The problem with story problems
I was trying to think today why it is that so many kids feel that word problems or story problems are difficult.
It didn't make sense to me initially. See,
So what is the problem with word problems?
It surely can't start on 1st grade. You know, someone tells you a story problem such as: There are five ducks on the lake and three on the shore. How many ducks are there total? And often the math book has a nice picture there to accompany it. Surely kids don't think that as being difficult.
My child has gotten to like "subtraction stories" pretty well - just simple situations where someones or some things go away. She has even made up some herself.
Could it be that they don't understand the language? Or, that they are hurried to solve them too quickly?
Please send in your thoughts on this. Also, what is the advice you most often hear on word problems?
Lastly, explore this list of problem solving and word problem resources online.
It didn't make sense to me initially. See,
- Most kids just love stories.
- Usually kids love words, too, based on the fact they use them a lot.
- And problems - I can't imagine that kids don't like word problems just because they need find an answer to something. Most of us even adults get fascinated by puzzles, for example.
So what is the problem with word problems?
It surely can't start on 1st grade. You know, someone tells you a story problem such as: There are five ducks on the lake and three on the shore. How many ducks are there total? And often the math book has a nice picture there to accompany it. Surely kids don't think that as being difficult.
My child has gotten to like "subtraction stories" pretty well - just simple situations where someones or some things go away. She has even made up some herself.
Could it be that they don't understand the language? Or, that they are hurried to solve them too quickly?
Please send in your thoughts on this. Also, what is the advice you most often hear on word problems?
Lastly, explore this list of problem solving and word problem resources online.
Comments
his books are kinda like really long word problems with amazing old fashion style illustrations
One reason is that the wording in story problems in the primary grades is more linear (just like a story). In your example, "five (5). . . and (+) three (3). . . How many . . . total (=)?" I can move from left to right, top to bottom, beginning to end, and solve the problem.
But consider this word problem from a grade 4 text:
"Matt's scores for a ring-the-bell game were 6, 5, and 10. What was his average score?"
The setup word here, "average," comes second to last in the problem. The problem is not a story in the sense that the other one was, because you cannot translate it mathematically from left to right, top to bottom, or beginning to end and have the right mathematical idea. You have to know what "average" is and then GO BACK and apply that knowledge to the information in the problem.
This process is nonlinear.
We teach a good deal of elementary mathematics in a linear way. When we present addition in texts, we show two birds on a branch, and then we show one flying in. The "result," we say, is three birds.
But 2 + 1 is THE SAME AS 3; it is not a story line that leads up to a finale.
By and large, the solution offered to problem-solving woes is a step-by-step problem-solving process. Everyone's got one. In the grade 4 text I mentioned, there are four steps: Understand, Plan, Solve, Look Back. In one middle-school program I am familiar with, it is the S.O.L.V.E. method: Study the Problem, Organize the Data, Line up a Plan, Verify with Action, Examine the Results.
Notice, though, that methods like this are really linear--they are step by step.
I have something here
http://mathandtext.blogspot.com/2006/01/lesson-notes3-add-numbers.html
(just scroll down to the bottom of the post and click on "GO TO LESSON") that I think demonstrates nonlinear instruction.
I don't think this is a cure-all for problem-solving difficulties, but I do think that instruction that emphasizes nonlinear reading can help quite a bit.
Addition of multi-digit numbers: lesson notes
Scroll down to see the link to the actual lesson.
the link is
Addition of multi-digit numbers: lesson notes
I think teachers (and homeschoolers too) would benefit from the services of a math specialist who could conduct inservice training and provide the missing context. Unfortunately, although we have reading specialists, I don't think there will ever be a math specialist in every school.
When you're solving a more challenging problem, the process more or like goes back and forth, you try something and then you re-evaluate the situation, try something else, again re-evaluate the situation. Kind of you try to understand the problem better as you try different things.
One time in the past I tried to write down my exact thoughts when solving a problem. It's here:
Proving logarithm property.
I have read of research in the past where they had kids observe an expert problem solver (math teacher) who was trying to voice all his thoughts whiel solving the problem, even all 'wrong leads' (though the thoughts of course go thru one's mind pretty quickly). That seemed to help the students. Can't remember what research it was though.
The trickiest word problems for the 3 kids I've taught algebra have been the rate problems, btw. I often have to look at the answers... even after studying examples of the same type of problems... over and over.
(sheepish grin)
I also think that students dislike them because of the way they are taught to solve them. There is almost a ritual you go through to get from reading the problem to solving it...the children don't get to just try to figure it out.
Here is an example for a group of students ready to learn multiplication:
You push a button on a box making machine, and 2 boxes fall out. (illustration)
You push the button again and two more boxes fall out.
(illustration)
How many boxes will come out if you hit the button 10 times?
After the lesson on how to multiply by 10, ask how many boxes will come out if you hit the button 12 times?
Mixing addition with multiplication will help them build a strong connection, while appreciating both.
This is a difficult word problem, but it's easy and hard at the same time.
You can introduce the problem again as:
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2
This might be problematic for even an older student, but perfectly solvable with some basic skills. This ability to ask and solve the problem will make them look for the simplest solution.
The example of adding necklace beads of .05, .10, and .25 to reach 3 is a good problem, but the restrictions work against it. Not allowing the student to keep the change, and looking for certain bead colour isn't necessary. There are many solutions and that is what makes this a good story problem.
I really like the fact you can turn this into another project, making necklaces.
For more advanced students real world problems can offer a challenge and sense of usefulness. Instead of making a story problem, ask for solutions to real questions. How many French-fries are served in the cafeteria each day? How tall is a brick building? How far is it from the top of the wall to the side-walk?
You wouldn't want to ask how many pencils would fill the swimming pool. This sort of question is similar, seems fun, but it is a lot of work and pretty pointless. It doesn't help them see the world in numbers. A better question might be, how many packs would transform the pool into Jello?
If it allows the student various solutions, or ways to a solution, the better the question.