Technique 17: Stretch it - Academic ethos

Teach like a champion 3.0: 63 techniques that put students on the path to college - Lemov Doug 2021

Technique 17: Stretch it
Academic ethos

In the classrooms with the highest academic expectations, right answers aren't the end of the learning process; instead, they open the door to further challenge. “The reward for right answers will be harder questions,” is how music teacher John Burmeister describes it to his students, and over time Stretch It, the simple habit of responding this way—perhaps not every time but often enough—builds a powerful culture of self-confidence and curiosity.

What does this look like in practice? Let me start by showing you two classrooms where this happens. The first, the video Arielle Hoo: How Did You Know?, is a middle school math class. Even before Arielle starts questioning her students, you can sense the heightened level of expectations that have become part of Arielle's classroom culture. Her student, Sarah, explains how she knew a proposed solution to a system of equations would be false: “I knew by looking at the graph, because the two lines are parallel so they would never intersect, which shows there is no solution.” Without being asked, Sarah uses technical vocabulary, and offers a full explanation for her response in a cogent and precise sentence.

Arielle is probably fairly happy with Sarah's response. Proud of her even. But instead of saying simply, “Great work Sarah,” she responds: “How did you prove that algebraically? What method did you use?”

Arielle's response to Sarah's answer shows both cause—how does one get a classroom where students answer like Sarah—and effect—what do you do to push the learning even further when you start to get answers like this.

“I used elimination,” Sarah says. “After I eliminated the x and the y I saw that it ended up with 0 = 2, but that's not true, so that's a false statement.”

“Awesome,” says Arielle before moving on to a question about a pair of coincidental lines.

Jaheem volunteers to answer this one and again we hear complete thoughts with technical vocabulary rather than simple one-word answers.

“The way you can figure out how many solutions [the system of equations] has is by looking at the graph, and you'll find that it has infinite solutions,” Jaheem says.

Which is true. And which causes Arielle to ask, “How do you know?” She wants to challenge Jaheem but also make sure the right answer is not a lucky guess. She wants to understand how he approached the problem and ensure he (and other students) can repeat the process on other problems.

Moments later, noting a tiny slip-up Arielle asks, “By two?” This allows him to catch his own error. “You'd multiply it by four and you would get the same equation,” he clarifies.

“Talk about the result,” Arielle continues, subtly giving him the opportunity to connect what he's said to other pieces of knowledge and thus build schema (connected bodies of knowledge).

Jaheem keeps going: “The result will be 0 = 0, which is infinite solutions.”

“Great,” says Arielle, “because it's what kind of statement?”

“A true statement.”

“Nice job. Send Jaheem some love,” she says to the class. His classmates make a gesture of support to “shine” on him while she says with a bright smile, “I loved your explanation.” This puts a bow on the interaction but even without the praise, I suspect Jaheem knows he's done well and feels a growing, well-earned confidence. He's connected the ideas he's begun learning into something cohesive. It's a great example of what a cognitive scientist would call elaboration, which takes place during retrieval practice. Arielle prompts Jaheem to review his understanding of an idea, connecting pieces and straining slightly to describe it in a new context and with new words. This elaboration will build Jaheem's knowledge and long-term memory, along with his confidence.

You can see a similar process in the video Michael Towne: Red Dye, from Michael's Physics classroom. Gathered around two beakers of water, one heated and one at room temperature, Michael places drops of dye in each and gives students a brief opportunity to discuss observations with a partner. The basic observation he knows they'll make is that the dye spreads more quickly in the warmer water. “It's way faster,” you can hear one student observe. But Michael's focus is not just on a simple observation but rather a deeper understanding of what students are seeing—as becomes clear when his questioning begins.

“What do you notice happening here? Go ahead,” he says, Cold Calling one student.

“The dye disperses faster in the hotter water than it did in the cooler,” the student responds. As in Arielle's classroom, you can almost hear him anticipating Michael's expectations: he's careful to use technical vocabulary (disperses) and to be precise in noting that he is comparing the ’“faster” movement of the dye in the warmer bath than in the cooler water. A correct observation made in a scientific manner. But this correct answer has opened the door to a new challenge and Michael decides to Stretch It.

“OK, so what?” he responds.

The student pauses briefly, suddenly realizing he will now have to explain what's happening at a more substantive level. He's unsure at first but as he starts to articulate what's happening at a molecular level, he starts to gain confidence.

