Students often struggle to connect math with the real world. Word problems—a combination of words, numbers, and mathematical operations—can be a perfect vehicle to take abstract numbers off the page.
Word problems can press students to think more critically and make sense of the “math story” being told to them. This inherent quality of word problems also turns them into a cognitive puzzle for students.
In every word problem, there are three things for learners to do: read and understand the problem’s narrative, determine what the problem is asking them to find, and identify one or more math operations to solve it. When students can reason through how they approach and solve the problem, it builds their confidence in connecting math to real-world scenarios.
Students need to work multiple levers of their brains to unpack a word problem. That’s why these problems can be a challenge for English learners or those who struggle to read or have a learning disability. If students spend all their time trying to understand the words, or the context, of a problem, they’ll struggle to understand which mathematical function to pick.
Teachers can employ several strategies, like using different visual representations, to make word problems more approachable, said Kevin Dykema, the immediate past president of the National Council of Teachers of Mathematics and an 8th grade math teacher in Mattawan, Michigan. But even before they get to that point, Dykema said teachers must get over their own discomfort with word problems.
“We have negative relationships with word problems because we remember, as elementary students, you do a whole bunch of [math] problems without the word problems—and then there was always that word problem at the end, and it was always posed as, this is the difficult type,” he said. “We need to move away from that. We need to recognize that what math is about is doing those type of problems.”
Opening a lesson with a word problem is one of Dykema’s favorite strategies to get students familiar with the concept. With a real-world context to it, the math problem may start to make more sense to students.
In an interview with Education Week, he detailed other strategies to help students, especially those who struggle with the language, tackle word problems. The interview has been edited for length and clarity.
For more on the best research-based strategies to improve math instruction, see Education Week’s new math mini-course.
How can teachers put word problems into a context that’s familiar to all students?
If the problem has a context that’s unfamiliar to everybody, find a Google image of whatever you’re talking about so they can make sense of that problem, or change the context of the problem so that it’s something that the students can relate to. If I’m teaching in Miami and I talk about how much snow you’re getting, it’s not going to be a contextual thing. In North Dakota, though, I can use a problem about sledding down a hill.
Often, when I’m dealing with the Pythagorean theorem in middle school, I talk about a softball diamond or a baseball diamond, and there’s a word problem that I like to use with that. But not all my students know what a softball or a baseball diamond looks like. I draw a quick picture for them. You have to help fill in some of those missing pieces so that students can start solving that problem [and] aren’t spending all their time decoding the words.
This makes the problem relevant and helps them recognize why math is not just a series of steps to memorize, but is helping us solve real-world problems.
Do keywords help to unpack work problems? How frequently should teachers use them?
We should move away from using just a keyword strategy. Keywords can work if the problem is set up in a specific way. For instance, if we are using “more” [in a problem], ever so often, more means to add. Students could get used to that connection and then, suddenly, have a problem where the “more” leads to a subtraction problem.
I try to encourage my colleagues and remind myself—don’t just rely on those keywords; keywords often fall apart. I want to have my students make sense of that problem, draw a picture, and do a variety of different things so that we’re not having to rely on those keywords that often unfortunately fail us, and fail the students.
Teachers also need to be strategic about when they’re using the word problems. If we’re using the word problems just at the end of a lesson, and the whole lesson we added, chances are that students will assume that the word problem at the end will be about addition. But if we start the lesson with a word problem, they will have to think [about the problem] and not just rely on the lesson or the keywords.
How can teachers involve students in breaking down word problems?
It is difficult because in a classroom, even if you only have 20 kids, the wide range of [learning] abilities can feel overwhelming. It’s important to get our students communicating with each other.
Too often, math has been that class where the teacher only converses with one student at a time. Let’s get more into peer-to-peer discourse. Think about other content areas in language arts: They read a passage, and then they talk about it in small groups. In science, they do an experiment, and they talk about it in small groups. But in math class, the teacher does all the talking, maybe with one or two kids at a time, and the other kids are like, “oh, I’m glad I’m not having to respond to that.”
Let’s find ways to get kids to collaborate with each other in groups. It’s through those peer-to-peer learning efforts that they start to make sense of the math. I’m always amazed at the number of times a student can say the exact same thing that I said, but it makes more sense to them because a peer said it. There’s something magical about that.
We’ve got to increase those opportunities when our students share their math discourse. It also increases the likelihood that they’re engaged in the deep thinking that’s required to make sense of mathematics.
