The Importance of Wait Time

Extending the Silence

Edutopia

Giving students several seconds to think after asking a question—and up to two minutes for some questions—improves their learning.

 

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How long do you think teachers pause, on average, after asking a question?

Several studies from the 1970s on have looked into the effect that the amount of time teachers pause after asking a question has on learners. In visiting many classrooms in the United States and other parts of the world, I’ve found that, with few exceptions, these studies are still accurate. For example, according to work done by Mary Budd Rowe in 1972 and Robert J. Stahl in 1994, pausing for three or more seconds showed a noticeable positive impact on learning. Yet the average length that teachers pause was found to be 0.9 seconds.

Wow.

I’ve observed this phenomenon in many classrooms, and there is a real need to increase the time granted to students to process what they know and to make sense of what they do not understand.

In differentiating instruction, process and learning preference are the keys. Process is how learners make sense of ideas, compose their thinking, and prepare a thoughtful answer. Learning preference, in the case of questions posed to the whole class, refers to how some students prefer to silently process the content, keeping their own counsel (Internal Thinkers), while others prefer to talk or express their thinking with an audience as a sounding board (External Thinkers).

The External Thinkers, those go-to students who can be counted on to talk within the first three seconds, may be shaping their ideas as they talk—they haven’t had sufficient time to fully process but speak out anyway. Meanwhile, the Internal Thinkers have also had insufficient time to process, but don’t feel comfortable responding.

One solution is for teachers to pause for five to 15 seconds before calling on students. The silence for some may feel unbearably long. Yet consider that the fastest male and female 100-meter sprinters in the world run at or under 10 seconds. The world record is under 10 seconds, which goes by quickly. Why not offer a similar amount of time for students to consider their responses to questions that require deep thinking?

STRATEGIES FOR PROVIDING STUDENTS WITH TIME TO THINK

Provide wait time: Give students five to 15 seconds to formulate a response to a question for which they should know the answer. Not every learner processes thinking at the same speed. Quality should be measured in the content of the answer, not the speediness.

I count in my head to 15. Most times, I get responses by 10 to 12 seconds. If you don’t get responses within 15 seconds, you can call on students, instead of asking for volunteers.

Give think time: Give students 20 seconds to two minutes to make sense of questions that require analysis to synthesize concepts into a different construct or frame. You can aid this by encouraging journaling, silent reflection, or partner discussions. Giving such chunks of time honors the work being asked of students. Quick responses probably mean that the question did not stretch the learners’ understanding. After the allotted time, any student can be called on to share their response.

Teach reflection: Coach students on the value and practice of reflection. Educators and students may appear to be uncomfortable with silence, hence the typical one-second pause time. Silence may be equated with nothing happening.

In reality, when students are provided with structured ways to practice thinking and specific directions about what to accomplish within the silent time, they can become more productive during reflection. Think From the Middle is a collection of approaches for students to hone their thinking processes during reflection and collaborative communication.

Teach students how to manage a conversation: It’s a beautiful thing to witness students running thoughtful conversations around topics that combine curriculum and real-world connections. Establish a culture for students to engage in such conversations, and they’ll soon be doing most of the heavy lifting during the lesson.

One powerful example I’ve witnessed in Michigan and Texas uses a guide for student-led conversation prompts called Talk Moves. This list of conversation stems provides students with communication tools for participating in and sustaining discussions. I’ve witnessed their use in science classes using the Next Generation Science Standards, and they’re equally useful in all subject area courses.

Students choose the starter stem that best supports the topic to be discussed. Teachers use the Talk Moves to coach and guide students to different levels of complex thinking by directing them toward different sections of conversation prompts. The intent is for students to own the conversation, which empowers their ability to process concepts for understanding.

PLACING STUDENTS AT THE CENTER OF LEARNING

We want students to become independent learners who can navigate challenging material and situations. Students learn at different paces, which seems less about intelligence and more about the time barriers put in the path of learning. There may be a place for timed responses and answering questions under the pressure of a clock, yet there are no standards that say that students should master concepts in less than one second.