“The hotter the molecules get, the faster they move around in the beaker so if you put …”

Michael steps in briefly here:

“Which molecules?” he asks.

“The water molecules,” his student answers, but the challenge continues:

“Can you see any molecules?” Michael asks.

“No, but the dye movement shows how they're moving around,” the student pushes on.

Now Michael turns unprompted to another student—the Cold Call reminding everyone of the importance of listening to peers—and asks, “What's he talking about, Melanie?” subtly giving the first student credit for knowing something scientific after holding up under a challenging bout of inquiry.

You can see Melanie composing herself before she answers. It's going to be a challenge to put all of this into scientific terms but after steadying herself, she goes for it.

“He's talking about that, when you put another liquid substance in the water, that's … the atoms are moving faster, so in this case when it's hotter, the atoms are moving faster than the ones that are in the cold water.” Again we see the idea of elaboration at play here, retrieving an idea from long-term into working memory but also connecting it and expanding upon it. It's long-term knowledge formation.

“Tell me more,” Michael says turning to yet another student. The Cold Call here seems part of the fun. The message to students is We're being pushed to the limits. Treated like working scientists; everybody's in the game of imagining ourselves in that setting.

“Atomic theory says that everything's made up of matter and the atoms in it,” the next student answers as the video closes—a small scene from a classroom marked by constant questions. No answer taken for granted. Always searching for why. Being in this classroom is like being a real scientist, in other words, and it just may be the kind of place that makes young people decide to pursue further studies in science.

When you give students ways to apply their knowledge in new settings, think on their feet, and tackle harder questions, they usually like it, at times quite a lot. This kind of questioning keeps them engaged and sends the message that we, their teachers, believe deeply their intellectual capability. Stretch It shows young people what they can do. You can almost see that in Melanie's response. She wonders for a moment, braces herself —she's beyond her comfort zone—but then she carries on and finds that she is up to the task. To find you can, over and over in the face of challenge, is to come to believe in yourself.

It's not just that students learn more in classrooms like Michael's and Arielle's; it's that, if you asked them, these would be those classrooms where they felt important as learners, valued and respected as students, most capable as thinkers. They're the places where young people rise to the challenge and start to think: Yeah, I'm a math kid, or Yeah, science is my thing. Many times, by challenging students, we tell them more about what we think they are capable of than when we say, “I think you are smart. I think you are capable of science.” Kids want proof, and in these classes, they get it, seeing themselves succeeding in the face of real challenges.

What Arielle and Michael show us is that by treating correct answers as a step in the learning process, Stretch It can help students build long-term memory, expand and connect pieces of knowledge into cohesive schema, and build curiosity and confidence. The greater challenge brings about a cultural change.

Stretch It involves:

· Making a habit of asking follow-up questions in response to successful answers

· Asking a diversity of types of follow-up questions

· Building a culture around those interactions that causes students to embrace, and even welcome, the notion that learning is never done

Other Advantages of Stretch It

Stretch It can often also help you learn more about student thinking and ensure the reliability of correct answers. In Jaheem's case, for example, I read Arielle to be deliberately making sure he understood the initial answer he gave and why it was true, challenging him to accurately explain his correct response rather than accepting it at face value and moving to another student. This allows you to avoid false positives—moments when luck, coincidence, or partial mastery can lead you to believe that students have achieved a more complete understanding than they really have.

Further, in classes in which there isn't necessarily one “correct” answer—analyzing complex literature, for example, or formulating a hypothesis—Stretch It questions give students the opportunity to pursue their singular train of thought, supported by their teacher's authentic curiosity about their insights. Stretch It is an opportunity to demonstrate your interest in students' thinking (rather than simply accepting a student's response that aligns with your objective or exemplar) and thus create an academic culture in your class that values students' perspectives and thoughtful engagement with the content.

Stretch It can also help you solve one of the thorniest classroom challenges: differentiating instruction for students of different skill levels. Asking frequent, targeted, rigorous questions of students as they demonstrate mastery is a powerful and much simpler tool for differentiating than breaking students into different instructional groups. By tailoring questions to individual students, you can meet them where they are and push them in a way that's directly responsive to what they've shown they can already do.

Varying Your Questions

In the next section, I describe six different categories of Stretch It questions. My purpose in doing so is to help teachers provide a rich and diverse range of ways to extend student thinking. Although there's value in categories, it's also important not to get too hung up on them. The categories are merely tools to help you think about how to bring variety to the important task of challenging students in the moment of success.

