Technique 15: No opt out - Academic ethos

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

Technique 15: No opt out
Academic ethos

Consider this moment from a recent lesson in Denarius Frazier's tenth-grade geometry class (video: Denarius Frazier: Quadrilateral). His students are about to attempt to prove that a given shape is not a square, but first Denarius pauses and asks the class, “Before we get into that, what is the definition of a square?” It's important that every student start with sound knowledge of the basics.

He calls on Aaron, who responds: “All four angles and all four sides are equal.” It's a solid answer, one that might suffice in another class, but Denarius says, “Hmm … that's about 80 percent of the way there. It can be a little more specific.” It's a bit of a Right Is Right moment (technique 16)—Denarius is holding out for all-the-way right rather than mostly right, even while acknowledging the value of Aaron's answer.

Next Denarius calls on Anastasia, who has raised her hand. She adds precision: “A quadrilateral with four 90-degree angles and four congruent sides.” At this point, with the fully correct answer having been shared, many teachers might simply move on and return to the proof. But Denarius has something else on his mind, and he instead returns to Aaron: “Back to you, Aaron. What was the difference?”

Aaron says, “I didn't add the quadrilateral.”

“The quadrilateral and …?” asks Denarius.

“And the degrees of the angle,” Aaron finishes.

“Yes, so it's, 90-degree angles and all four sides are congruent.” Denarius confirms before moving on to the proof: “How can we prove that this is not a square?”

Denarius's standard of correctness is high and that helps make his classroom a rigorous place. And his preparation is impeccable. But the heart of the interaction is something else subtle but powerful called No Opt Out, which is the name for the moment when he returns to Aaron, whose initial answer was not correct.

When a student does not answer correctly, teachers often call on another student or provide the correct answer themselves. But the class hearing the right answer is different from the original student understanding it and being accountable, with caring and humanity, for expressing that understanding.

When Denarius returns to him, Aaron explains the difference between his own answer and Anastasia's. The “return” closes the loop and ensures understanding.

There are a variety of ways to return productively in a No Opt Out. For example, Denarius could have asked Anastasia not to answer herself but to provide a cue (a focused and productive hint) to Aaron and then returned to him for the answer. Or he could have asked Anastasia for the correct answer but, in returning to Aaron, had him begin by repeating Anastasia's answer in an effort to encode it in long-term memory. Or he could have shared a gold standard definition of a square himself and then returned to Aaron to ask for the gap between the original answer and the model. He could have asked Aaron to both repeat Anastasia's answer and explain the gap between his own and hers. If it had been a problem such as What's the measure of the angle here?, he could have given Aaron another example to try and succeed on, upon returning to him. I'll discuss these variations later, but the core idea is that when a sequence beginning with a student unable or (as we will discuss) unwilling to answer ends with a return in which the student answers successfully the result is progress toward mastery—and a culture that promotes learning.

For now, though, it's most important to focus on Denarius's tone. He's emotionally constant, signaling steady support with his voice and body language: In this class, we get things wrong and then get them right and we keep moving. That's normal. You're doing fine. A teacher executing a No Opt Out should avoid indicating frustration at the original response but also, in most cases, go easy on the “awesome awesomeness”—that is, in praising a student's small success so highly that the teacher seems either disingenuous or surprised by the student's success (OMG, you got it right!).

In this example, Denarius chooses his words wisely in other ways as well. “About 80 percent of the way there,” he says, which both diffuses any anxiety for Aaron—after all, he's mostly right—and also cues him to attend carefully to Anastasia's response because there's a fair chance that Denarius is coming back to him to close the loop. In some cases—for example, earlier in the year before students have come to understand that Denarius commenting on the almost-ness of the answer is a signal that he is probably going to coming back to with a question—Denarius might be more explicit: “Not quite. Listen to the next answer and I'll come back to you.”