Most people need adequate time to process their thoughts if they are expected to contribute to a conversation. Life is not a 30-minute game show with rapid-fire questions that require low-level answers, plus commercial breaks. Even if it were, one would need time to develop and master the processing skills to compete.

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The Future of Coding in Schools

Edutopia

Mitch Resnick, one of the creators of Scratch, on why he thinks coding should be taught in all schools—it’s not the reason you’d expect.

For more than three decades, Mitch Resnick has immersed himself in educational technology and innovative learning models. Now a professor at the MIT Media Lab, and a co-creator of the popular Scratch programming language, Resnick remains a tireless advocate for student-centered education, collaborative learning environments, and the idea that coding is a form of literacy.

His new book, Lifelong Kindergarten: Cultivating Creativity Through Projects, Passion, Peers, and Play, is a look at our current educational moment. “Roughly two-thirds of grade school students will end up doing work that hasn’t been invented yet,” Resnick contends, hinting at the emerging worlds of artificial intelligence, self-driving cars, and “smart” houses. How do we prepare today’s students to meet that challenge?

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We talked with Resnick about the importance of coding in our school system, his thoughts on the changing roles of teachers, and new ways to engage students—and assess their work.

EDUTOPIA: You moved from journalism—writing about computers and business—to the field of educational technology and learning in the 1980s. What inspired that move?

MITCH RESNICK: The most important shift for me in thinking about computers and learning was actually the spring of 1982, the West Coast Computer Faire—which is like an early form of Maker Faire—and Seymour Papert was giving a keynote address. When I heard Seymour talk, it gave me new vision of what role computers might play in people’s lives: They weren’t just machines to get a job done—they could enable people to express themselves in new ways, and change the way people thought about themselves and thought about the world. That was very exciting to me.

EDUTOPIA: Are we still struggling with Papert’s early insight—almost astonishing at the time—that the computer isn’t just a processor of information but a platform for constructing human knowledge?

RESNICK: Yes I think so, and it mirrors a struggle in the education system that has nothing to do with technology. Many people think of learning and education as a process of delivering information or delivering instruction. Other people see learning and education as student-centered—learning is about exploring, experimenting, creating. Those are very different visions that predate the computer, but of course the computer can fit into either of those two models. It’s a wonderful device for delivering information, but it can also be a wonderful device for creating, exploring, and experimenting.

EDUTOPIA: There are influential people, like Apple CEO Tim Cook, saying, “What we need to do is get coding into every single public school. It needs to be a requirement in public schools across the board.” Is that right?

RESNICK: If it were up to me, I would introduce it. But I want to be careful because I don’t want to embrace it for the same reason that some people might. The first question I would ask is: “Why should we learn coding at all?” Many people embrace coding in schools as a pathway to jobs as computer programmers and computer scientists, and of course they’re right that those opportunities are expanding rapidly. But that’s not a great reason for everyone to learn how to code.

Very few people grow up to be professional writers, but we teach everyone to write because it’s a way of communicating with others—of organizing your thoughts and expressing your ideas. I think the reasons for learning to code are the same as the reasons for learning to write. When we learn to write, we are learning how to organize, express, and share ideas. And when we learn to code, we are learning how to organize, express, and share ideas in new ways, in a new medium.

EDUTOPIA: What does that look like in the school system? Does coding sit alongside math and reading? Is it integrated in some way?

RESNICK: These days I talk about our approach in terms of these four words that begin with the letter p: projects, passion, peers, and play. So that’s the approach I would take with coding, but also with any other learning: getting students to work on projects, based on their passion, in collaboration with peers, in a playful spirit. And each of those p’s is important. I think work on projects gives you an understanding of the creative process, how to start with just the inkling of an idea and then to build a prototype, share it with people, experiment with it, and continue to modify and improve it.

We know that kids are going to work longer and make deeper connections to the content when they are passionate about the ideas—when they care—and when they’re learning with and being inspired by peers. And I’d want to have kids experience coding in the same way.

EDUTOPIA: You’re describing a high-choice learning environment rooted in student passion and project work. Where’s the teacher in that mix?

