Real math appears in grocery stores

This Tuesday was one of my best days with the students yet, but all of my joy came from the last fifteen minutes. We, the group leaders, wrapped up the day by sharing our STEM experiences, with the hopes that the students will internalize the fact that, if they enjoy STEM, they will belong and excel in the community. The activity started with the students asking us questions about our academic paths, and transitioned to us sharing each of our thoughts. Here is a sketch of what our exchange looked like — perhaps some parts are idealized, but this is how I remember it :)

Student: “Is the work hard?”

Me: “Yes, but keep in mind that everything worth doing is hard. There is a big difference between the work in the past, like when I was your age, and now. When I first started out, I struggled a lot with the material and problems, but I just kept doing it, even when I didn’t think I would be able to solve the problem. Now, I go into the problem knowing that it is going to be hard, but I have full confidence that I will solve it. And trust me… Nothing is better then the ah-ha moment when you solve a problem.”

I couldn’t let this opportunity pass us by, especially since her thoughts were not unique. Many students haven’t had the opportunity to develop their problem solving confidence. Even though they all have a problem solver itching to get out, they need to learn how to deal with their mental barriers, because those are never going to go away. After our little moment of glory, the kids ran out of questions pretty quickly, which made sense, given that they had little exposure to STEM fields. We switched gears to talk about our academic paths.

When I spoke about myself, I told them that, like them, I was not really as engaged with the material presented to me, especially in math class. “It felt like rote memorization,” I told them, “and if I goofed a detail, then the answer is completely wrong, even though I knew how to do it.” For most of your academic career, math is viewed ad right or wrong, but this puts too much emphasis on the end result (answer) and seems to ignore the process (path to answer). Many times, the process can be massaged into one that will yield a correct answer. The students seemed to agree with my observations. As a thought experiment, I decided to hypothesize the optimal grocery store design, and support my claims with reason, with the hope to convey math’s “gray area.”

Me: “Why do all grocery stores look the same? You enter, see the fruit, continue, get to the milk and cheese, and then finally get to the freezer section. Why doesn’t the freezer section ever come first?”

Student: “[long pause] Hmm, I guess I never really thought about that…”

Me: “It seems reasonable to me. Fresh produce expires way faster than frozen food does, so most grocery stores want to sell the produce to restock, which maintains a constant supply of fresh fruits and veggies. If frozen food were at the front of the store, people would fill up their carts too quickly in the beginning with frozen items, and then, later, once they get to the fresh produce, they wouldn’t grab as much because their carts are already more full. This means that the store doesn’t buy fresh produce as often, because people don’t buy as much of it anymore. Since stores don’t want to risk spoiling their fruits and veggies, most decide to put them at the front of the store.”

Student: “Oh! That makes sense! Plus, it’s healthier to buy fruits and veggies instead of that frozen fruit, so stores kind of force people to be healthier.”

Me: “That’s an interesting thought! I agree. When you enter a grocery store, produce just looks way nicer than a freezer aisle, so it makes the shopping experience more pleasant. As you can see, grocery stores must think about the shopper’s mindset. On a similar note, haven’t you also noticed that apples, oranges, onions, and other common fruits and veggies tend to be in a stand in the middle of the store (not against the wall)?”

Student: “Well I guess it just looks nicer, right? So you want the store to look nice?”

Me: “True, and I think there may be more to it than that. Since more people want to grab the prettiest apples and onions, as opposed to any lettuce and cucumbers, you want to put those in the middle to decrease traffic. There is less space for people along the wall than in the middle.”

Student: “Yeah, that makes sense! Also, most people look at a bunch of apples to pick the prettiest ones, so they take longer than someone who is just grabbing a head of lettuce or whatever.”

Me: “Exactly — that is a great point. A grocery store’s design should focus on trying to maximize the profits and customer experience, while minimizing traffic and spoiled food. Many mathematicians go through a similar process for other situations too, which we call math modeling. The grocery store design can be solved using graph theory, which also models many other parts of life, like predicting which Facebook posts will be trending. My point in all of this is that math is less right-and-wrong or plug-and-chug as most make it out to be.”

This discussion induced the longest silence I’ve ever heard from the students. They were engrossed. I wanted to talk about an example that was interesting and relevant to them. During the whole discussion, I never said the word math until the very end, because math is all about rigorous analysis and applying general problem solving frameworks. Most importantly, this thought experiment was meant to convey the fact that everything in life can be analyzed in an interesting way, even something as seemingly mundane as grocery stores. I’ve never formally solved this grocery problem, but this seemed like a problem that is solvable using network analysis (aka graph theory).

Now, I can only hope that, the next time they are in the grocery stores with their families, the students will bubble and share this narrative with their family. An even bigger hope is that, in the future, they will decide to analyze other things in quotidian life.