It's worth noting that teachers often promise students they “will come back” to a student when they struggle publicly but, barring their use of No Opt Out, often forget to do so. I suspect this is because (a) our working memory is always taxed when we are teaching, so the longer the amount of elapsed time, the harder it is to remember that a student got it wrong or what she got wrong, or (b) we intend to go back but can't exactly imagine what that would look like, so mostly we are announcing our intent. I am concerned that you struggled and know I should address it. I should not leave this as is. If we don't have a technique for putting that intent into practice, we're likely to insert a bookmark that we never return to.

One of the benefits of No Opt Out is that it gives you a model—or a series of models—for how to go back to a student and quickly so you don't lose sight of the moment. This is not to say that you should use the tool reflexively—not every erroneous response needs to trigger a No Opt Out. A thousand good things exist in balance and compete for time and focus in a classroom. There's plenty of discretion to be had in when, how often, and what type, but the idea is powerful—returning to a student who hasn't gotten an answer correct and allowing, encouraging, sometimes prompting them to answer again ensures that students rehearse success rather being left dangling when they don't succeed. Done well it often goes a step further, affording a student who's struggled an opportunity to “get it right” in front of peers. It can also be an effective response to learned helplessness—the awkward moments when a student simply won't try. But we will come to all of that.

For now, let's watch a second example from one of Denarius's classes. In Denarius Frazier: Cosine, ninth-grade students are solving algebraic equations during guided practice. “Two cosine theta equals the square root of 2,” Denarius says, explaining the next step to students.

“Wrap this problem up … Shayna,” Denarius says. He's going back and forth between modeling steps himself and allowing students to solve parts of the problem, using what Barak Rosenshine would define as guided student practice and others might call the “we” stage in an overall lesson arc of I do/we do/you do. The class's pace is quick and efficient—the Cold Calls are predictable—and Shayna hasn't raised her hand but she also doesn't seem the least bit surprised to be called on. And the tone is supportive.

“Divide [by] two on both sides,” Shayna advises.

“And we're left with what?” Denarius asks. Shayna responds and Denarius sends the class into a Turn and Talk (see technique 43) to solve the problem in pairs (“Turn and talk to your partner; I want an answer for theta in thirty seconds”).

Out of the Turn and Talk, Denarius Cold Calls Deandrea and she's ready with the answer: “Forty-five degrees.” Other students snap to show they agree.

But Denarius wants to test for reliability, to make sure students understand the process Deandrea used to solve. “What do we have to do to get that forty-five degrees? Michael?” It's a Cold Call—crucial in checking for understanding, as Denarius is doing here. And it's a good thing he asked because, despite snapping along in support of his classmate, Michael is a bit unclear. “Um … reverse?” he says, before trying again, “Oh, I'm sorry … secant?”

Michael is confused and, rather than waiting for further guesses, Denarius steps in. “We're coming back to you,” he says, warmly and without judgment, before calling on Kayla, who begins: “We have to do the inverse of cosine …” Moments later Denarius returns to Michael: “Why do we have to do the inverse of cosine, Michael?” Whereupon Michael explains the importance of solving algebraically.

Denarius’s tone is supportive throughout, but he also signals normalcy. Of course some students were momentarily confused. Of course Michael got it right in the end. “Go ahead and flip to your Exit Ticket. You have three minutes,” he says.

Before his “return” to Michael, Denarius uses that phrase, “We’ll come back to you” here. The powerful thing is that with a clear procedure or recipe to follow that outlines his reaction—a technique he'd made familiar almost to the point of automaticity—he actually does return to Michael and helps him progress in his understanding.

Theme and Variation

No Opt Out, as I mentioned, comes in various forms and it's worth comparing the two examples from Denarius's classroom to begin considering both themes and variations.

In both cases, going back to the student who was initially incorrect (or partially correct) provides them the opportunity to improve or clarify their original answer. It also gives another student in the room the opportunity to provide an “assist.” Allowing students to help their peers in a positive and public way builds community and culture—or, more precisely, if you've established an intentional culture where teamwork thrives, and students support one another, then No Opt Out enhances that culture richly and lets students help their peers via their academic accomplishment.

