Archive of ‘STEM education’ category

Four ways teachers can help students connect abstract ideas to the real world

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.

How can we prepare students to take academic risks?

Students model the directionality of RNA polymerase, to understand which strand of DNA is used as a template during transcription.

When it comes to student work, audience matters. My students simply care more when they know they’ll share their work with the school community or outside experts instead of just with their English teacher. They think more purposefully about what they say and how they say it. The extra effort and thoughtfulness show in the quality of their work, and education research bears out my anecdotal experience.

But authentic audiences also provoke fear and anxiety. What if my ideas are wrong? What if I seem stupid? These nagging questions keep students from taking risks in public. In her study of behavior in a girls-only middle school math class, Janice Streitmatter observes:

without taking academic risks, asking or answering questions in the classroom, a large part of students’ lives may be excluded from their conscious or subconscious deliberations during this period of identity.

Chase Mielke echoes this insight with a provocative question:

Imagine the growth potential if 100 percent of our students attempted to answer 100 percent of the questions we asked 100 percent of the time. But they don’t—at least not at the secondary level. There’s no physical danger in raising your hand in class, only social danger.

I remember well what that social danger felt like in high school – the knotted stomach and fluttering heart, the loud voice in my mind warning me what others might think. I stayed silent far too often.

Useful resources abound suggesting interventions to make classroom culture or assessments more supportive of risk-taking. But I was reminded last week when I sat in on my colleague Ashley Gam’s biology class that instructional delivery can make or break students’ willingness to share out their ideas.

Ms. Gam structured her lesson so that student thinking moved in stages from entirely private to increasingly public, first using individual writing, then small-group discussion, small whiteboard visualization, and finally, whole-class presentation with peer feedback. At every step, she moved through the classroom, peppering individual students with Socratic interrogation to refine and extend their thinking. Below, I look at each step and offer some thoughts about why this model is so effective at getting kids to take risks in class.

First, it always bears repeating that well-planned instructional delivery is purposeless without meaningful learning goals. Ms. Gam’s lesson forms part of an ambitious study of evolutionary history inspired by the quirky, award-winning book Your Inner Fish by vertebrate paleontologist Neil Shubin. By the end of the unit, kids will have produced a timeline tracing human biological adaptations back millions of years — and they might also come into class fully costumed as some of our evolutionary ancestors in a culminating exercise (can’t wait!).

Using trade texts instead of textbooks helps students see that what they’re learning is part of ongoing conversations by researchers and academics. By engaging this material, students are participating in the ongoing production of scientific knowledge.

Stage 1: Individual Writing

Class began with the outward appearances of a conventional high school biology class: students grouped at lab desks to record short responses to prepared questions. But as Ms. Gam walked around the classroom, I noticed that she used Socratic-style questioning to tailor this exercise to each student’s abilities. I tried to transcribe a representative exchange:

  • Ms. Gam: “In the nucleus, when MRNA is produced, what’s the process called?”
  • Student: “Transcription. But what’s the purpose?”
  • Ms. Gam: “What do you think?”
  • Student: “It’s just a copy.”
  • Ms. Gam: “Yes, it’s just a copy. Why do we need a copy?”

She continued prodding the student until it was clear the concept was fully understood. Ms. Gam’s parting words to the student were, “You already knew the answer.” That’s exactly how these exchanges felt: like each student was uncovering knowledge that was already hanging around somewhere in their mind, and Ms. Gam’s questions were just helping them call that knowledge up.

Perhaps best of all, Ms. Gam was visibly, genuinely excited as students happened upon new understanding.

Ms. Gam helps students construct their own knowledge in one-on-one conversations.

Stage 2: Work in Small Groups

Once she felt everyone had a working familiarity with the lesson’s key concepts, she directed kids to confer in small groups about their responses. She told them:

I’m going to assign you one of these questions to diagram and share with the class.

Ingeniously, though, she didn’t tell groups which question they’d be assigned. It seemed to me that this ensured two things: 1) students felt responsible for discussing and understanding each question, just in case; and 2) Ms. Gam was able to listen in on the group conversations and assign questions based on student ability.