RESNICK: The teacher still plays an incredibly important role, but in this approach it’s not so much about delivering instruction. One role the teacher is playing is the role of connector—connecting peers with one another to work together on solving problems. Teachers also act as catalysts by asking provocative questions: “What do you think will happen if…?” or “That surprised me, why do you think that happened?”

They’re consultants, too, and it’s not just about consulting on technical skills, but also about things like how you continue to work on something even when you are frustrated, or suggesting strategies for working with diverse groups of people. Finally, the teacher can be a collaborator, working together with kids on projects—because kids should see teachers as learners too.

EDUTOPIA: It sounds like a more democratic, open system, which seems to imply breaking down a lot of barriers?

RESNICK: I think breaking down barriers is a good way to think about it. When I think about the type of things that I might change in schools—and I know none of it is easy—a lot of it is about breaking down barriers. Break down the barriers between class periods, because 50-minute chunks are too constraining if you want to work on projects. Break down the barriers between disciplines, because meaningful projects almost always cut across disciplines. Break down the barriers between ages and have older kids work with younger kids—both groups benefit. And break down the barriers between inside of school and outside of school—have kids work on projects that are meaningful to their communities and bring people from the communities into the schools to support the teachers.

That’s one way of dealing with the challenge of a single teacher committed to 30 or more kids. It doesn’t have to be that way. Older kids can be helping younger kids, people from the community can be helping.

EDUTOPIA: A fair question—and a common criticism—is: How do you figure out whether kids are learning anything? How do you assess it?

RESNICK: I would take a portfolio-like approach, looking at what kids create. That’s what we do in our Scratch online community. You can see that a kid has created several dozen digital projects, and you can look through their projects and see their progression. For example, you might see the gradual adoption of new strategies—new types of artwork, but also new and improved programming structures.

I acknowledge that it’s difficult to arrive at quantitative measures, but I also think we each don’t necessarily need to. I sometimes make the analogy to the way I’ve been evaluated here at MIT. There are actually no quantitative measures in the process. Basically, they look at my portfolio: They see what I’ve created, they look at the trajectory and the progress over time, and they ask other people’s opinions about it. You’ll sometimes hear, “Well that’s not serious, we need quantitative measures to be serious.” Are they making the claim that MIT is not serious? I understand the criticism that it’s inefficient, but I think those are things we are going to need to deal with.

Again, it’s a big change and I’m not saying it’s easy, but I do think we need to move in that direction.

The Harvey Weinstein Challenge: Combating Sexual Harassment In and Out of School

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I don’t know what the world record is, but I’m pretty sure I’m close: My first experience with sexual harassment occurred within the first 10 minutes on my first shift at my very first job.

Newly hired as a hostess for a local restaurant, I was excited to have landed a summer job between college semesters. I was nervous, too, because I had no idea what to expect. What I definitely didn’t expect was Mr. Leonard.

As the restaurant manager, Mr. Leonard, a married man in his mid-40s, made a point of “joking” with every new hire that while he lived on Maryland’s Eastern Shore, once his car crossed the midpoint on the Chesapeake Bay Bridge on his way to work every morning, he was “single.”

At first, and in my naïveté, I wasn’t quite sure what he meant. It soon became clear. I heard him repeatedly telling obscene “jokes” about sex, and witnessed him ogling and making disgusting comments about waitresses’ bodies to their faces and from behind them. Once, I saw him snap the bra strap of a woman who bent over to take something out of a case. One day he told me he could see the outline of my bra under my hostess dress (which he was staring at) and then sent me home to put on a slip to avoid “offending the customers.”

I lasted two weeks. While the term “hostile work environment” had not yet been coined, I knew emotionally I was in one. Looking back, my most important lesson was recognizing that I left because I couldThe older women did not have the privilege of quitting. Most were caring for children at home, and the loss of income would have been devastating for their families. Their only option was to suffer through it in silence. Besides, to whom could they complain, since the perpetrator was also the boss?

A Pervasive Problem

Sexual harassment was a ubiquitous problem that had no name until the early 1980s, when federal courts defined it as an illegal form of “gender discrimination” in violation of the 1964 Civil Rights Act. The U.S. Office of Equal Employment Opportunity (OEEO) was charged with creating mechanisms for filing complaints and procedures for ongoing enforcement. Later court cases made these new rules applicable to school environments as well.