In both cases, tone matters: Denarius is consistent, clear, and steady. Culture of Error (technique 12) thrives: Mistakes are useful learning tools. When confusion emerges, the class works through it. There's no blaming of the learner but also not a profusion of “awesome awesomeness.” In most cases a sprinkle of subdued positivity suffices (“Well done, Aaron” or “Now you've got it, Michael”). There will be occasions when celebration is warranted; it will sing more if it is reserved mostly for those moments.1

A subtle difference between these two clips also highlights the flexibility in the technique. Michael is confused; Aaron's response was strong and very close to gold standard, so Denarius “previews” for Michael—that is, he lets him know explicitly that he'll be coming back to him. This makes the process transparent and reminds Michael to listen carefully to Kayla's response.

The setting is also worth noting in the two clips. The first happens during a brief interval of retrieval practice. The second comes at the end of guided practice and right before students solve on their own. Both of these moments of transition are critical from a Check for Understanding perspective when you would especially want to ensure student knowledge. You can't always use No Opt Out but Denarius has chosen his timing strategically.

The second example also might have offered Denarius the alternative of using a cue if he'd wanted to. That is, instead of asking Kayla for the answer he could have first previewed—“OK, Michael, let's get you some help. I'm going to come back to you”—and then asked, “Without giving Michael the answer, who can tell him one word that will help him here?” Let's say that here Kayla raises her hand and replies, “Inverse. He has to use the inverse of something.” He can see now in Michael's face that this has been enough and returns to him: “Ready now, Michael?”

“Yes. We need to take the inverse of cosine and then …”

We've come across three terms that are helpful in using to the technique so far. The return is the part of the No Opt Out when you go back to a student who initially struggled to answer fully. A preview is when you tell that student explicitly that you are coming back to them to encourage them to listen carefully to peers, as in: “OK, listen carefully and I'll come back to you.” You don't have to use a preview, but it can be helpful in establishing familiarity with and transparency in the process for students. Just make sure to remember to return to a student when you've said you will! Finally there's the cue. That's the idea that you can sometimes ask additional students you call on to provide key information that the initial student can use to answer after the return rather than the complete answer. This allows the initial student to do more of the work (and show that he or she can do more of the work). Note that, as I discuss below, a cue is different from a hint because the teacher guides the student to give especially useful information.

On Cues, Hints, and Questions

If I ask James to identify the subject of the sentence “My mother wasn't happy” and he can't answer, I might say: “Can anyone give James a hint to help him find the subject?” and a helpful student might offer, “It starts with the letter m.” This would help James guess the answer, but it wouldn't teach him anything that would help him in future situations.

I use the word cue in place of hint then to refer to a prompt that offers additional information that is useful in building understanding.

Five types of cues are particularly useful in a No Opt Out. Here are some examples and the answers they might yield. You'll likely find even better ways to cue students in your own subject and grade.

1. The place where the answer can be found

“Who can tell Julia where she could find the answer?” [It's in the diagram at the top of page 3.]

2. The next step in the process that's required at the moment

“Who can tell Justine what the next thing she should do is?” [Justine, try to distribute first.]

3. Another name for a difficult term

“Who can tell Kevin what distribute means?” [Kevin, when you distribute you multiply the outside term by each term inside the parentheses.]

4. An identification of the mistake

“Who can explain what Roberto might have done wrong here?” [He might have dropped a negative sign when he distributed.]

5. A word that might be useful

“Who can tell Michael a word that might be useful to him in solving?” [Michael, the word distribute is really important here.]

An alternative to cuing is to allow students to ask questions as part of a No Opt Out. I got this idea from Michael Towne, one of the winners of the 2014 Fishman Prize, a national award given to top teachers in the country. “If I ask them, ’What's the speed of the magnetic flux here?’” Michael told me, “I want them to be able to say, ’I'm actually not that clear on what you mean by magnetic flux.’” To Michael that's a sign of maturity, so he explains to students that they always have this option and encourages them to use it. But the sequence still ends with a No Opt Out: “OK, now that we've clarified what magnetic flux is, what's its speed here?”

