Teachers and students consistently cite word problems as a difficult challenge for students to master. In Fall 2022, the widely respected adult educator Lynda Ginsburg published the article, Mathematical Word Problems in Adult Education: What the Research Says, in the journal Adult Literacy Education, summarizing recent research about adult learners’ responses to word problems and strategies that we might use to help our students be more successful.

Some of the ideas that stood out to me in the article:

• Adult students use math in their daily lives and have likely developed strategies that could be shared and considered in a math classroom.
• When real world examples from word problems are unfamiliar or outside students’ experience, students are unlikely to use the knowledge and strategies they already use in their own lives.
• Understanding the words in a math problem can be a challenge for adult students, including English language learners. Many math words are also everyday words, but have a different meaning in math. Examples include mean, odd, even, table, etc. The additional meanings in math create additional challenges for students.
• Students often use numbers in word problems randomly, without a clear rationale for the operations they use.
• When students have an opportunity to discuss, or even better, explain a problem, they do better on questions related to the problem.

The article inspired me to compile a few teaching strategies we have been using that are in line with the research from the article. (To read Lynda’s article, look for the PDF above.)

Numberless Word Problems

To create a numberless word problem, remove the numbers from a word problem. Allow time for discussion with students. Then, give students the original problem with numbers. Does it help them think about relationships and model the problem mathematically without jumping in and randomly adding, subtracting, multiplying, and dividing?

This is a normal word problem:

Ivan has 8 quarters and 3 dimes in his pocket. Gaby only has quarters. Gaby has 4 more quarters than Ivan. Who has more money?

This is a numberless word problem:

Ivan has quarters and dimes in his pocket. Gaby only has quarters. Gaby has more quarters than Ivan.

Discussion around numberless word problems can be prompted by questions such as:

• What is going on in the problem?
• What can you picture in your mind?
• What do we know about the quantities and relationships in the problem even though there are no numbers?
• What is the question asking us to find out?
• What do you know about the answer?
• Can there be more than one answer?
• How do you know?

(Questions compiled from Ginsberg’s article and the web site, https://numberlesswp.com)

Remove the Question

This simple strategy prevents students from leaping into calculations without thinking carefully about the situation. Simply remove the question from the word problem and replace the question with What do you notice? and What do you wonder?

Original word problem:

The actual distance between Springfield and Martinsville is 54 miles. On a map,
Springfield and Martinsville are 3 centimeters apart. On the map, Martinsville and
Quincy are 12 centimeters apart. What is the actual distance between Martinsville
and Quincy?

Remove the question:

The actual distance between Springfield and Martinsville is 54 miles. On a map,
Springfield and Martinsville are 3 centimeters apart. On the map, Martinsville and
Quincy are 12 centimeters apart.

What do you notice? What do you wonder?

There are a number of benefits of removing the question on a word problem like this. The discussion might allow for conversation on the following issues:

• It’s a confusing situation. Miles and centimeters? Two different measurement systems. How many students are comfortable in both?
• It would be helpful to visualize the situation before calculating. About how far is 54 miles? About how far is 3 centimeters?
• And students can bring up other background knowledge and questions…

Students should brainstorm possible questions. Some possibilities:

• Which two cities are farther away?
• How far is Springfield from Quincy?
• How many inches apart are Springfield and Martinsville?
• How many miles are in each centimeter?

You might ask, “What question could be asked with this word problem if it were a test?” to see if you get some more possibilities. When it feels like everyone fully understands the situation, you can reveal the original question.

As a follow-up, students might want to answer some of the other questions they came up with.

Will This Be on the Test? – Test Practice Questions and Test Talks

Written by Sarah Lonberg-Lew, Will This Be on the Test? introduces an instructional routine called a Test Talk. Test Talks will help you create and nurture a classroom culture that values flexible thinking and conceptual understanding and that explicitly prepares students to apply their learning in the context of standardized tests. The bulk of this packet is examples of test-like questions that can be used with this routine. There are 22 separate test-like questions, which explanations of multiple strategies included.

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What strategies do you use to help students use their background knowledge and problem-solving skills when approaching word problems?