Sera (9th) is guided through the classroom by Evalynn (7th) to introduce the concept of the coordinate plane.

Students want to know that what they’re learning is relevant. As this Edutopia article points out:

Relevant, meaningful activities that both engage students emotionally and connect with what they already know are what help build neural connections and long-term memory storage (not to mention compelling classrooms).

But before kids can appreciate why a given skill or content area matters in the world, they first need to see what it looks and feels like in the world. They need to see the abstract take concrete shape.

Great teachers do this across the disciplines, giving their students direct sensory experience with what otherwise would be intangible. One of my earlier posts showed what this looks like in an AP Physics course: our science teacher David Romero used roller skates and a jump rope to help his students feel “in their bones” the way “the universe works.”

Here are four more examples from math, philosophy, science, and English at LSG.

1. Math

The concrete-repesentational-abstract instructional sequence is a “best practice” in math education for good reason: research shows the approach helps students develop their own mental representations of mathematical concepts.

In my colleague Rita Lahiri’s Algebra I course, students experienced the coordinate plane as a thing they could inhabit with their bodies.

Rita asked a student, Sera, to leave the room as the rest of the kids hid a piece of paper. When Sera returned, she had to close her eyes. Her classmate Evalynn guided her with directions: two steps forward, three steps to the right, etc. The other kids watched (and giggled), taking down their observations. After a few minutes, Sera found the paper – it was placed inside a textbook on one of the shelves.

The class repeated this experiment several times; kids eagerly volunteered to be the “finder” and the “guide.”

Once students got to see their peers move through the classroom toward a specific point, Rita gave them the chance to reflect on their experience by thinking and writing about two questions. She asked:

Each of you guided your person differently. Was one way more efficient than others?

Why is this relevant? Why are we doing this in class?

As the kids reflected, they made sense of the concept in light of their direct experience. In subsequent lessons, when her students encounter the coordinate plane as a pictorial representation, they will remember watching kids walk through space toward a fixed point.

The new, abstract concept will build on something they already had seen and understood.

2. Philosophy

The study of philosophy is often beautifully and infuriatingly abstract. What kinds of instructional approaches can make these ideas accessible and meaningful in students’ actual lives?

Here is a really cool article that wrestles with just that question. It’s about teaching philosophy to teens in Brazil’s favelas after the nationwide mandate that all secondary students learn philosophy. Check out this relevant excerpt:

But can philosophy really become part of ordinary life? Wasn’t Socrates executed for trying? Athenians didn’t thank him for guiding them to the examined life, but instead accused him of spreading moral corruption and atheism. Plato concurs: Socrates failed because most citizens just aren’t philosophers in his view. To make them question the beliefs and customs they were brought up in isn’t useful because they can’t replace them with examined ones. So Socrates ended up pushing them into nihilism. To build politics on a foundation of philosophy, Plato concludes, doesn’t mean turning all citizens into philosophers, but putting true philosophers in charge of the city—like parents in charge of children. I wonder, though, why Plato didn’t consider the alternative: If citizens had been trained in dialectic debate from early on—say, starting in high school—might they have reacted differently to Socrates? Perhaps the Brazilian experiment will tell.

Kevin Oliveau and I are co-teaching a course called “Philosophy Wars” this semester, giving students the chance to engage competing ideas about ethics, human nature, epistemology, and metaphysics. We want students to understand what it means to see the world through the lens of these various philosophies. We hope that the course helps us all develop the capacity to break out of our own particular, entrenched perspectives, finding ways to generously imagine alternate ways of seeing and being in the world.

One of the ways we encourage this is by conducting regular role-playing exercises during class. We pose a question: in the case of the video above, the question was, “Does material reality exist?” We require that students argue from the position of various philosophers rather than their own perspective. Sometimes, this means they draw an index card of their choice with the name of a philosopher, and respond in the way they think he or she would. In the video above, certain students were designated as “skeptics,” others as materialist George Berkeley, and still others as Renee Descartes.

This exercise in intellectual empathy is in the same vein as the “stakeholder wheel” approach to journalism education explained in The Elements of Journalism and the “Offend Yourself” challenge I tried with my students in 2015. These structured assignments force students outside themselves to explore the world from other vantage points.