You can see a really engaging example of cuing in the video Derek Pollak: Fifth Root, shot at North Star Academy High School in Newark, New Jersey. Notice Derek's warm and encouraging demeanor as both he and then a peer provide cues to a student solving a problem during retrieval practice.

I mentioned previously that there were variations to the No Opt Out technique. I'm going to map them out a bit more now.

Options for What Happens Before the Return

Go to another student and ask for the answer. Return.

“Not quite. Who can tell us the definition of juxtaposition?”

Go to another student and ask for a cue. Return.

“Not quite. Who can give Kayla an example of juxtaposition? And then, Kayla, I'll ask you to tell us the definition.”

Give a cue yourself. Return.

“Not quite. Kayla, what if I told you that juxtaposition always involved two characters, images, or things. That help?”

If it didn't help, you might go to another student for the answer—“OK, who can give us a definition of juxtaposition?”—and then return yet again to Kayla after: “Great, now, Kayla, you tell me.” The last step might seem unnecessary, but it does several key things. It ensures that Kayla listens to the answer. By causing her to repeat it, it helps her to encode it in long-term memory, and it reduces the chances that Kayla might use “I don't know” on purpose to avoid having to answer. I'll return to this idea later.

Give a gold standard answer. Return with “Try to tell me that back.”

“Not quite. I'll give you what I think is the ideal definition of juxtaposition, then you try to tell me back. Juxtaposition is when an author places two unlike objects or characters in close proximity within the text to emphasize their contrast. See if you can tell me back?”

This is the least common form of No Opt Out (I'll discuss at least one application later), but if you do use it be sure to follow it with a Stretch It (technique 17) to give the student the chance to show that they can do more than repeat. As in, “Good. Now that you've got the definition, can you think of an example from the play?” Or, “Good, now that you've got the definition, who is Callie being juxtaposed with in the novel?” Or, to use a different example:

“Jasmine, an inverse is what I multiply a number by to get a product of 1. What's an inverse?

“What you multiply a number by to get the product 1.”

“Good, so what would I multiply one-half by to get 1?”

“Two.”

“Good, and what's the inverse of one-half?”

“Two.”

“Yeah, and what's the inverse of two?”

“One-half.”

“Beautiful. Now you've got it.”

Options for What You Ask a Student to Do After the Return

The point of No Opt Out is to cause the original student to give the correct answer and successfully solve the problem or encode the information. After that you can add other steps that increase the value of the interaction.

Explain why the answer is the answer.

Ask the original student to explain or analyze the answer in some way. Denarius uses this in the second example. “Why do we have to take the inverse of cosine, Michael?”

Explain the difference between original and final answers.

Denarius uses this in the first example: “Back to you, Aaron. What's the difference?” Aaron has to note what he left out.

Apply the idea or complete a similar example.

“Good, now that you've got the definition, Kayla, who was the author juxtaposing Martina to in the opening scene?”

Or perhaps:

“What's eight times six? Justin?”

“Fifty-six.”

“Hmm. Listen carefully to Danielle because the eights are tricky. Danielle, what's eight times six?”

“Forty-eight.”

“What's eight times six, Justin?”

“Forty-eight.”

“Good. What about eight times seven?”

“Um … fifty-six.”

“And eight times eight?”

“Sixty-four.”

“Good. And eight times six once more?”

“Forty-eight.”

“Well done.”

Some Combination of the Above

Once a student gives you a correct answer, you may want let them use it or apply it in a variety of ways. Balancing the needs of time is always a challenge. There's only so much time you can spend doing No Opt Out, so you won't be able to do it with every wrong answer. But often it's surprising and unexpected to a student to have a teacher cause them to succeed on a question when they first appeared to struggle, so occasional opportunities to let a student shine a bit after the return can be powerful.

