To me, one of the criteria for a gifted child should be the true ability to solve 'real world' math word problems. These provide a test to show logically thinking, math knowledge, as well as knowledge of the environment related to the problem, etc.

If you visit the following link, there are useful 'real life' problems suitable for testing a gifted child's ability.

www.mathwords.weebly.com

Harold (Hal) Schneider

hals99@sbcglobal.net

I clicked so you [fellow Davidsoner] don't have to :-) Here's a quote from the page:


[Unashamedly sticking my neck out]

No. If a child can understand English, and understands mathematics, s/he does not need to learn 55 rules or think mechanically about translating words into operations in order to solve "word problems". If your child has trouble with word problems, take it as a sign that there is something fundamental s/he's not understanding, and tackle that - don't teach rules.

The question is why has word problems been a major problem for many decades (ask any student to get an opinion like 'I HATE THEM !' This includes many good students in English as well as good math students.

It is easy to make generalities to 'tackle the fundamentals' without definition of what 'fundamentals' are... nor any indication of how to do it ! I believe that this attitude is one of the reasons for the persistent problem that truly exists !

Experience with my students proves mine approach works !

After viewing the sample pages for the pushed product, I came away with a low opinion of it as well. I also (without meaning more offense than is unfortunately unavoidable from the statement) wouldn't trust my children's word-problem teaching to someone who garbles English so badly.

It sounds good to me, but I never was very good at math.
It includes the free shipping by e-mail, that's good.
But at 80 pages at $7.95., if it was $8 it would be $0.99 cents a minute
But the decimals are throwing me off with that .95, I wish they would round off.
LoL

I certainly do not mind criticism ! But, I was hoping to start a rational conversation of the technical issue of why math word problems (MWP) are indeed a long standing problem.

First, do any readers disagree that MWP are a problem ?

Second, do any readers have specific reasons (based upon actual experience) for this situation ?

Third, rational criticism should involve counter technical arguments to my proposed solution.

I guess that's not to be.

I think perhaps you are approaching the wrong audience. My very mathy kid who also reads far above grade level, does not struggle with math word problems. His only problems come when the wording of the question is vague or the expected answer is unclear, as is often the case in his mediocre, multiple-choice math tests at school.

Example- recent word problem from his book (dates modified because I do not remember the specifics).

John went to the park 7 days ago. If today is Sunday, June 12th, what day did John go to the park?
a) Sunday June 19th
b) Monday June 6th
c) Wednesday, June 1st
d) Saturday June 11th

Um... well the choice of Sunday, June 5th wasn't available. So we were left to figure that 7 days ago must have been inclusive of the current day, meaning that Monday, June 6th was the only possible answer.

hals99,

I took a look at your book and at your questions below. I have a few comments.

1) MWP are a problem for the majority of students, regardless of their mathematical ability because they usually do not actually read the whole problem. They skim it looking for the numbers and then the question at the end and then try to "figure it out" based on that info.
2) Why do they do this? many different reasons, often because the idea is that "this is math, not reading, so I shouldn't have to read to answer math questions". Also, a number of word problems in school math books are random and not linked to what the students are actually involved in with their life. Even if the authors write it with hopes that students will find it interesting, purely because it is written in a math book they will not be interested in it. (This is true for most subjects, not just math problems)
3) Another issue that needs to be addressed is that when word problems are first introduced, it is often the teacher who cements it in the students' minds that word problems are hard and difficult to do. This view is then reinforced by the students' experience when they try to do some on their own.
4) Being good at math and/or good at English does not mean that a child can then read a mathematical or scientific problem and understand what is being asked. Math and science based word problems are usually written by math and science people, and is not written the same way we use language in everyday speech or in any other aspect of our lives. If we really want students to be good at solving word problems, we first need to teach them to be able to read scientifically written articles.
5) While I use word fractions all the time to help my students understand word problems, the problem with using them is that fractions in and of themselves often makes students shut down faster than word problems! Also, if we again look at what most teachers will accept for work on word problems, the problem is usually assigned within a certain topic and the teacher wants the students to use that particular new skill to solve the problem, not simply apply word fractions to them all. In fact, I know many teachers who would mark problems wrong if they did not use the new skill to solve them. They consider it cheating to use dimensional analysis. (Yes, this is from first hand experience as both a student and a teacher.)
6) And finally, many times teacher mistakenly believe that they do not have to teach students how to actually solve word problems, but assume that if they understand the new skill being taught that they should be able to read a word problem and know the steps needed to solve them. It is similar to the situation that often occurs with graphing - the science department assumes that the math department has taught the skills and they shouldn't have to, while the math department only teaches the skills of graphing mathematical functions and usually not graphing data for analysis.