But, it was not until 1991, during Clarence Thomas’s U.S. Senate Supreme Court confirmation hearings—when Anita Hill famously accused Thomas of sexual harassment, while both were working at the OEEO, which he headed, no less—that the entire nation, all at once, received its first meaningful education about this scourge. Now, it had an official name as well as the force of the federal government behind its adjudication.

As recent high-profile events make clear, nonetheless, sexual harassment remains ever-present in our society, even in the lives of women (and men) who are powerful in their own right. This time, however, I’m much more optimistic about the prospects for lasting awareness and change.

The Prospects for Change

First, and really only within the past five years, American society has finally begun to treat the problem of sexual assault—sexual harassment in its most extreme form—with the seriousness it deserves. Moreover, a new standard for defining “sexual consent” has emerged: What counts is no longer “the absence of no,” but rather “the unequivocal presence of an enthusiastic verbal yes.” This is no mere linguistic change, since as a very practical matter it shifts the onus for establishing consent squarely on the person who desires sexual activity, not the person they desire. Verbal permission before crossing another person’s sexual boundaries is required.

These two developments have been hugely important in helping us and our students to better understand and help prevent sexual assault. Now, as our collective attention is drawn to highly publicized disclosures of chronic sexual harassment perpetrated by powerful, well-known men across diverse businesses and professional fields, another new and potentially transformative element is in the mix: public accountability.

The swift, hard fall from positions of enormous power, status, and wealth for many of these men delivers a resounding message: “This behavior, once and for all, is intolerable and will bring serious consequences.” Public accountability inevitably begets more public accountability, because victims feel supported in knowing they are not alone and can recognize, finally, they were in no way at fault; it also exposes to public scrutiny the hidden malignancies that keep entrenched patriarchy and “toxic masculinity” alive.

What About Our Students?

Sexual harassment statutes pertain only to schools and workplaces, because students must go to school and most people have to work. (If someone is the recipient of catcalls on a particular street, on the other hand, they can simply take another route.) Educational institutions, of course, are both workplaces and schools. Without question, it is incumbent upon all schools to establish policies and practices that provide clear, equitable procedures for reporting, investigating, and resolving sexual harassment complaints—involving students of all sexual and gender identities—and maintaining safe school environments. A recently launched campaign, #MeTooK12, aims to lobby and support schools in improving their efforts. Read about it here.

It’s vital to recognize, though, that most of the sexual harassment today’s students perpetuate and/or experience does not occur in formal settings like schools and workplaces, but within their everyday social interactions, much of it in the form of hostile, cruel, degrading, and coercive online communication. Regardless of venue, though, it is shaped and fueled by the very same patriarchal mix that defines “real” masculinity in terms of superiority, entitlement, dominance, winning at all costs, and the conflation of sex and power.

Before men are men, they are boys. Until parents and schools commit to intentionally raising both boys and girls with high expectations and a single standard of values based on empathy and fairness—with sex and gender being no exception—we can expect these harmful and oppressive patterns to continue. Now is a very good time to take on this challenge. 

Will Letter Grades Survive?

Edutopia

A century-old pillar of the school system is under fire as schools look to modernize student assessment.

Under pressure from an unprecedented constellation of forces—from state lawmakers to prestigious private schools and college admissions offices—the ubiquitous one-page high school transcript lined with A–F letter grades may soon be a relic of the past.

In the last decade, at least 15 state legislatures and boards of education have adopted policies incentivizing their public schools to prioritize measures other than grades when assessing students’ skills and competencies. And more recently, over 150 of the top private high schools in the U.S., including Phillips Exeter and Dalton—storied institutions which have long relied on the status conveyed by student ranking—have pledged to shift to new transcripts that provide more comprehensive, qualitative feedback on students while ruling out any mention of credit hours, GPAs, or A–F grades.

Public Domain

Choate Rosemary Hall in Connecticut is one of 157 private schools that are part of MTC.

Somewhat independently, schools and lawmakers have come to the same conclusion: The old models of student assessment are out of step with the needs of the 21st-century workplace and society, with their emphasis on hard-to-measure skills such as creativity, problem solving, persistence, and collaboration.

