Wednesday, June 6, 2012

Word Up! How Word Problems Can Boost Critical and Creative Thinking

I  recently had a dinner to celebrate my niece's seventh birthday.  My brother and sister-in-law had recently moved to Singapore, so I asked how schooling was going for Ariel.  I was relieved to know that she was adapting well and surprised to know that despite the many field trips that have interrupted our formal homeschooling sessions at home, Katelynn was at or above what was being taught in Singapore.  (O.K., I admit that we are dismally behind on our BM, and somewhat behind in Chinese but that's another story which doesn't apply to Singapore.)

But what really caught my attention in our conversation about what Ariel was learning in Singapore was the use of story problems for math.  Apparently her new school in Singapore uses these problems frequently in its math syllabus. The wording of the problems was giving Ariel a bit of trouble, it seems. I could say the same for Katelynn.

I went home thinking about this. I had not really thought very much about the story problems we had done at home.  I did them as an afterthought because they happened to be in the workbook I was using. This new conversation awakened a curiosity in me to find out more about this way of learning math and what I discovered changed our approach to math and might just change yours.

Do the Two-Step
The first thing I discovered was that one-step word problems really don't help teach children how to apply what they learn in math.  They are too easy to figure out without really thinking about them.

Think about it.  Do you remember those story problems you used to get with your math homework?  Often, to solve them, all you had to do was use the same operation you had been doing in the other traditional equations on the same page. They went something like this: Ernest has 6 balloons. He gave his friend Sally 3 balloons.  How many balloons does Ernest now have?  So, you knew that you only had to plug those numbers into a similar arrangement with the same operation to solve them. No thought required.

What helps children apply math better is a multi-step problem where more than one step is needed to solve it.  Something like this: There 18 balls in the gymnasium. In all there are three types of balls: footballs, basketballs and kick balls. 6 balls are footballs and 5 balls are basketballs.  How many balls are kick balls?  Of course this is a very simple example, but you get the idea of what is meant by multi-step here.  You have to add five and six together first then you have to subtract that from eighteen before you can get the answer.

Mix It Up
Even if it wasn't the same operation (maybe your teacher was a little trickier and gave you a mixed selection), because it was a one-step problem, a simple cursory reading would tell you what operation to use.  There really wasn't much thought to it.

So the lesson here is use multi-step problems and use problems with a mix of operations. It can be two or more operations in one problem (like the one above) or two or more operations in a group of problems (some problems on the page require addition, others require subtraction).  It gets learners out of robot mode and requires them to think more about what needs to be done to solve the problem.  Not only that, most real-world problems are not one-step problems. They often involve two or more steps and more than one operation to solve them. So this is good practice of life skills!

(I will stop here for a moment to give a caveat.  You should use one-step problems with your six or seven year old the first few times with word problems.  It helps them get acquainted with this type of problem and what different words like "how many all together, how many more, how much less", etc.. After a few rounds you can start introducing simple two-step problems.)  

Talk About or Write About the Word Problem
I had heard about math journals as a method of getting kids to explain how they solve problems.  I've haven't tried these yet because Katelynn is not very speedy at writing, but with older kids, you could require them to explain their strategies for solving word problems.  (See the link below to learn more about them).  Another way is to get them to explain orally.  Whatever method you use, make sure you don't just include how the problem is solved, but also WHY they solved the problem a particular way.  

The big word for this is metacognition.  It's being aware of how you think and what strategies you should use to learn or accomplish something.  It's a very powerful skill that can help your child become a powerful thinker. That's why it's important to talk about the word problems (or anything else you're learning about), discussing how they were solved and why that method was used.  You can also discuss whether there were any other ways to solve the problem.  Are these ways better?

Create Your Own Problems
Actually what I mean is have your child write their own problems.  Once they've done enough word problems to understand the wording, they can write their own.  I do this with Katelynn. She write problems for me and other family members to solve.  This makes it more fun than just solving something someone else created.  Not only that, when children write their own, their grasp of story problems is much stronger.

Do Word Problems Often
Multi-step word problems help develop logic, abstract thinking and discipline.  Right now, as I do these multi-step problems with Katelynn, I can see that she often just wants to give up.  She'll just shrug her shoulders and say, "I don't know."  But, I persist and get her to break the problem down into smaller steps.  I start by asking her to tell me what she would do first and so on.  So it's important to keep using word problems frequently with your child and building up the complexity and types of operations as you go.

Frequent exposure and practice with these types of problems will train your kids to not give up easily, help them develop metacognitive skills, logic and abstract thinking, as well as problem solving skills.  What's not to like about that? Wish I had started earlier, but I'm definitely going to include them more often in our math sessions from now on!

Some Great Sources for Story Problems

I mentioned math journals.  Here's a Scholastic article on them with tips about how to use them.  It'll change the way you do math.

 Math Playground: Has lots (I mean hundreds) of excellent multi-step word problems for all ages and for many areas of math.

Figure This! This site offers more real-life problems.  Recommended for mid-upper primary.

 Aunty Math's Challenges: Stories with word problems for K-5.

Study Guides and Strategies Math Series: Solving Math Word Problems.  Lots of tips on terms used in word problems and what operations they relate to.  Some word problems with various types of math at the bottom.

PDF document with multi-step problems.

 IXL: Has multi-step word problems under the heading "Mixed Operations" for grades 3 and up. Also has lots of practice for many areas of math. Practice is online.  This link takes you to grade 3, but if you check the menu you can get to the other grades.


  1. Thanks for the great maths article. When you talk about metacognition, it trigers me because i just read some information about it at

    Dr Derek Cabrera and his partner created a technique in how to think.

    It's very interesting and i suggest you take a look at it as it will help our kids to think.


  2. Thanks for sharing :) I recommended your post in my blog too.