younger sibling.

 

 

That is an excellent point. I saw my Son did better with Algebra this year. I knew something was differnt that teacher was done and i thought she just nagging. and I honestly thought that I didn't like that because get forced to write the process down seem very boring. But now you mention this. THIS IS EXACTLY what DS's teacher had him do. About middle of the year the teacher exempted him from homeworks and sometimes the tests. He got perfect scores even without taking the test. I was.. well.. a bit concerned..But In exchange, the teacher asked him to teach some of the kids that were behind. Mybe that WAS IT..

 

I guess PS teacher aren't so bad after all.

 

[mathwonk]

there is a famous book on problem solving by George Polya, "How to solve it". Some place in there he says roughly that solutions are like grapes, they come in bunches. I.e. when you solve one, look around for another you can solve with the same idea. You might enjoy reading this book. I gave copies to all my returning teacher - students in one class.