Ask How or Why

The best test of whether students' answers are reliable—of whether they can get questions right consistently on a given topic—is whether they can explain how they arrived at the answer. Asking a student “why” can push them to explore their own thinking and go beyond a “simply” accurate answer into new depths of insight or nuance. In his sixth-grade English classroom at Brooke East Boston, Rue Ratray stretched a student in this way during a discussion of a pivotal moment in The Giver:

Teacher:

What can we infer about how Jonas's father feels about what he did?

Student:

He didn't give much thought into what he did to the baby and he acted fine with it.

Teacher:

Why?

Student:

He was talking to the baby like he talked to Gabriel.

Teacher:

Why?

Student:

On the last sentence, it says, “a shrimp” and he's acting like this always happens, and he's talking to the baby in a baby voice.

Ask for Another Way to Answer

Often there are multiple ways to answer a question. When students solve it one way, it's a great opportunity to make sure they can use all available methods. Arielle Hoo is essentially using this approach in her math class when she asks students to “solve algebraically” what they have understood from looking at a graph of the system of equations, and you can tell from Jaheem’s and other students' responses that they almost expect, having initially solved graphically, to be asked to solve via another method as a follow-up.

Alternatively, imagine a teacher is reviewing a short, written paragraph by a student about a scene in A Raisin in the Sun as she circulates around the classroom. The student has written:

Responding to Asagai, Beneatha says, “You didn't tell us what Alaiyo means … for all I know, you might be calling me Little Idiot or something.” This reveals her skepticism.

Her teacher might respond. “Nice choice of supporting evidence, now see if you quote Beneatha indirectly rather than directly.”

The student might then revise:

Beneatha reveals her skepticism by asking Asagai what Alaiyo means and suggesting, perhaps with a hint of cynicism, that it might mean “Little Idiot.”

The teacher, circulating around the class a few minutes later, might follow up with a further Stretch It: “Nice change. How do you think it changed the argument to quote the play indirectly rather than directly?”

Ask for a Better Word

Students often begin framing concepts in the simplest possible language. Offering them opportunities to use more specific words, as well as new words with which they are gaining familiarity, reinforces the crucial literacy goal of developing vocabulary. Pushing for the inclusion of vocabulary can also develop students' confidence in their thinking and support mastery of new words.

I mentioned regarding the video of Michael Towne's class that the first student to answer seemed to me to be anticipating Michael's follow-up question and deliberately using the most technical vocabulary he could. You could imagine a day previously where a student might have said, “The dye spreads faster in the warm water.” To which Michael might have said “Can you use a scientific term?” or “a term from our Knowledge Organizer,” or perhaps, “a more precise term for that idea.”

“The dye disperses.”

“Yes, thank you.”

Similarly you could imagine the day when a student said in Arielle's class: “The lines cross once.” And she said, “What's the technical term for that?” allowing the student to retrieve the term “intersect.” Students make a habit of using advanced vocabulary because teachers push them to. Once that becomes a habit they do it even when not promoted. They self-stretch.

This can also happen in nontechnical cases.

“How did Kika respond when she received the trophy?” a teacher might ask her students.

A student responding, “She smiled” would be correct, but the teacher might stretch her by asking: “Can you capture more of the feeling of her response in your word choice?” Or “Can you use one of our vocabulary words?”

Hopefully she'd then get a more powerful word, like “She beamed.”

If she got a response like “She smiled strongly” or “She had a broad smile on her face” the teacher might stretch again. “Yes, much better. Glory for you if you can capture ’a broad smile’ in a single precise word. Can you?”

Ask for Evidence

By asking students to describe evidence that supports their conclusion, you emphasize the process of building and supporting sound arguments. In the larger world and in college, where right answers are not so clear and the cohesiveness of an argument is what matters, this will prove invaluable practice. You also avoid reinforcing weaker subjective interpretations, a task that is often challenging for teachers. You don't have to label an argument as inadequate; instead ask for the proof and give the student an opportunity to reflect, refining her response and potentially revising herself.

You might ask students for evidence to support a student's assertion that Beneatha is struggling to express her identity in A Raisin in the Sun. Or for evidence of times when she seems more and less confident in what she believes. Or you might say, “Yes, I think that's true. But many people remark on the way she subtly changes in the course of the play. Can you find me some evidence to support or refute that reading?” Or perhaps, “Yes, I think that's true, but can you find me an example of how that struggle becomes more intense when her mother is present?”

