Shifting Your Approach to Teaching Math Word Problems

Practical word problems are often considered one of the most complex parts of elementary school mathematics. They require students to understand the context of a math problem, identify what the specific problem is asking, and then apply mathematical skills to solve it.

Mathematical skills are of course an important aspect of solving math word problems, but research shows that strong language comprehension skills are actually a better predictor of student success. In fact, a 2018 study focused on math word problems concluded that elementary school students with strong language comprehension skills but weaker math skills consistently outperformed peers who had strong math skills but weaker language comprehension skills. 

With that in mind, educators should consider shifting their thinking and instructional approach to teaching math word problems. Below are several strategies, progressions, and scaffolds designed to help students work through an always-tricky part of elementary school math.

Explicit Modeling

This step-by-step metacognitive approach can help teachers model how to take on a math word problem.

Step 1: Read (and reread) the word problem.

First, encourage students to read the word problem in its entirety, in order to gain a greater understanding of the context. Rereading word problems for clarity is also a useful strategy for supporting comprehension of the text.

Step 2: Chunk and annotate the problem.

Chunking the problem into smaller parts reduces the cognitive load on comprehension. From there, annotating the problem allows students to home in on different parts, so they can identify what, exactly, is being asked of them. Here are some key annotations:

• Identifying the question(s) of the word problem
• Underlining or highlighting important numbers and relevant information
• Circling any parts of the text that are not understood (unknown words)
• Eliminating or crossing out extraneous information not needed to solve the word problem

Step 3: Retell the problem in your own words.

Restating the problem helps identify what the word problem is actually asking.

Step 4: Establish a plan for how to approach or solve the problem.

Determine which equation(s) or steps are needed to answer the question at hand.

Step 5: Apply mathematical skills.

Utilize necessary mathematical supports or strategies to solve the equation. Specific problem-solving approaches can vary. They might include an oral discussion of the solution, drawing a picture to represent one’s thinking (a mental model), or working within the CRA (Concrete Representational Abstract) framework.

Progressing Through Increasingly Complex Problems

In order to support students as they are concurrently building up their language, comprehension, and mathematical skills, I recommend guiding them through a progression of word problem contexts from least complex to most complex.

Least complex: Numberless word problems.

Numberless word problems are contextual math word problems with the numbers removed. When we start with these types of problems, the focus can remain entirely on context and comprehension.

An example: Some bees are flying around the garden. Some more bees join them.

Less complex: Single-step word problems.

In single-step word problems, the numbers are added back in, but only relevant information is included. Less intensive vocabulary is incorporated, and there’s only one mathematical operation to solve.

An example: 12 bees are flying around the garden. Five more bees join them. How many bees are flying around the garden altogether?

Moderately complex: Single-step or multistep word problems.

Moderately complex word problems might entail single-step questions with extraneous information and intensive or content-specific vocabulary. Or, they might entail multistep word problems, with some of the aforementioned attributes.

The complexity here increases because students have to determine which information is relevant, which is irrelevant, how many steps are needed to solve the problem, and how to set up the proper mathematical equation.

An example: It is a rainy, humid day in April. Twelve bees are flying around the garden. Five more bees join them. Then a bird chases seven bees away from the garden. How many bees are still in the garden?

Most complex: Rich math tasks.

The most complex word problems are open-ended, rich math tasks that have a variety of possible representations, answers, and explanations. Rich math tasks require students to deeply engage in how to approach the provided context(s), understand what the task is asking, and use critical thinking and creative problem-solving.

An example: Julia picked 30 oranges at Citrus Groves. She wants to pack the oranges into boxes so she can bring them home, but she also wants an equal number of oranges per box. Show three different ways that Julia can pack the 30 oranges.

Using Targeted Scaffolds to Access Math Word Problems

If students are not quite ready to independently work through math word problems, there are additional scaffolds to consider.

Explicit teaching: This concept encapsulates a number of useful teaching models: think-alouds, preteaching critical vocabulary, and reinforcing mathematical concepts or skills that students will need to know in order to accurately solve a given word problem.

Explicit teaching of math-specific vocabulary builds students’ background knowledge, so they can better understand the context of math word problems. Explicit teaching of language in general is also useful: It supports students’ understanding of what a word problem is asking. Furthermore, explicit teaching builds mathematical skills and fluency with basic operations, before students progress to applying those mathematical skills to word problems.

Worked examples and completion tasks: Worked examples are when students are given a step-by-step guide that explains and models how a specific problem is solved. The worked example reduces the cognitive load on students; it chunks the learning down into actionable steps. The worked example can be referenced later on when students start solving their own math word problems. Whereas completion tasks present students with partially completed word problems, and students have to fill in the missing steps.

Error analysis: During an error analysis task, students are given a worked math word problem with an error embedded within the completed task. For example, if the word problem calls for subtraction, the proposed solution might incorrectly show an addition equation instead. Another structure is when two or more solutions are given; students have to figure out which solution is correct and which is incorrect, and then justify their reasoning.

Independent application: When students are attempting to work independently within math word problems, consider giving them concrete models or manipulatives (e.g., base 10 blocks, or red and yellow counter chips), as well as adequate work space to plan out their thinking, draw pictorial models, and write down relevant mathematical equations. Additionally, graphic organizers are a nice way to chunk a word problem into more comprehensible parts while building in probing questions that hone metacognitive awareness.

Ultimately, rather than solely prioritizing mathematical skills in solving word problems, we need to also consider the importance of language and comprehension.