“Competency-based education is a growing movement driven by educators and communities focused on ensuring that students have the knowledge they need to flourish in a global economy,” said Susan Patrick, chief executive officer of iNACOL, a nonprofit that runs the website CompetencyWorks. “The future of jobs and the workforce will demand a new set of skills, and students’ capacity to solve complex problems for an unknown future will be essential.”

For their part, colleges—the final arbiters of high school performance—are signaling a surprising willingness to depart from traditional assessments that have been in place since the early 19th century. From Harvard and Dartmouth to small community colleges, more than 70 U.S. institutions of higher learning have weighed in, signing formal statements asserting that competency-based transcripts will not hurt students in the admissions process.

The emerging alignment of K–12 schools with colleges and legislators builds on a growing consensus among educators who believe that longstanding benchmarks like grades, SATs, AP test scores, and even homework are poor measures of students’ skills and can deepen inequities between them. If the momentum holds, a century-old pillar of the school system could crumble entirely, leading to dramatic transitions and potential pitfalls for students and schools alike.

PICKING UP STEAM

Scott Looney, head of the Hawken School in Cleveland, was frustrated. His school had recently begun offering real-world, full-day courses in subjects like engineering and entrepreneurship, but he was finding it difficult to measure and credit the new types of skills students were learning using A–F grades. Looney started reaching out to private high schools and colleges looking for alternatives.

Courtesy of Scott Looney

Scott Looney, head of school at the Hawken School in Cleveland, Ohio.

Though he found that many educators shared his desires for a new assessment system, he came up empty-handed.

“The grading system right now is demoralizing and is designed to produce winners and losers,” said Looney. “The purpose of education is not to sort kids—it’s to grow kids. Teachers need to coach and mentor, but with grades, teachers turn into judges. I think we can show the unique abilities of kids without stratifying them.”

Looney began brainstorming a new type of transcript for the Hawken School, but quickly realized he would need a critical mass of schools to influence college admissions offices to accept it. With the initial support of 28 other independent schools, Looney formed the Mastery Transcript Consortium (MTC) in April 2017. The group has since expanded to 157 schools, including both historic institutions like Phillips Exeter and newer alternative schools like the Khan Lab School.

In joining the MTC, each school commits to phase out its existing GPA- and grade-based transcripts for a digital, interactive format that showcases students’ academic and enrichment skills, areas for growth, and samples of work or talents, such as a video of a public speaking competition or a portfolio of artwork.

The purpose of education is not to sort kids—it’s to grow kids. Teachers need to coach and mentor, but with grades, teachers turn into judges.

While the transcript is still in its infancy, organizers say it will resemble a websitethat each school will be able customize by choosing from a menu of skills like critical thinking, creativity, and self-directed learning, along with core content areas such as algebraic reasoning. Instead of earning credit hours and receiving grades, students will take courses to prove they’ve developed key skills and competencies. Looney insists that the transcripts will be readable by admissions officers in two minutes or less.

The MTC’s work is not entirely original, though, and takes its lead from a number of public schools—most notably in New England—that have been rethinking traditional methods of assessing students for more than a decade.

Some are supported by the nonprofit group Great Schools Partnership, which helped influence Maine, Connecticut, Vermont, Rhode Island, and New Hampshire to adopt state board of education policies or legislation in the last decade on proficiency-based assessment systems. Other districts, in Florida, California, and Georgia, have made similar changes more recently, and pilot programs have emerged in Colorado, Idaho, Utah, Illinois, Ohio, and Oregon.

©iNACOL

A map from iNACOL estimates that 48 states have at least some policy supporting competency-based education.

There’s also backing from colleges. The Great Schools Partnership was able to garner the support of more than 70 colleges and universities, suggesting that higher ed admissions offices are ready for the change.

“We are accustomed to academic reports from around the world, including those from students who have been privately instructed and even self-taught,” said Marlyn McGrath, Harvard University’s director of admissions, replying via email about the transcripts. “In cases where we need additional information, we typically ask for it. So we are not concerned that students presenting alternative transcripts will be disadvantaged because of format.”