In reference to your particular book, I think that many people would find it overwhelming to see that many rules needed to solve word problems. It looks like a good reference for teachers who need to help students understand dimensional analysis. However, it still doesn't get the student to actually know how to solve the word problem using a particular skill that the problems were designed as an application of.

Harold,

Kids do not like rules. That's why many Math books have instruction book for the teacher (separate edition to include rules). My DD won't read them.

Most gifted students will cruise through problem solving Math questions (without bothering the parents and sometimes we are amazed that they can do questions that we were quite sure above their capability including long and complex questions). There are many word problems today than years ago. So far, my favorite has been Math for gifted kids by flashcards and primary grade challenge Math by Edward Zaccaro. If my DD wants more, I'll probably try yours as well.

But keep writing and publishing Math word problems. The more choices, the better for us. (I would not have posted the way you did though). :-)

Harold,

I think that you are onto something, but offered a wrong solution.

As other posters noted, people do not like rules, especially so many of them. For gifted ones, it is the last thing we want to do to make them robots.

In my opinion, the problem lies in reading comprehension. Reading math and science literature is different from reading novels. There is a level of details often skipped by a faster reader, which leads to missing information, and repeated reading, and slow down the process of problem solving. So if you can devise a way of training in "precise reading", it will be better appreciated.

Here's what you're up against. �Mr. Google gives away 25 of your 50 rules For FREE! Here:
http://www.purplemath.com/modules/translat.htm
Google quote:
Over 16000 math word problems for grades 1st through Advanced 6th. Available both in English � New problems are added regularly. �that's a paid site here:
http://www.mathstories.com/
which, since you're selling "for gifted kids" makes more sense because when they get into something they over-do it.
I'm just an avid consumer not a marketing professional. �I do buy things like what you're selling which is an exhaustive summary of one thing without all the extras even knowing there's webpages giving it away. �I do. �If I were buying it your advertisement would not sell me. I would buy from amazon. �I would spend 2 or 3 nights flipping back and forth through all that's available on amazon �and buy the most stream-lined, exhaustive, no frills book, which yours actually is. �Amazon has a thing that you put your e-book for sale as a book and they only print copies as people buy them. �

Just as feed-back for advertising that I see and am sold by, here's the friendly, informative blog:
http://www.tutorhand.com/tutoringblog/teaching-mathematical-word-problems/
I see they give away broad, useful information, enough so that you can use it and do it yourself, but just enough so you can see how much work it would be and hire them instead. �It's hard to buy from this sales pitch because I look at it and say "amature" and wonder if they really know any more about it than I do. �Are they worth paying?
There's this guy: �which is like you, got a good looking product but just looks so darn flashy, gimmicky, sales man. �Granted, this formula might look like a sales pitch because it actually makes sales and has successfully over time. �But I looked into that guy selling this outline a few years back, his name escapes me at the moment. �
http://www.good-child-guide.com/

What I more often buy from more quickly and without hesitating for so long over more often looks like this:
http://www2.nvusd.k12.ca.us/apps/pubs.asp?Q=2&T=Board+Math&P=52
Granted, that's a school, but the layout... If you made pretty whiteboard problems showing over and over how you're rules apply repeatedly to all conceivable types of word problems you could show me how your program works convincingly without even just telling me�
Quote




Not quite what you expected when you wandered into a gifted forum, huh? �Makes me feel for the teachers who wander in to teach a gifted class thinking it will just be more of the same but less work for them because the kids are gifted. �Makes me feel for the kids who get such a teacher as well. �Makes me very grateful that people are creating different environments for gifted children to learn in.