Because everyone had received candid, immediate, and kind feedback from Ms. Gam already, kids were more willing to share their ideas with one another. It’s a small detail, but I was struck by how frequently students looked up from their papers at each other’s faces.

Students discuss their answers and use textual evidence to refine their ideas.

Stage 3: Small Whiteboard Visualization

Students work together to prepare their model on a dry erase board.

In his published work on the acquisition of expertise, Anders Ericsson argues that superstar athletes and musicians develop their skills by creating sound mental representations, or structures that help people encode information into their long-term memory. (Here is an interview in which he discusses potential pedagogical applications).

As Ms. Gam’s student groups discussed their answers, she handed them whiteboards and asked them to represent certain concepts visually. Their whiteboard work actively engaged students in the task of constructing mental representations for the lesson’s key concepts.

This is one of those times when tools matter. I’ve done variations of this activity with posters, graphic organizers, and post-it note parking lots. But by using a whiteboard, Ms. Gam minimizes student anxiety: mistakes can be erased effortlessly and completely, at any time. Knowing that, kids can put their ideas down with little risk at all.

The whiteboard makes student thinking even more public: it’s large enough for anyone walking by to see, and its size accommodates easy collaboration. By this point in the lesson, most of the students are confident enough in their understanding to make their ideas visible.

Groups were at various stages of the process by this point, and the classroom was a bustling and dynamic space. Some kids needed to go back to the text to rework their models; others were ready to share their work out with the class. (To the latter group, Ms. Gam suggested “If you want, take this opportunity to add to your notes in your notebook.”) Everyone was busy doing something.

The classroom was a bustling place, with students at various stages of the process.

Stage 4: Whole-Class Presentation and Workshop

Students respond to feedback on their models of key genetics concepts during a whole-class workshop.

Forty minutes into the hour-long period, Ms. Gam called the class together and asked the first group to present. She gave explicit instructions to the class to make sure everyone knew this was a workshop: everyone will be responsible for accurately constructing knowledge. She said:

The purpose of this is to review and make sure everyone’s on the same page. While you’re listening, make sure that what is being talked about is consistent with what your group identified. If there are any discrepancies between what you found and what the group is presenting, that’s your opportunity to ask questions to either help the group come to a better understanding, or to improve your own understanding.

As students shared their ideas, she’d prod the class: Do you guys agree with that? Did others have different ideas? The presenters made changes to their model in real-time.

Ultimately, Ms. Gam consistently pushed her students into an active role throughout the lesson, but she also started with lots of support and scaffolding to ensure kids felt comfortable trying. Her lesson plan methodically removed layers of support as students became ready.

Here are some ways I can imagine using this four-stage process in my English classroom:

  • For teaching vocabulary or literary terminology (students start with a list of words from a text or unit of study, work individually to research and understand their denotation, work together to extend their knowledge, and visualize one or more words on the whiteboard)
  • For studying poetry: same process, but groups are assigned stanzas
  • For analyzing text structures: how particular paragraph examples from genres are organized (I’ve seen a great visualization of the standard academic essay here, for example)

Looking forward to trying some of this!

To Feel Science in Your Bones

AP Physics students moved back and forth between theory and practice today in an exercise inspired by physics educator Eugenia Etkina, and I got distracted from Writing Lab by their awesomeness. After reading and discussing models for understanding force and circular motion, the students moved to the center of the school with a rope and some roller skates. One student stood in the middle, holding an end of the rope firmly. Mr. Romero, on skates, held the other end of the rope and directed a second student to push him at varying speeds. Kids took time experiencing both roles.

Toward the end of the exercise, Mr. Romero explained how the force toward the center causes circular motion. He reminded students:

When people hear this explanation, they hear “science science science” or the sound adults make on Charlie Brown. But the purpose of this exercise was so that you feel it in your bones. This is how the universe works.

Isn’t that the ultimate learning goal — to have such a personally meaningful experience with a concept that your understanding becomes lodged “in your bones”? What would instruction look like if we placed those kinds of experiences at the center of our planning?