MASTERY VERSUS SEAT TIME

But the new transcripts are just the tip of the iceberg, according to supporters, part of a larger movement to do away with a system where kids can progress through grades or courses without really understanding material and be promoted for seat time and good behavior. When students move on to harder topics, they continue to accumulate gaps in their knowledge—a setup for failure in the later grades or collegiate years.

Under a competency model, kids can no longer just “get by,” said Derek Pierce, principal of Casco Bay High School in Portland, Maine, which has used a proficiency-based transcript since 2005.

The new transcripts “get kids focused on doing their personal best on meeting or exceeding standards rather than getting a better grade than the kid next to them,” said Pierce. “There is no longer a ‘gentleman’s C’.”

However, without widespread agreement on the necessary skills and knowledge required for core classes, proving mastery may be just as elusive and arbitrary as the current system. Even MTC member schools won’t rely on a shared understanding of what mastery means. Instead, each school will be able to quantify it independently, leaving college admissions officers—according to critics—without a clear basis of comparison.

Our learning structures have to be much more nimble to allow today’s learners to navigate through opportunities where they can see themselves as the authors of their own education.

While competency-based education proponents argue that the new transcripts will identify students with skills that academia has traditionally overlooked, others worry about equity for marginalized students, who already struggle in the current system. Some critics have suggested that the new transcripts may be a way for wealthier schools, especially private schools like those in the MTC, to give their students an even greater advantage when competing for limited positions at the best universities.

©Khan Lab School

Competency-based transcript proponents like the Khan Lab School, pictured here, believe the new assessments are necessary to foster 21st-century skills.

There are other unanswered questions and challenges to be worked out, too. Will college admissions counselors have enough time, especially at large public colleges, to look meaningfully at dense digital portfolios of student work? Will the new transcripts create too much work and new training for K-12 teachers, as they struggle to measure hard-to-define categories of learning? Perhaps most importantly, will parents buy in?

“There’s still plenty of work ahead and some pretty radical changes taking place,” explained Mike Martin, director of curriculum and technology at Montpelier Public Schools in Vermont, whose district starting transitioning to a competency-based model in 2013.

Many public and private schools, like Martin’s, are still years away from full implementation, and others are grappling with the nuts and bolts of how to implement dramatically new systems for student learning and assessment. Those on the forefront of these changes, though, remain hopeful that the new system will push all students to develop the skills they need to succeed in college and careers.

“Our learning structures have to be much more nimble to allow today’s learners to navigate through opportunities where they can see themselves as the authors of their education,” said Martin. “Proficiency-based education is about getting every single student up to a certain skill level and ensuring every student can succeed.”

Finding the Beauty of Math Outside of Class

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Math trails help students explore, discover, enjoy, and celebrate math concepts and problems in real-world contexts.

©Shutterstock.com/Jon Bilous

A math trail is an activity that gets students out of the classroom so they can (re)discover the math all around us. Whether out on a field trip or on school grounds, students on a math trail are asked to solve or create problems about objects and landmarks they see; name shapes and composite solids; calculate areas and volumes; recognize properties, similarity, congruence, and symmetry; use number sense and estimation to evaluate large quantities and assess assumptions; and so on.

This is one of those creative, yet authentic activities that stimulate engagement and foster enthusiasm for mathematics—and so it can be particularly useful for students in middle and high school, when classroom math becomes more abstract.

A math trail can be tailored to engage students of any age and of all levels of ability and learning styles. Its scope and goals can be varied, and it can include specific topics or more general content. And best of all, it can make use of any locale—from shopping malls to neighborhood streets, from parks, museums, and zoos to city centers, to name a few. Any space that can be walked around safely can work.

A DAY OF EXPLORATION

My school has used a ready-made math trail designed by the Mathematics Association of America. Although it’s designed for Washington, DC, its general ideas can be applied in any city or town. It could be particularly appealing for teachers because it’s open-ended and can be tailored to the curricular and educational needs of the students. In addition, as schools from all over the country visit the nation’s capital, it provides a math activity that can be easily added to the many history, art, and civics lessons elicited by such a field trip.