The discussion took on a particularly concrete application right around minute 1:10 in the above video. Michael, who is supposed to be a skeptic, notices that his peer Enoch drinks mistakenly from his mug. As Michael argues against the existence of things outside ourselves, he calls out Enoch:

Michael: As a skeptic, almost like a Descartes type argument, you could say that – that’s my glass

Me: How do you know that’s your cup?

Kevin: Aha! What was the problem there? I sensed a problem. You put the cup down rather quickly, didn’t you? Why was that? You knew it was his cup!

Enoch: I did not!

The dispute about the mug revealed precisely the concrete stakes of what it would mean to sincerely doubt that things outside our mind exist in the real world. If Enoch truly entertained such metaphysical doubts, he’d have no problem drinking from Michael’s mug.

Since that exchange, the mug has become a shorthand for understanding concretely what it means to doubt. Role playing offers an engaging and memorable way to test the real-world implications of abstract ideas.

3. Science

Research typically focuses on moving gradually from concrete to abstract — for example, this piece describes evidence supporting the “concreteness fading” method in STEM instruction. But my colleague David Romero points out that in his physics courses, students study abstractions so that they can better understand and describe the physical world. In other words, sometimes the concrete is the target.

An activity in his middle school science class helped students observe and experience the concept of relative motion. (Check out the video above to see part of the lesson in action.)

David sets up three groups of students on wheelie chairs and designates the other students “pedestrians” meant to observe and record. He gives these instructions:

We can run through this once or twice, and if you have a question for one of these people, feel free to ask.

We’ll have time to talk about what we’re seeing.

Both David and Rita’s lessons reveal the crucial interaction between enactors and spectators: by asking some students to experience relative motion, for example, and others to observe it, David ensures that the class works collaboratively to piece together an understanding from different perspectives. The insights of those who sat on the chairs augment the observations of those who stood and recorded what they saw.

The comments of Aidan, an eighth grader and “pedestrian” during the activity, illustrate this well:

David: Pedestrians, you want to describe what happened, what you saw?

Aidan: I saw that there was two chairs, Matt and Nadia, floor, and then two chairs, Matt and Nadia, floor. So I saw chairs, Matt, and Nadia move this way.

David: Oh and you’re using the floor to compare.

Aidan: Yeah

David: Awesome.

In this case, students are moving from abstract to concrete: David had introduced the concept of relative motion in an earlier lesson; in this later activity, students were able to use key terms and definitions to describe what they saw in the physical world.

4. English 

High school students cut up Hemingway’s “The Short Happy Life of Francis Macomber” to piece together the story’s chronology.

My students are usually blown away when I explain to them that the “full story” – told in all its detail from beginning to end, with no narrative gaps – is a thing that does not exist outside their own minds.

But they think about it quietly for a bit and realize: of course it doesn’t. No story takes the reader through all the excruciating minutiae of human existence. Our narratives – whether written or oral, literary or gossip, and everything in between – contain pauses, omissions, flashbacks, flash-forward, and repetitions.

Time in narrative is complex. And temporality, as a literary concept, is also highly abstract.

Russian formalists have a complicated theoretical language that distinguishes, for example, between the order in which events are narrated (the sjuzhet) and the “actual” order of the story (the fabula – as in fable, or a thing that is not real).

Ernest Hemingway’s short story “The Short Happy Life of Francis Macomber” is useful for illustrating the nuances of narrative temporality. The story flashes back and forth to reveal the deep roots of the titular character’s unhappy marriage and the more recent catalyzing incident: Macomber’s seemingly unredeemable cowardice at the lion hunt.

To help students see the impact of nonlinear temporality on narrative, I ask them to cut Hemingway’s story into pieces.

I print out four copies of the story and ask groups of kids to physically separate each scene from the next: make a cut where the temporality shifts to flash backwards or forwards. Then, students rearrange them chronologically along a series of desks or cubes. As the photo illustrates, this is a get-out-of-your-seat-and-work-with-your-hands activity.

Students invariably come up with different ways to order events, revealing that part of what non-chronological structure does is to render the reader an active participant in the collaborative construction of meaning.

Like the activities in math, philosophy, and science, the act of cutting up Hemingway’s story helps students see what crucial abstract concepts look and feel like. This is an indispensable first step in making classroom content relevant and personally meaningful to all students.