Ask Students to Integrate a Related Skill or Additional Knowledge

In the real world, questions rarely isolate a skill precisely. To prepare students for that, try responding to mastery of one skill by asking students to integrate the skill with others recently mastered.

Teacher:

Who can use the word stride in a sentence?

Student:

“I stride down the street.”

Teacher:

Can you add some detail to show more about what stride means?

Student:

“I stride down the street to buy some candy at the store.”

Teacher:

Can you add an adjective to modify street?

Student:

“I stride down the wide street to buy some candy at the store.”

Teacher:

Good. Now, can you add a compound subject to your sentence?

Student:

“My brother and I stride down the wide street to buy some candy at the store.”

Teacher:

And can you put that in the past tense?

Student:

“My brother and I strode down the wide street to buy some candy at the store.”

For students to encode concepts in their long-term memory, they need to consolidate knowledge from multiple sources. Stretch It questions can help students practice this consolidation.

Teacher:

What might Bradbury be alluding to in this image?

Student:

Maybe a bomb that went off, destroying the whole town.

Teacher:

What do we know was happening in America at the time Bradbury was writing?

Student:

The United States ended World War II by dropping nuclear bombs on Hiroshima and Nagasaki.

Teacher:

So what might Bradbury be alluding to specifically?

Student:

This image might be an allusion to nuclear destruction, like what happened in Japan in 1945.

Ask Students to Apply the Same Skill in a New Setting

Once students have mastered a skill, consider asking them to apply it in a new or more challenging setting.

Teacher:

Which letters make up the digraph in the word “stop”?

Student:

“ST.”

Teacher:

Excellent. What word in this sentence contains a digraph? “Last, he jumped.”

Student:

“Last.”

Teacher:

And what is the digraph?

Student:

“ST.”

Prompting

For the most part, the six types of Stretch It I've presented are directive: They guide students to think further in a specific way about something they've shown mastery of. Questions like “Can you give me a better word?” or “Can you tell me why?” and “How would the answer be different if the exponent was a zero?” shape the way students think about their original answer, and that's part of their strength. There are times, however, when it's also valuable to be nondirective. Prompting is a form of Stretch It that is nondirective, and the teacher's intervention is kept to an absolute minimum. Saying “Tell me more” or “Can you develop that?” doesn't tell a student how to think, merely to think further. Nondirective prompts allow students to decide what they think is most important to talk about and help students develop intellectual independence.

Prompting is often beneficial because it minimizes the disruption to a student's thinking. “Say more” comes faster and with less disruption to a student's train of thought than does a specific question about the author's purpose. It's easier for a student to immediately pick it up and develop it, so student thought remains center stage. As the buzzing of our electronic devices constantly proves, even a few seconds' distraction is enough to break the spell of deep thinking. The absolute simplicity of prompting is critical, and many of the ways we see champion teachers prompting are about minimizing interruption and shifting the ratio toward student thinking. Prompting is also helpful for those moments when you just need to know more about what a student is thinking in order to know how to respond. A simple “tell us more” opens up the floor for them to expand on their idea without influencing the content, and gives you valuable data about what the student is able to understand independently and in what areas he or she may need additional support.

The most common type of prompting is the verbal variety, whereby a teacher vocally indicates that a student should continue developing a particular idea. Some typical examples include:

· “Say more.”

· “Keep going.”

· “Develop.”

As teachers make prompting a habit, they can begin to remove the verbal portion of the prompt and replace it with a nonverbal prompt, which yields the ultimate in minimal transaction cost. It's also the least directive type of Stretch It. Effective nonverbal prompts include:

· Making a rolling gesture with your hands, like the “traveling” signal in basketball

· A head nod and/or sounds of encouragement (“Mmm hmm”)

· Raised eyebrows or other distinctive facial gestures

One caveat to offer on nondirective prompts is that while they clearly offer students more autonomy, and that can certainly be a very good thing, people often assume that increased autonomy always leads to increased rigor. It's not necessarily true that prompting a student with “Say more” is more rigorous than asking, “How is Langston Hughes's vision of internalized anger different from that of another author we've read this semester?” In fact, the opposite is often true. The specificity of a good teacher's question is just as likely, if not more so, to result in rigorous thinking as a student's merely adding whatever was on her mind. (It may be helpful to state the obvious here that, of course, teachers will likely be more ready to respond with this kind of directive prompting if they've planned out the target response they are looking for, as discussed in technique 1, Exemplar Planning.) Answers that are left open to chance are, well, open to chance, which can mean high-or low-quality answers, answers that are relevant and useful for classmates to reflect on, and answers that are meandering or derail the class's progress toward an understanding.