Our math trail is loosely structured on purpose: As the whole Grade 7 takes part in this trail and as many chaperones are not math teachers, we make it clear that the purpose of the day is for the students to explore, discover, enjoy, and celebrate the beauty of math and its presence all around us. Using the MAA’s Field Guide and a map of the National Mall, each group spends the first hour of the day planning their route. How they spend their time is up to each group—this freedom is what the students like the best about the day.

Some students want to visit the newly renovated East Building of the National Gallery of Art—a treasure trove of 2D and 3D geometric ideas, patterns, and artifacts. Can we calculate or estimate the volume of its octagonal elevators or triangle-base stairwells? Even without measuring tape? Others can’t wait to ride the Mall carousel while thinking of the trigonometric function the ride’s motion describes.

Other students look at a more pressing problem: Considering the scale of the map, what is the shortest route to Shake Shack from the Sculpture Garden? Is that path unique? Is the distance the same in Euclidean geometry? Walking at a fast pace—say 4 mph—how long will it take to get there? Can we get our food and make it back to the bus on time?

Another group might estimate how many people visit the Air and Space Museum in a day. And how do we go about solving this problem?

©Shutterstock.com/Lissandra Melo

In Washington, DC, students can use their math skills to discuss architectural elements like the curves at the Hirshhorn Museum.

Another group will examine the shape of the Hirshhorn Museum complex. Why does it look so appealing?

Where do we see symmetry in the World War II Memorial? Where do Fibonacci numbers and/or fractals appear in the National Garden? What’s the scale of the Voyage model of the solar system along Jefferson Drive? Given that scale, can we estimate the distance between Mars and Saturn? Turning our thoughts back to Earth, how is the map of Washington, DC, structured? If transferred to Cartesian coordinates, what is the origin? The possibilities—in DC and in your town—are probably endless: Teachers can tweak all of these questions to fit other contexts.

BACK AT SCHOOL

Each group visits various sites and takes photos, and after we’re back at school the students research the mathematical significance of the symbols or objects they’ve chosen, write and/or solve the problems they posed, annotate their photos and post them on an electronic bulletin board or map of the Mall, and express what they’ve learned and enjoyed in other creative ways such as movies, kahoots, songs, game shows, etc. These projects are shared at a later time in assembly and affirm the fun mathematical times.

There are many excellent resources about math trails, including already created trails and virtual trails as well as clear directions on how to create your own. Math trails are cooperative—not competitive, as mathematics learning is often seen—and they offer the opportunity of doing and talking about math. Making and using connections among mathematical ideas, recognizing and applying mathematics in contexts outside of math class, communicating mathematical thinking to others clearly, and analyzing and evaluating the mathematical thinking and strategies of others are all basic tenets of the NCTM process standards.

The collaborative nature of a math trail makes it a great opportunity for bonding. After our first math trail, we understood better the potential of this activity and realized that it could be integrated in our seventh grade Advisory program, particularly at the beginning of the school year, when it can help facilitate the transition into middle school.

Teenage Inventor Alexis Lewis Thinks That Kids Have the Solutions to the World’s Problems

Watch This Great Video on Alexis

With a patent to her name and more likely on the way, the 15-year-old has made it her mission to inspire young innovators

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Benjamin Franklin invented swim flippers when he was 12 years old. Frank Epperson, age 11, conceived of the popsicle, and 16-year-old George Nissen thought up a trampoline.

Just last year, Kiowa Kavovit, then 6, became the youngest to pitch her invention—a liquid bandage called Boo Boo Goo—on ABC’s “Shark Tank.”

In the United States, there is no age requirement for filing a patent.

Alexis Lewis, a 15-year-old inventor in Chapel Hill, North Carolina, wants children across the country to know that an inventor isn’t something you have to be when you grow up; they can be one now. Lewis holds a patent for a wheeled travois—a triangular load-carrying device with a bamboo frame and a bed of netting that she designed to serve Somali refugees, who need to transport their children many miles to camps and hospitals. Her patent-pending emergency mask pod is a football-shaped canister with protective gear that firefighters and first responders can throw through a window of a smoke-filled building to those trapped inside.

