“Why do we have to learn this…?” Getting to the Root of One of Our Students’ Favorite Questions

If you’ve taught any core subject, and maybe even other subjects as well, you’ve likely heard this question at some point: “Why do we have to learn this?”

As a teacher, this question can make you feel a lot of ways. Maybe you’re frustrated because you just need to get through the content, or maybe you come up with a great example of how you used math in real life, but the question still plagues our profession.

I know when I was in school I wondered this from time to time, but I have to believe that in an age of information, where the value of education varies greatly across households, states, and cities, this question has to be more prevalent and in more need of a good answer today.

I was recently invited to a webinar on humanizing mathematics where this question, or how we respond to it, was asked of myself and the participants. There were some fantastic answers thrown out by the group. Data science gives us a space to explore real social issues and empower students to solve problems that are affecting us. Having this mathematical knowledge can open doors or allow you opportunities to solve questions that others around you may not be able to, pair this with anecdotes and we have some even more compelling stories.

Even though these are good answers, I found myself reflecting afterward and thinking, “Is this really enough? Are these the answers that will satisfy today’s students?”

I started thinking back to my time in the classroom. I spent 6 years teaching math in grades 6 through 8 and was asked this question on more than one occasion. In my early years, I would try to find real-world examples of how the content could be used, but later I started to think about things more broadly. I ended up landing on the idea of telling my students that if they couldn’t see the value in the content, find comfort in the fact that I’m teaching them how to learn something and apply that learning, which is a skill that stretches out far beyond school.

Again, I still think this is a good answer, but is it enough? Does it honor the nuance and beauty that comes with learning math or any of the other subjects? I don’t think it does.

As I’ve continued to reflect on the webinar and this question, I’ve had a new line of thinking that has come to the front of my mind. I think we can take that idea of learning skills and applying them and dig a little bit deeper and start to realize that each of our core subjects has something unique to offer us in a general sense.

In English, we learn about communication. We learn how to talk more intentionally through the examples of others. We learn how to describe ideas in ways that make more sense through literary devices like metaphor and personification. In History, we learn about people. We learn about what makes us tick, what we’ve done in the past to predict what we might do–or should avoid doing–in the future, what other ideas might exist out there, and how can I use that to better understand my own situation and the situation of the world. In Science, we dig deeper into our understanding of the world, learning about the phenomena that exist around us and all the amazing things that we come in contact with on a daily basis. And finally, with Math, we look at problem-solving. We analyze patterns, we pick up new skills, and then we look at problem situations and see how we can use these tools to find solutions.

I’d love to explore these ideas more in other content areas, but as an educator with a background in math, I feel like this is the space that I’m most qualified to talk more on. So let’s explore.

I want to start by looking at an example from a middle school math problem. The problem below is from Illustrative Math’s eighth-grade curriculum and comes from a lesson on the volume of a cone. In this lesson, students are working on deriving the equation that can be used to find the volume of a cone using what they know about the volume formula for cylinders, and then practicing the application of that formula…

A cone-shaped popcorn cup has a radius of 5 centimeters and a height of 9 centimeters. How many cubic centimeters of popcorn can the cup hold? Use 3.14 as an approximation for pi, and give a numerical answer.

Let’s think about an approach to this problem and ask ourselves a handful of questions first:

• What are we trying to solve for here? – The volume of a cone.
• What information is known? – We know the length of its radius, we know its height, and the problem has also told us that we’re using an approximation for pi.
• What skills/resources do I have? – We know the formula for finding the volume of a cone. If we want to dig a little deeper, we also know how to find the area of a circle, and we know how to do this math by hand, or maybe how to put it in a calculator using the tools that are available to us. I also might have some understanding of the commutative property of multiplication, which is going to make my calculations a little bit easier in this case because I would know that I can take 1/3 of 9, my height, and get an easy three, so I don’t have to worry about that pesky fraction.
• What do I need to learn? – Now, maybe I need to do this math by hand but I’m not confident in some of my fluency skills, or maybe I’m still not sure how that 1/3 in the formula works. This would be a point where I might consider asking for help from a classmate or touching base with the teacher again to clarify some of my misunderstandings.
• How can I use those skills/resources with the information I have to solve the problem? – This is where I make my plan and I say okay let’s take those numbers, put them in my formula, run my mathematics, get my volume of 235.5 cubic centimeters.

Okay, so as a math teacher, this is a fun little problem where I get to exercise some mental mathematics, come away with an answer to a problem, and feel good about my abilities. I also understand that this is a very real-world example that feels relevant for needing the volume of a cone. But again, as some of our students might say, why do I need to know this? I’m never going to calculate the volume of my popcorn container before eating it.

Fair point. In that sense, I can see how it’s a bit contrived.

So, if math is about problem-solving and practicing problem-solving, what would this look like with very little math at the forefront? Let’s take a situation that feels less contrived and is maybe more relatable to a lot of students.

According to data from weareapartments.org, there are 38.9 million apartment residents in the United States. Let’s say you’re one of these apartment residents and you’re looking to move because your lease is up. You can stay at your current apartment and pay the $300 a month increase, or you can find a new place to live. What are you going to do?

Let’s take the same approach to this problem that we did with our math problem:

• What are we trying to solve for here? – Do I stay in my current apartment, or find a new place to live?
• What information is known? – my lease is up, it’s going to cost me $300 extra a month to stay here.
• What skills/resources do I have? – I have internet access and could do some research on the market. I can do some quick calculations to find out how much more I’m paying a year at this place and get a sense of that information. I can also judge other relevant factors that may weigh on my decision like amenities or the cost/trouble of having to move.
• What do I need to learn? – what other options are available to me? What would make it worth it for me to move?
• How can I use those skills/resources with the information I have to solve the problem? – With all this information I can plug in what I know, cross-reference that with how I feel and assessments of other intangibles, and use that to make a decision that I feel good about.

Even though math isn’t at the forefront, the problem-solving approach that we’re practicing in our math class can still be applied, using a different set of variables and formulas that are related to the task at hand.

The fact that students and teachers, myself included, aren’t seeing and talking about this connection more feels like a “missing the forest for the trees moment”. Accounting historian and economist H. Thomas Johnson said, “Perhaps what you measure is what you get. More likely, what you measure is all you’ll get. What you don’t (or can’t) measure is lost.”

With standardized testing looming over us, it’s easy to focus and talk about the content, the fluency, the practice problems, but since measuring your ability to problem-solve is challenging, it gets lost in our line of sight and becomes something that I don’t think we talk about enough.

The math classroom is fertile ground for working on these problem-solving skills that are highly necessary in today’s world. Indeed, LinkedIn and many others have listed problem-solving as one of the top skills employers look for in candidates.

There are great curricula out there, like Illustrative Math, that provide opportunities for kids to solve problems and think about math in a way that promotes this type of skill growth. All we need to do is give them the chance to practice and help them see what’s really going on and how this beautiful subject, which has so many possibilities for creativity, joy, and wonder, can also set them up for success outside of school.