Aidan Thomas Sticks with It

You can see another example of No Opt Out in the video Aidan Thomas: Y Intercept. The clip starts with Aidan calling on Jahiem to plot a point on the graph of a line. He's asking for the y-intercept, in other words the point (0, X). It looks as if Aidan thinks this question will yield a quick and easy right answer, but Jahiem answers that it's the origin. “No,” Aidan chimes in. “That’s the trick. Not anymore.” His language is masterful here in normalizing the error and making Jahiem feel supported. Jahiem learns that what he thought was the answer (the same answer to a recent problem) was in fact “a trick.” This suggests that a common and natural mistake has been made.

He refers the question to Shawn, who answers that the y value is —1 and Aidan quickly makes his return: “Yeah, why is it —1, Jahiem?” The return shows faith in Jahiem. By asking him to explain Shawn's answer, he's arguably giving him the harder question. My reading of it is that Aidan thinks he'll get it right and have a chance to shine.

Unexpectedly, Jahiem struggles a bit, but with a bit of prompting, fixes his mistake. Aidan's response—“Nice self-correction,” he says, in a steady constant tone—is another bit of culture building. It reinforces the idea that making a mistake and catching it is normal and natural and lets Aidan give Jahiem credit for doing something well: spotting and fixing a mistake. Note that he doesn't overdo the positive reinforcement.

But the data also tells him Jahiem is confused, so eight minutes later, he Cold Calls to ask a question that again causes Jahiem to find the y-intercept. “What's the point on this graph that we know … [pause for everyone to think] … Jahiem?”

Again we see Aidan's mastery of creating an environment characterized by a supportive tone but that also ensures that Jahiem is caused to get lots and lots of practice at something he hasn't yet mastered. “You're just using the wrong language,” he says when Jahiem struggles. There's no judgment or frustration in his tone. If anything, he's reminding Jahiem that he's closer than he thinks, but he avoids the temptation to gloss over his mistake (e.g. “You meant to say ’y-intercept,’ right?”) and instead causes Jahiem to use the correct term.

Still Jahiem guesses wrong. Aidan goes to Tavon for the answer (0,2), and then returns again with a Cold Call, informed by the previous question Jahiem could not answer. It's still part of the No Opt Out in my mind—“That's called the what, Jahiem?” Jahiem's a little flummoxed, but once DJ gives Aidan the correct answer, he circles back to Jahiem and another student, CD, to make sure they lock in the term and, incidentally, hear themselves getting it right.

Throughout this sequence of events Aidan's tone remains warm and supportive. His positivity and equanimity show students that this No Opt Out is an expression of caring from an adult who seeks to ensure that they solidify their knowledge and help them succeed.

One thing you've probably noticed about the classrooms in which we've studied No Opt Out is the larger culture. Denarius has clearly established a climate of trust with his students. In both cases his students give full effort on the initial question and on the return. In Aidan Thomas’s and Derek Pollak's classrooms, they persist even on multiple returns.

What if that's not the case? What if individual students or a roomful of students are not yet willing to struggle forward like that? What if they do not yet fully trust the process and are reluctant or resistant? What if they start not at a very good answer, as Aaron does, but at “I have no idea”? How to help them then?

Worse, what if they start at “I have no idea and am not sure I wish to try”? Or even “I have no idea, so leave me alone”?

The reality of teaching is that we are often tasked with addressing reluctance, resistance, learned helplessness, or even outright refusal on the part of students. Some students may give up in the face of what seems to us like a minor challenge. You ask and the answer is very quickly “I don't know.” Others may not be willing to even try in the first place. You ask and the answer is “I don't know,” and whether they realize it or not, if the I don't knows continue, they create an easy out for themselves because in many cases teachers don't know how to respond to “I don't know”—times 100 if it's delivered with a bit of sharpness, as if to say I already told you I don't know. When teachers don't know how to respond to that, the result is often that they leave the student alone for the rest of the class.

Or the rest of the week.

Or the rest of the year.