K. �I'll can it unless you want me to tell you more ideas of more work for you to do, but I won't charge you. �

Thanks all for some valid comments. It is true that the book was not especially written for gifted children ..

Most of the 55 rules are basic math truths but written (with examples) for improved understanding by those that need it ...
Nothing particularly unique about them ! but they are needed to understand the math validity of the unique Word/Fraction technique

However, I wonder if any readers took the time to read the website's tab called 'WORD/FRACTION TECHNIQUE'. Please try the example problem on your gifted students (review their writings..
% correct)

Here is a summary of a technique which I believe is both unique and effective for those that the many that have difficulty.

1. No arithmetic until the equation is written !!! (see below)

2. Word/Fractions (W/F)can be inverted at will
(60 miles/hour = hour/60 miles)

3. Conversion W/F (3 feet/yard) (all equal to 1 may be added as
as a product in the equation)

4. Step # 1 in creating the equation is to write down the name of the answer ( = ? miles/hour)

5. Write an equation using a data from the problem (mostly products) ...(which is probably incorrect initially)

^. Using dimensional analysis, invert any or all W/F in order to cancel all words (as NUM/DEN pairs) on the left side equation until the remaining words equal the answer name.

Comments of the above basic concept of the book is welcomed (e.g. why it is not an improvement to any existing methods, if there any overall detailed methods)

Your comments are getting closer but still pretty general with no comments on the W/F and that MWP are a problem due to reading ,etc.

Thanks for the info. I still believe that all of your gifted students would benefit form my unique WORD/FRACTION technique..
if only educators would give it a try. But, I do not have a warm feeling that they are interested in any radical approach (even though it really, really, really works)

�� � � � � � � � � MY TAPE RECORDER �RUNS AT A SPEED OF 7 1/2 INCHES PER SECOND. �HOW MANY HOURS�
�� � � � � � � � �CAN A 1800 FOOT ROLL OF TAPE BE PLAYED ? � � � � � � � � � � � � � � � � � �


7.5 " per second
1800 ft per xhours
1800 x 12 to turn it to inches
21,600" /7.5"�
2,880 s.
2,880 s =48m.

My grandmother came up with the same thing.
1800
12
------
3600
18000
---------
21600 inches

Etc...,
She came up with the same 48 minutes.
So, 1/4 hour.
I used my lifeline. �

Someone here mentioned the only thing is that you're selling to student's parents, not to teachers. �Know your audience, know your competition. �As they pointed out teachers tend to teach their own technique and they get an attitude with the kids if they use any other method. �But. But. But.
You know something. �You know how to show it to somebody else. �That, my friend, is called intellectual property. �It has monetary value but it's a beast to wrangle in this day and age. �I can offer one more marketable bonus for you, tutoring. �Consider skype to expand your marketable services along the same lines. �Skype and Amazon's print as you go are two more client bases for you.
The alternative, given that teachers dislike kids learning outside of the box methods, is to contact the houghton mifflin publishers and see how you can get in. �If you think you're more along those lines than private tutor over Skyppe let me know, I'll help you look up some appropriate venues. �What is your vision and how can I help?"

I really think that targeting this toward parents or teachers of gifted kids is barking up the wrong tree. Gifted kids typically grasp things like the associative and commutative properties of addition and multiplication the first time they are taught them. They are not typically the kids who are applying an algorithm without understanding why it works. If they make mistakes on word problems, it is usually because either they over-complicate them, or because they are being asked to do 10 or 20 or 50 problems of a type they know how to solve, and that are essentially identical, and they lose interest halfway through, so they don't notice when one of the problems switches things around.

