Word problems try and tell students a story about the math problem in front of them. They are a useful way to connect abstract numbers to concrete situations, so students can learn early on to apply math to solve real-world problems.
The challenge is that the combination of words and numbers can turn into cognitive puzzles, and students need to work multiple levers of their brains to unpack them. These problems can especially be a challenge for English learners or students who struggle to read or have a learning disability. In a nationally representative EdWeek Research Center poll, 29 percent of math teachers said less than a quarter of their English learners can solve word problems on their own.
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. But making word problems too basic or easy, or teaching students specific “hacks” to solve a word problem, doesn’t work, either, experts say.
In every word problem, there are three things that students need 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.
Students who are successful problem-solvers think about what they’re doing to solve the problem, and how they are doing it. When students are coached to reason through and solve the problem, it helps build their confidence.
Yet in the EdWeek Research Center survey, conducted this spring, about a third of math teachers said it’s “very challenging” for them to teach multi-step word problems, and a quarter said it was “somewhat challenging.” Fourteen percent said they don’t teach this type of word problem.
Here’s what the research says about the best ways to teach word problems.
Solving word problems isn’t a solo process—teachers should join in
Students shouldn’t encounter word problems for the first time in an assessment. Teachers need to bring the right word problems into rotation during lessons and expose students to mathematical language early. It’s important for math teachers to have a deep understanding of their students’ reading levels, prior knowledge, and cultural background.
Kevin Dykema, a math instructional coach in Mattawan, Mich., said he likes to present a word problem that uses a softball or baseball diamond to teach the Pythagorean theorem. But not all his students know what a softball or baseball diamond looks like, so he draws them a picture.
“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,” he said.
Students need to understand the context and “type” of each word problem. Researchers suggest that teachers should play around with the information provided in the question to get students thinking conceptually about problems.
Numberless word problems can be used to do this—a teacher can introduce a problem without any quantities, which compels students to first think about the relationship between the entities in the problem and then the mathematical function they’d choose to solve the question.
A teacher may say, for instance, “Leo has some toy cars. Eric has a few more than Leo. How many cars do they have altogether?” The teacher can then gradually introduce the quantity of cars.
Or teachers can switch between missing quantities in the problem. For instance, students could be asked to solve for c in a+b=c. Then, they could be asked to solve for a or b to test how well they understand the relationship between the different values.
When teachers use “think-aloud” strategies—discussing steps with students as they solve a problem or visualize it—they should talk about why they chose a particular strategy. Research indicates that it’s just as important for students to explain their rationale for solving or visualizing the problem as it is to arrive at the right answer. Students should expect to be asked how they solved the problem and be ready to answer.
Teachers should avoid having students look for keywords, a hack used commonly to connect words with mathematical operations. In the EdWeek Research Center survey, a majority of math teachers—70 percent—said they ask their students to look for keywords “every time” they solve a word problem.
But this hack isn’t foolproof, say experts like Dykema. For instance, the word “more” within a word problem may mean students need to add the numbers, but a slight variation, like “how many more,” could change the required operation to subtraction. Connecting words to specific strategies won’t help students when the context of the problem changes.
Research suggests that getting students to reflect on their strategies will hone their problem-solving skills for higher-level problems, too. Teachers have to prompt this thinking through task lists (identify quantities, draw out the question, find the mathematical operation) and starter questions (What is this problem asking me to find? Have I solved a similar problem before?).
How to help students who struggle to read and comprehend the problem
Students should learn to visually represent different types of word problems in the form of bars, tables, number lines, or schematic diagrams before they jump to solving the equation. This strategy, research indicates, works well for English learners and students with disabilities.
Visualizations help students break down the problem into digestible bits—what do they need to find, and how they can find it? Some visuals work well for specific problems, like strip diagrams for problems that involve comparisons.
Pro tip: Use a handful of visualizations consistently to explain the word problems, instead of confusing students with too many representations.
Before jumping into a lesson on word problems, assess your students’ reading abilities. Experts suggest that teachers work with colleagues who assist English learners or those with disabilities to design their instruction accordingly. However, don’t assume that students who are still learning English are unfamiliar with the underlying mathematical concepts, too.
Using “Bet Lines” for English learners can boost their engagement with word problems. Bet Lines are a discourse strategy in which teachers read half a question and then wait for students to chime in with what they think happens next.
For instance, a teacher may read out, “Five cats went to the playground. What do you think happens next?” Students could respond by adding or subtracting cats from this equation. The Bet Lines strategy, experts say, will help build a student’s mathematical reasoning.
Data analysis for this article was provided by the EdWeek Research Center. Learn more about the center’s work.