It's a case of the Band-Aid Paradox. We're asked to do what's difficult and sometimes scary. It's easier to make “the deal” with students, which is basically, I will expect nothing challenging or effortful from you if you agree not to disrupt my class or behave negatively. You can sit in the corner and I will call on someone else. We all know that there are classrooms where this happens. Students may not see the long-term consequences of this terrible bargain, but teachers should be able to. I hope it is obvious to say that adults who care about young people cannot leave students alone like that and allow them to opt out of learning. That's not love and that's not respect.

Let me be clear—I recognize the complexity of such situations. They reflect Adeyemi Stembridge's observation that “Learning depends on trust that the ground will not give way beneath us, trust that effort is worthwhile.” Fixing a context where some students seek to opt out of learning requires a broad range of remedies. We always have to be building trust, for example—in the processes, in ourselves as teachers, or in the endeavor of school—and seeking to ensure that students who don't yet feel that trust come to do so. We need to build cultures that make students feel safe, successful, and known. Much of this book is about that struggle. It's why robust positive cultures that seek not just to limit negative behavior but build positive pro-learning behaviors like Habits of Attention (technique 48) are so profoundly important. People's actions are shaped, more than any other single thing, by the norms of others around them. When students are asked a question in class, whether they see their peers' encouraging faces supporting them, or the backs of uninterested heads goes a long way toward determining whether they take the risk of revealing what they know and what they don't. Similarly, we have to build cultures of error (Chapter Two), seek to motivate and inspire, and establish the caring and expectations of Warm/Strict (technique 61).

But even as we do these things, even if we have accomplished them for the majority of students in our classes, the moment will come when a student will not be able to answer or won't want to answer and will choose to opt out. The student will say I don't know in one of the ways described above, or will say nothing at all, or will say nothing at all with their words but a great deal with their eyes, and no matter how much you understand the imperative of trust and relationships, in that moment you will still be standing there in need of a solution that can bring the situation toward a positive resolution, set basic expectations around effort, and reinforce both caring and accountability. Just telling students you care and want the best for them every so often is not likely to be sufficient to shift established behaviors and mindsets. You will require some option other than “the deal.”

Using a No Opt Out in this situation gives you a viable and productive response. In order to help students make the change from reluctance or refusal to effort, teachers must first reduce or eliminate the pathway to the “easy out,” forestall the opportunity for students to not engage a question when they don't know or don't want to try. It reduces the chances that a student might use “I don't know” on purpose to avoid having to answer because you have required effort of them (even if merely repeating an answer) and so have reduced the incentive. Then teachers must make a base level of effort a habit. That teachers should do this with understanding, humanity, and emotional constancy and that students should do it in a safe environment characterized by mutual respect and decency among students goes without saying.

No Opt Out can also help you to understand the student more. If you're not sure whether a student is trying, then simplifying the task, even to the point of asking for a mere restating of an answer, helps to reveal whether you are dealing with a confused student or an unwilling participant. A confused student can always make an effort to repeat. Once they've done that, you can start building them up, via little successes, Stretch Its, and positive reinforcement. The path forward involves showing them that they can succeed—at first perhaps at small tasks and because you have insisted. Their success will grow from there.

In fact it's worth noting that while the culture you see in Denarius's classroom clearly supports his use of No Opt Out it is also in part a result of his use of the technique as well. His students eagerly engage because Denarius has insisted along the way, with care and humanity, that they do so. He has forestalled the easy out and his students, encouraged to take the riskier path, have mostly come to appreciate that and to trust him. In the end most students know the teacher who makes “the deal” is not the one who cares most about them.2

And while the progress a student makes in answering correctly via No Opt Out may seem trivial, research on motivation tells us that succeeding makes students want to try more. This is true even of small successes. So when students are stuck and they don't know, letting them see themselves answering correctly not only helps in the short run but in the long run.