My son glanced at your page with the first chapter excerpts. His immediate response: "He hasn't really thought this through. His rules don't work for every case. Let's say that you have a problem where someone gave you half of a zebra, and someone else gave you another half of a zebra. That would be (1/2 * 1 zebra) + (1/2 * 1 zebra) by his rules. So according to him, that would be equal to 2*(1 zebra/2)= 1 zebra. And that method would be correct if you were talking about liters of water. But you aren't, you are talking about zebras. Just because you have two halves of a zebra, that doesn't mean that you have a whole zebra. You might have two right halves. You might have half of a male zebra and half of a female. And even if you had two halves of a single individual, that still wouldn't give you a whole zebra without an awful lot of repair work."

When gifted kids have issues with word problems, it is not generally because they can't figure out what the words mean, or how that should translate into an equation, but because they can see too well what they mean.

I was never very good at math, yet did very well with word problems; possibly because I was in advanced English courses in high school. (1980's)

A DVD that I like that teaches how to decode word problems: Mathtacular 4

There's also a workbook.

I have been so impressed recently with my third graders ability to solve word problems! I think it is surprising just how much they really can do! She surprised even herself when she did them. She did get somewhere that "these are hard." She sometimes doesn't read the whole problem. But I think that is because she thinks she is smart enough not to.

I have been on her about reading the whole problem lately and I think it is sinking in!

I think that word problems are a great way to figure out if a child knows the material all the way or just the short cuts! It is very clear to me that she understands the material when she can figure out these "missing number" word problems without having had any algebra or any advanced math classes. Many times she hasn't even been taught the math to DO the word problem, (long-division, decimals, mixed fractions) but she can figure the answer out anyway!

I wonder if NOT teacher her these "short cuts" in math yet is actually making her a stronger math student. She has to thoroughly understand every part of the problem and use problem soving skills to find that answers, rather than writing down 98654/3...and soving that. It really IS amazing!

I gave her the Sexton Math placement test to see which level workbook I should buy for the summer. She got 100 percent on 4th and 5th grade Math! I did, however had to tell her that the 'z' stood for the entire top number in the addition problem and not just the number that would have been in the one's place...That was funny to me!

She and I were AMAZED that she could do that much math without ever having been "taught it!"

As I said before, I wonder if "teaching" math processes...like long division and multiplication, mixed fraction solving...too early is taking away from the overall understanding and problem solving skill that are so important for solving word problems...

Any thought?

I should say that I'm not a teacher of children and I acknowledge that what suits my DS might not suit all children, but... yeah. I think the issue is teaching an algorithm at a stage when it looks to the child like magic. If the child really understands why the algorithm works - I don't mean so that s/he could write a formal proof of it, but so that s/he can see which modifications of it are legitimate and which are not, through really understanding what the algorithm does and why this is a useful thing to do - then learning the algorithm should be quick and easy, and might even be unnecessary, as s/he might be able to invent one when it's required.

On the other hand, if the child doesn't have the background understanding or isn't developmentally ready to learn what's needed, then the algorithm is hard to learn and prone to being misremembered. It will then certainly not be correctly remembered in later life. The child might be able to do that kind of question in a test, but won't have much chance of doing problems that require a slightly different method. It's hard to think of a case where there's really any point in that sort of learning.

There must be a middle ground - a tricky judgement area for teachers, I expect - where the child hasn't quite got there but almost, such that practising the algorithm might actually foster the missing understanding.

As a parent, I try to watch how much input DS needs to do a problem. If it's a quick hint/reminder (e.g. recently when he was trying to turn a recurring decimal into a fraction, and couldn't remember how to go about it, "what I'd do is multiply by something so as to get rid of that pesky infinite decimal" was enough to remind him broadly of the technique he needed - see how little info there is there compared with the full algorithm) then I see the problem as being in his ZPD and don't worry. If he needs a hint, and then another hint, and still isn't there, I reckon he's missing something and go for a more basic problem.

