Fix-It: Five Ways to Fix Word Problems

Word problems aren’t the problem. A novel is a sprawling word problem. A video game is a symbolic word problem. An argument in a relationship is a word problem. Though none of those examples are mathematical, they demonstrate that we are often solving problems in ways that are relevant and engaging.

People use math to solve problems all the time. If I’m on a road trip, I’m thinking about miles per hour and miles per gallon as I figure out when and where to stop for gas. When I’m on a long run along the canal, I use the Pythagorean Theorem to figure out distance. When I multiply a recipe, I’m multiplying fractions.

Math word problems often suck, because they are bad stories. I want to point out that none of this is new. I’ve seen Dan Meyer, David Wees and Jose Vilson write about these ideas. And the truth is that constructivist educators have been pointing out these ideas for years. But here are my thoughts on how we could fix word problems:

  1. Let kids develop their own problems based upon a scenario. In other words, give students part of a problem and let them wade through the information on their own. For example, I asked students to find the “best division in football” and students compared winning percentages and difficulty of schedule. It was a word problem, true, but it was more of a scenario and a set of resources. 
  2. Use a real context. Our math book asks students to play the role of a catcher using the Pythagorean Theorem to throw out a runner on second base. I would love to interview Buster Posey and ask him how often he uses math. My guess is it’s more often than it first appears. But my second guess is that it never involves the Pythagorean Theorem. Note: it also works well to use a fantastical context. So, add a few dragons and maybe a unicorn or two. How else do you explain math wizards? 
  3. Write better stories. Use the Elements of Literature: I wrote about this seven or eight years ago and I still find it valid. Kids love good stories. They love real conflict. So, when using linear equations, let them find which taxi is a better deal or whether Dish or Direct TV work out better for customers. Make it interesting, not simply by adding pop culture or sports figures, but by finding real conflicts that might need to be solved. 
  4. Use fewer problems and engage students in discourse. Let them share their processes and talk about the most effective ways to set up and solve a problem. Let students use manipulatives or draw pictures if necessary and then help them see how an algorithm is like a cheat code in a video game. Allow students to use mental math to build up their number sense. 
  5. Support language. I know this might pertain more to my own context, but some kids struggle with word problems because they are written with passive voice or they use the future perfect verb tense. So, help students grammatically as you craft word problems. 

photo credit: Nick Sherman via photopin cc

John Spencer

My goal is simple. I want to make something each day. Sometimes I make things. Sometimes I make a difference. On a good day, I get to do both.

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6 responses

  1. It's kind of unfortunate we call them "word problems" because the words aren't the point, are they? The point of a word problem is to present some isolated data and ask students to figure out what to do with that data to answer a question. We could do that with real-life models, or videos, or comic strips.

    There's actually a great TED talk that walks through why word problems suck and very practical steps to un-suck them.

    1. Thanks for the link. I think that's my thought. Let's make them not suck so bad.

  2. I never liked word problems as a student and they haven't gotten any better over the years. The textbooks have spent so much time trying to make problems politically correct (with names) and continue to use obscure situations. All they are doing is causing more confusion among students. I have watched as third and fourth graders stumble over the names and are unable to even get to the problem. Once they insert names of classmates, they can then tackle the math. That is if the math makes sense in their lives. If not, change it. If we can relate the problem to the student's lives and environments they will have a better chance of getting to the math rather than stumbling over the words.

    1. The situations themselves are so absurd that they become laughable.

  3. I always hated word problems as a student. Now, I get them, but I have no idea what changed in my head that enables me to solve them without much trouble. I teach high school algebra, and my students hate word problems. If it's a multiple choice question, they will either randomly pick an answer, or multiply all of the numbers in the word problem and pick the answer that is the closest. If it's not multiple choice, a lot of them won't even attempt the word problem. It's unfortunate, because most of the math in life is word problems.

    I've been trying to do some of Dan Meyer's problems, which a few of the students get into, but most of them have such a block built against word problems. They are convinced that word problems don't make any sense and shouldn't make any sense. And, given the problems they see on tests and in the textbook, I'm afraid that they are right.

    1. What do you think is the biggest barrier to problem-solving and word problems?

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