And if your No Opt Out reduces the task to something very simple and a student persists in refusing to try, then you know clearly that you will have a time for limit setting, a different conversation, perhaps in private, along the lines of: “Charlie, you don't have to get the answers right in my class, but you will be expected to try. You're too capable not to.” There are, sadly, students for whom we will have to make it harder not to try than to try. I hope that most of your use of No Opt Out is not in such settings. I too wish that such cases were not the reality of our world, but they are and it's our responsibility to be prepared.

Adding Rigor to No Opt Out

Over time my team and I have found that No Opt Out often works best when it is most rigorous—the more it rehearses success and lets a student have something to be genuinely proud of at the end of the sequence, the better. This turns setback to triumph and I've often noticed that many of the most able teachers with No Opt Out follow up right away to add a challenge or an extra practice, much as you'll read about in Stretch It (technique 17).

Consider this very basic interaction:

Teacher:

What's three times five? Carson.

Carson:

Eight!

Teacher:

It's not eight. Who can tell Carson what operation he used?

Jalani:

He used addition instead of multiplication.

Teacher:

That's right. So, Carson, what's three times five?

Carson:

Three times five is fifteen.

Teacher:

Yes, good. And what's five times three?

Carson:

It's fifteen, also.

Teacher:

Good. And four times five?

Carson:

Twenty.

Teacher:

Oh, you've got it now! I can't stump you.

This teacher not only gives Carson extra practice at a skill he struggled with but also engineers the experience so the sequence ends with Carson showing that his success was no fluke. He answers several questions correctly; his teacher can't “stump” him. Consider how this sort of interaction turns the tables after a “wrong” answer. Or consider how some small tweaks of this interaction could make it not only positive but more rigorous:

Teacher:

What's three times five? Carson.

Carson:

Eight!

Teacher:

It's not eight. Who can tell Carson what operation he used?

Jalani:

He used addition.

Teacher:

That's right. So, Carson, what's three times five?

Carson:

Three times five is fifteen.

Teacher:

Yes, good. And if I wasn't sure, what operation could I use to check that?

Carson:

You could use division.

Teacher:

Good. Tell us how.

Carson:

Well, you'd divide fifteen by five and get three, and you'd know your multiplication was right.

Teacher:

Thank you, Carson.

In this case, the teacher has focused on asking not another version of the same question, but a different, related question. In both cases, she is using her follow-up to shape Carson's experience of success, as well as to push his skills.

The following case studies show ways you might use a “stretch” after a successful No Opt Out to build rigor and culture.

Case Study 1

Ms. Klein:

What's the definition of vengeance? Carla.

Carla:

Um …

Ms. Klein:

Shakani? Vengeance?

Shakani:

Vengeance is violent revenge, getting back at someone who got you.

Ms. Klein:

Thanks, Shakani. So what's vengeance, Carla?

Carla:

Violent revenge.

Ms. Klein:

So who seeks vengeance in Romeo and Juliet, Carla?

Carla:

Tybalt, when he says, “This must be a Montague. Fetch me my sword.”

Ms. Klein:

Tybalt is doing what when he says that?

Carla:

Looking for vengeance.

Ms. Klein:

And would you agree that examples of people seeking vengeance are rare indeed in the play?

Carla:

No. Pretty much everyone is seeking vengeance.

Ms. Klein:

Nice, Carla. It does seem like just about everybody had vengeance on the brain.

Case Study 2

Mr. Vaca:

What's the multiplicative inverse of negative three, Jason?

Jason:

Three.

Mr. Vaca:

But if I multiply negative three times three I get negative nine. Who can tell Jason what the multiplicative inverse of negative three is? Carlos?

Carlos:

The multiplicative inverse of negative three is negative one-third.

Mr. Vaca:

What is it, Jason?

Jason:

Negative one-third.

Mr. Vaca:

Good. Why, Jason?

Jason:

Because negative three times negative one-third equals one.

Mr. Vaca:

Good. So now tell me the multiplicative inverse of negative one-fifth.

Jason:

It's negative five.

Mr. Vaca:

And four?

Jason:

One-fourth.

Mr. Vaca:

(Smiling) Well, now you're just showing off.