Numberless Word Problems (NWP) are contextualized story problems that help children develop math knowledge. By emphasizing children’s sense-making experiences, NWPs help children understand and apply math strategies and operations, while they support shared classroom experiences grounded in exploration, creativity, and collaboration.

Different from traditionally used word problems, quantities are initially omitted from NWPs. Instead of specifying how many of anything is being considered, numbers are revealed gradually in ways that help children make sense of the context of the problem and explore potential scenarios, approaches, and outcomes. For example, a common word problem might state Damon was playing with three dolls. His friend, Kai, had two more dolls than Damon. How many dolls do they have altogether? An NWP version of this problem might start with, Damon was playing with some dolls. His friend, Kai, had a few more dolls than Damon. The problem will unfold as children and educators engage in conversation and exploration, with the numbers and a specific math problem to be solved eventually revealed.

Why remove the numbers?

Research has shown that when students are presented a word problem, they often demonstrate a “compulsion to calculate.” What this means is that they ignore the context of the problem. Instead, they pluck out numbers and perform some kind of calculation with them. They might:

• add all the numbers together because that’s the easiest thing to do or think that’s what they’re supposed to do
• choose the operation that matches the one being studied in the current math unit, or
• base their decision on some “key word” in the problem that they associate with a specific operation.

You may be asking, if there are no numbers, then what do students do? Removing the numbers from word problems allows educators to invite students into rich conversations: They might ask learners:

• 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 problem asking us to find out?

Consider the earlier NWP: Damon was playing with some dolls. His friend, Kai, had a few more dolls than Damon. Here’s what learners can uncover through conversation:

• There are two friends, Damon and Kai.
• Each friend has some dolls.
• Kai has more dolls than Damon.

After bringing these ideas to the surface, students are set up for greater success they make sense of quantities and relationships. Then, as a group, they can talk about questions that might be interesting to solve or what they want to know about the situation. After engaging in such conversations and developing a better understanding of the context of the problem, the pre-posed question, including the numbers, can be revealed.

In our example, the NWP might now look like, Damon was playing with some dolls. His friend, Kai, had a few more dolls than Damon. How many dolls do they have altogether? In this example, there is now a specific goal: We need to find out the total number of dolls the two friends have. The teacher can supply the numbers as a next step, choosing quantities that will be helpful for her students’ learning.

NWPs offer opportunities for fundamentally changing the way learners engage with word problems — shifting the focus from simply solving to understanding the problem.

When engaging with NWPs frequently, learners begin to see similarities among problems. For example, they may notice that stories where items are being joined or combined can be solved by addition while with situations where amounts are separated, or we need to find the difference between amounts we can use subtraction. These are important insights students need to develop to better represent real life in mathematical ways.

NWPs from a racial justice perspective

We see several ways that NWPs and pedagogical practices that accompany them can promote racial justice values and practices including:

• The humanization of math teaching and learning: Honoring and making space for children’ agency, voices, and multiple ways modalities knowing as well as centering cognitively demanding and joyful learning, are humanizing teaching practices that support the developing of positive and robust mathematics identities.
• Windows and mirrors: NWPs are great opportunities to provide ways for children to see themselves, their families, and their cultural practices in math. They also allow for students to engage with cultural traditions and ways of being in the world that differ from their own. As a tool for windows and mirrors, NWPs support the development of classrooms where (i) funds of knowledge of children and their families are centered, (ii) children are seen as mathematics experts, and (iii) racist stereotypes are disrupted.
• Social justice focus: We believe that children should engage in critical conversations about social injustice and explore ways to disrupt them. NWPs allow space for engaging in these conversations and helping children understand how mathematics might be an important tool to understand social issues and promote justice.

1. Givvin, K. B., Moroz, V., Loftus, W., & Stigler, J. W. (2019). Removing opportunities to calculate improves students’ performance on subsequent word problems. Cognitive Research: Principles and Implications, 4, 24. https://doi.org/10.1186/s41235-019-0175-2; Stacey, K., & MacGregor, M. (1999). Learning the algebraic method of solving problems. The Journal of Mathematical Behavior, 18(2), 149-167.