When Will I Ever Have to Use This?

At some point, nearly every mathematics teacher hears the question: “When will I ever have to use this?” It can be tempting to hear the question as a challenge – or even a dismissal of the mathematics being taught. But it is a question worth taking seriously. When students wonder where mathematics shows up beyond the classroom, they are asking about its relevance, usefulness, and connection to their lives. And helping students build those connections is an important part of helping them become mathematically proficient.

Seeking opportunities to connect mathematics to students’ lives can support their engagement in learning, help them build a positive perception of mathematics’ utility, and prepare them to recognize situations in which mathematics can help them solve problems. And these aren’t just nice-to-have features of a math class; they are part of what it means to develop mathematical proficiency.

According to the National Research Council¹, mathematical proficiency consists of five interwoven strands:

• Conceptual Understanding: Comprehension of mathematical concepts, operations, and relations

• Procedural Fluency: Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

• Strategic Competence: Ability to formulate, represent, and solve mathematical problems

• Adaptive Reasoning: Capacity for logical thought, reflection, explanation, and justification

• Productive Disposition: Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

All five strands must be developed together to support a robust and meaningful understanding of mathematics. That means that helping students build a productive disposition—including seeing mathematics as sensible, useful, and worthwhile—is a necessary part of our work as mathematics educators.

So, we should encourage students to ask how the mathematics they are learning might be useful.

But let’s face it—sometimes answering that question can feel like a stretch.

It may be easy to point to the importance of fractions when baking or angle measures when building, but the everyday applications of other foundational mathematical topics are not always so obvious. For these topics, helping students see the usefulness of what they are learning can feel like a heavy lift. Perhaps, then, we need to broaden what we mean when we talk about how we “use” mathematics in our daily lives.

Looking Beyond the Content

Expectations described in standards documents make it clear that learning mathematics is not just about acquiring mathematical content. It is also about developing the mathematical habits of mind students build as they engage with the content.

The Common Core State Standards for Mathematics, for example, identify eight Standards for Mathematical Practice (shown below). Many states have adopted their own, similar sets of mathematical processes, practices, or proficiencies as important outcomes of mathematics instruction.

• MP.1 Make sense of problems and persevere in solving them.

• MP.2 Reason abstractly and quantitatively.

• MP.3 Construct viable arguments and critique the reasoning of others.

• MP.4 Model with mathematics.

• MP.5 Use appropriate tools strategically.

• MP.6 Attend to precision.

• MP.7 Look for and make use of structure.

• MP.8 Look for and express regularity in repeated reasoning.

Instructional materials often try to build relevance by showing students how the particular mathematical concepts and skills they are learning can be applied in real life situations. However, some of the richest real world uses of mathematics are found in the thinking and reasoning skills that are developed through the mathematical content.

How are students learning to make sense of complex situations? To choose and use strategies? To recognize patterns and structure? To evaluate whether an answer is reasonable? To communicate and justify their thinking to others?

Students may not encounter every piece of mathematical content they learn in their everyday lives. But they will encounter situations that require them to make sense, reason, decide, problem solve, look for patterns, and communicate their thinking.

Sometimes the answer to “When will I ever use this?” lies not only in what mathematics students are learning, but in how they are learning to think mathematically.

A Careers Focus

One way to help students see the broader utility of mathematics is to examine how career professionals actually use math on the job.

These conversations can go beyond identifying the mathematical content a professional uses to exploring how they think and reason mathematically. After all, the value of mathematics in a career is not limited to knowing how to calculate, measure, or apply a particular formula—it lies in how a person applies reasoning to solve problems.

What problems do they have to make sense of? What information do they need to identify and interpret? How do they select an approach, evaluate whether a solution makes sense, or communicate their reasoning to others?

Students can examine these ways of thinking in the work of career professionals and recognize the Mathematical Practices not as skills reserved for the mathematics classroom, but as habits of thinking that have value in the real world.

In this career interview with an Economist, notice how he indicates that his job extends beyond simply using mathematical skills. He talks about using mathematics to tell stories, thinking critically about what money means, observing and collecting data in real life, and then using that data to tell a meaningful story. Mathematics in a career is not simply about knowing math content, it is about using mathematical thinking to make sense of the world and communicate that meaning to others.

Challenge your students to look for mathematics in the work and everyday lives of the people around them. But don’t stop at asking What math do they use? Encourage students to notice how people think mathematically, even when the mathematics itself isn’t obvious.

As students explore a career, watch a video, interview someone, or simply observe the world around them, invite them to consider:

• What mathematical content do you notice a professional using?

• How is the person thinking mathematically? Is the individual making sense of information, looking for patterns, choosing strategies, estimating, reasoning, or evaluating whether something makes sense?

• Where else might you use similar ways of thinking—even if the mathematical content is different?

The next time a student asks, “When will I ever have to use this?” consider helping them look beyond where they might use the math to how they might think mathematically.