Given the trade-offs between directive and nondirective forms of Stretch It, the best approach is probably to seek balance, in two ways: by using both directive and nondirective prompts or by combining the aspects of both approaches in semi-directive prompts. To do that, a teacher might use the “Say more” prompt, for example, but direct it to a specific part of the answer that she thought was most worthy of follow-up.

Let's say I ask my students how Jonas is feeling during a section of The Giver where he is experiencing both horrible and pleasurable feelings for the first time. A student replies, “Jonas is confused and feeling scared. He never felt any of this before, and he feels isolated.” One solution would be to say, “Tell me more about his confusion” or “Tell me more about why he feels isolated.” Now I'm giving my student significant autonomy, but still helping her see where the most productive part of her observation might be. This would be a semidirective prompt.

***

As you're probably starting to recognize, you could put a variety of Stretch Its on a spectrum to reflect their degree of directness. Figure 4.1 arranges three different levels of prompting according to the degree of direction they offer.

It's important to see these possibilities as a spectrum, not a hierarchy. Sometimes the power of Stretch It lies in your capacity to shape the answer and steer students to the most important ideas and concepts. In other situations, the most important factor is a low transaction cost or a student's decision about what's worthy of further comment. There's a place for both directive and nondirective forms of Stretch It, and I suggest using all types. That said, where to strike the balance is a necessary question.

Part of finding that balance lies in recognizing the synergy between directive and nondirective versions of the technique. Asking lots of rigorous directive Stretch It questions is likely, over time, to teach students how to think more productively about developing their own answers. Then, when you stretch those students with less directive follow-ups, they're likely to do so, out of habit, in rigorous ways. This suggests that it may be worthwhile to invest time at the outset in directive questions, working in more nondirective prompts over time.

The type of question you're asking and the type of discussion you hope to have will also impact the balance of directive and nondirective versions of Stretch It you use in your classes. When you are eager for an array of answers—when exploring affective responses to a text, for example, or engaging in literary analysis that encompasses a range of plausible thinking—nondirective Stretch It prompts can yield a fascinating array of student thinking, perhaps even unearthing meaty insights you hadn't predicted. On the other hand, if there is a specific outcome you have planned for, the balance probably shifts in favor of more directive prompts. In short, you'll want to match the decision you make about the balance you strike among Stretch It prompts to your objective. If you want students to understand how isolated Jonas feels, be more directive. If you want students to reflect on how Lowry's language reflects his isolation (or identify moments in which they empathize with Jonas's feelings of isolation), be less directive.

Table represents Stretch It Prompts: Degree of Directedness.

Figure 4.1 Stretch It Prompts: Degree of Directedness

Stretch It Loves Objectives

Let's assume you asked a student to add three and five. After she correctly gave you an answer of eight, you decided to Stretch It a bit and reward correct work with harder questions. Here are a number of ways you might stretch her:

· “Good. What's 13 + 5?”

· “Good. What's 30 + 50?”

· “Good. What's 8 — 5?”

· “Good. What's 5 + 3?”

· “Good. What's 4 + 5?”

· “Good. Can you write me a story problem?”

· “Good. Can you show me how you know?”

These are all fine follow-ups to the original problem, but which one do you choose? With so many options for stretching even a very simple question, how do you keep your stretching from becoming scattershot and haphazard? How do you keep your lessons from stretching all over the map?

Your being aware of a variety of types of questions can help you push yourself to be broad and diverse in the ways you challenge your students; at the same time, some strategic focus can help you ensure that your use of Stretch It accomplishes important, objective-aligned goals in your classroom.

Regardless of the type of question, it's always useful to remember lesson objectives. Although it's good to do some “lateral” stretching (that is, into new areas), and it's good to do some reinforcement stretching (that is, to keep skills students have mastered alive by circling back to them for occasional practice), reserve most of your Stretch Its for questions that align most closely to your objectives for that day or your current unit. This will help you keep the technique focused and productive.