COOL! I am learning so much from watching my daugher learn! I'm not even close to a teacher and don't have the vocabulary to do with what I am learning about learning! But I'm so glad that at least one person agrees with my observation.

I did teach her long division when she was drawing pictures to come up with the answer...and she was like "OH! Why didn't you tell me this before!" lol..So, I have asked to school to skip her to 5th grade math in the fall, but I wonder if 'not knowing' the tricks is actually a better way to go. I would worry that in 5th grade, they might teach her things that she would be better off not know for a little while, even though it might cause her to take a little longer than it would otherwise, to do the problems. I suspect in the long run, she will be stronger for it!

Colin'smum, this reminds me of an article I read talking about very young children and helping them discover vs showing them things. They gave small kids a toy with several functions, and either said "hmmm, I wonder what this does?" or "let me show it, it can light up". The kids who were shown how it lights up would make it light up a few times, then wander off, the kids who were handed the toy and asked a question discovered many more of the functions and played with the toy for longer.

I'm not a teacher of adult or children, but I try and use that sort of technique, to have them figure out the rule or algorithm themselves.

I remember that one! I think it was in a Carol Dweck book that I read about it. I hadn't connected, but you're quite right, it's very much related.

F.A.I.L.
Lol, I reviewed my previous post and 48 minutes is not 1/4 hour.
Why did nobody tell me I had spinach in my teeth?
And you guys are my friends.
Geezh.

�thanks for the pm.
You are a tutor, very good. �It seems like tutors are expanding their area of service by use of skyppe these days. �As your "crowd" grows you can use video conference to include larger groups of students at a time.
I am only the mother of very young children (one pre-k and one infant) so I'm unsure what the schools are using to teach word problems. �I have noticed among the regular posters on this board there is only one teacher, a couple of professors, and one blogger of gifted resources. �Maybe they could better tell you what works and what does not work about your program. �
I was offering only a consumer-response survey that I liked the look of one website over another.




I would like to help you with this. �I believe by keep questioning and refining we can discover and resolve what is not working about getting your useful method to people that could benefit. �From the wording you have used I feel like you're trying to prepare young children for higher maths. �I would like to better understand what you're trying to do AT THIS POINT with your educational material. �Are you trying to refine the technique itself? �Are you certain of the core math it's built around? �Do you need help refining the delivery or teaching method? �Or is everything fine except for the marketing? �What pre-requisite knowledge should a child have before attempting to understand your program? �Let's keep talking about this. �I have time. �It won't bother anybody else. �Maybe somebody who teaches can further review the material. �I hope you view criticism as constructive. �And, well, rejection is part of getting published. I know ur not trying to get published, necessarily, but the idea is the same. �You're trying to get out there.

Your page reminds me of this other blogger's page that I read recently saying that "what's wrong with kids these days is they just don't have a clue what a equals sign means". It seems like your method has some kind of built in mechanism to compare apples to apples and oranges to oranges. Perhaps you could demonstrate the steps in your method for solving the following equation. I visualize better by example.
� � � � � � � � � �MY TAPE RECORDER �RUNS AT A SPEED OF 7 1/2 INCHES PER SECOND. �HOW MANY HOURS�
�� � � � � � � � �CAN A 1800 FOOT ROLL OF TAPE BE PLAYED ? � � � � � � � � � � � � � � � � � �

Also, did you create a new theorum?

It is a 'theorem' if you want to call it that. "Equality of an equation also includes the dimensional names, if any, of the numerical elements "

This is the basis of 'Dimensional Analysis' used by all sciences (and taught in all such university courses).It is the cornerstone of my Word/Fraction technique which expands upon that concept.

Hope you got my private E-mail to you