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鈥檒l struggle to understand which mathematical function to pick. But making word problems too basic or easy, or teaching students specific 鈥渉acks鈥� to solve a word problem, doesn鈥檛 work, either, experts say.
In every word problem, there are three things that students need to do: read and understand the problem鈥檚 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 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鈥檚 鈥渧ery challenging鈥� for them to teach multi-step word problems, and a quarter said it was 鈥渟omewhat challenging.鈥� Fourteen percent said they don鈥檛 teach this type of word problem.
Here鈥檚 what the research says about the best ways to teach word problems.
Solving word problems isn鈥檛 a solo process鈥攖eachers should join in
Students shouldn鈥檛 encounter word problems for the first time in an assessment. Teachers need to bring the during lessons and expose students to mathematical language early. It鈥檚 important for math teachers to have a deep understanding of their students鈥� 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.
鈥淵ou have to help fill in some of those missing pieces so that students can start solving that problem [and] aren鈥檛 spending all their time decoding the words,鈥� he said.
Students need to understand the context and 鈥渢ype鈥� 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鈥攁 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鈥檇 choose to solve the question.
A teacher may say, for instance, 鈥淟eo has some toy cars. Eric has a few more than Leo. How many cars do they have altogether?鈥� 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 鈥溾�攄iscussing steps with students as they solve a problem or visualize it鈥攖hey should talk about why they chose a particular strategy. Research indicates that it鈥檚 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鈥�70 percent鈥攕aid they ask their students to look for keywords 鈥渆very time鈥� they solve a word problem.
But this hack isn鈥檛 foolproof, say experts like Dykema. For instance, the word 鈥渕ore鈥� within a word problem may mean students need to add the numbers, but a slight variation, like 鈥渉ow many more,鈥� could change the required operation to subtraction. Connecting words to specific strategies won鈥檛 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 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 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鈥攚hat 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鈥� reading abilities. Experts suggest that teachers work with colleagues who assist English learners or those with disabilities to design their instruction accordingly. However, don鈥檛 assume that students who are still learning English are unfamiliar with the underlying mathematical concepts, too.
Using 鈥溾�� 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, 鈥淔ive cats went to the playground. What do you think happens next?鈥� Students could respond by adding or subtracting cats from this equation. The Bet Lines strategy, experts say, will help build a student鈥檚 mathematical reasoning.
Data analysis for this article was provided by the EdWeek Research Center. Learn more about the center鈥檚 work.