The two-time winner of the ePals-Smithsonian Spark!Lab Invent It Challenge, a competition for young inventors age 5 to 18, is a vocal advocate for “Inventing 101” courses to be a part of middle school curriculums.

Why should more people invent?

I think not only is it important to tell people that they can invent but it’s important also to tell them that they should be [inventing] because they have their own unique perspective on the world. Everybody has lived a different life, everybody has seen it [the world] slightly differently and I think everybody has a slightly different take on each problem. And I think if we all work together we can solve a tremendous number of problems.

What motivates you to invent?

My inventions are motivated by one of two things usually. One, it’s a humanitarian issue, basically people who aren’t getting the help they need, people who are dying unnecessarily when they could be saved. Another reason that I often invent is that I’ll get myself absolutely buried in a piece of physics, just learning about it obsessively. Then, I start to realize that there are little things that can be done to make technologies revolving around it a little bit more efficient here, a little bit more effective there.

 

Can you tell us a little bit about the environment you grew up in and how that’s impacted you as an inventor?

My mom would always read to the family about various world issues. When Hurricane Katrina hit [Alexis was 5 years old], we learned all about that—what a hurricane was, how it worked, the effects of Hurricane Katrina itself, what they were doing to help clear out floodwaters, all sorts of fascinating stuff. Being homeschooled, I had a lot of free time in which I was encouraged to basically go and do and build almost anything I wanted. I had access to videos on any subject, so I got to learn about the science of everything, and I read voraciously. I think having those channels of knowledge open to me was completely invaluable.

Do you think you have some advantages as an inventor given the fact that you’ve started young?

I don’t mean to put adults down, but when you’ve grown up and you’ve seen the world for a long time, you think its one way. I’d say that starting young has had an advantage in that I have the ability to look at something and not think, “oh this is a problem that can’t be solved,” but instead think maybe we’ve been looking at it just a little bit wrong. Kids, since they haven’t been told this is something that would never work over and over, have the have the ability to do that.

What is Inventing 101? Where did the idea come from, and why is it important to you?

It’s a class I hope to have administered to middle school students across the country that would basically tell them that they are capable of inventing. It would show them kids who have already invented. If people aren’t told when they’re young that they can invent, it’s going to be much harder to convince them that they can.

I had this idea when I was looking back at the stuff I had done, at my inventions and realizing that these are some simple [designs.] It’s not going to necessarily be the collapsible travois with custom made specially fabricated joints, it’s going to be the simple bamboo one that anybody can make. It’s not necessarily going to be the $700 grenade launcher, it’s going to be a little football-shaped pod that costs all of $4. People are stunned when they hear what I’ve done. But these are things that I know for a fact a lot of people can do. So I thought there’s got to be some way to awaken that self-confidence in people to enable them to do that.

How does your Emergency Mask Pod (EMP) work?

The emergency mask pod is basically a two-part football canister that holds a smoke mask made by Xcaper Industries, a pair of goggles and a little light-emitting device, most likely a LED light strip in the final version. The goggles allow people to concentrate more fully on getting out without having to worry about their eyes burning. The mask gives people the ability to breathe without dealing with the toxic effects of the smoke, and the light strip allows people to more easily locate the pod when it flies into a dark smoky room.

Designing the EMP pod was a process of trial and error. I’m a kid. I like things that go boom and shoot, and so my first thought was let’s just launch it up there. I did a whole bunch of research, and I was looking at a couple of different launcher mechanisms. I had the mascot of a local sports team fire a pneumatic cannon, basically a t-shirt cannon, into an open window from a very close distance, and accuracy was pretty abysmal. I went from a pneumatic cannon, which didn’t work at all, to a couple of so-so throwable devices, and ended up finally with a throwable canister with an accuracy of over 75 percent.

People think that the inventors of the world are the crazy mad scientists and white lab coats working long hours developing crazy new technologies. But that’s not the case. It’s not something reserved for Edison, Graham Bell, all the greats. Inventors are basically anybody and everybody who’s ever tried to solve a problem.

Why Students Should Take the Lead in Parent-Teacher Conferences

Mind/Shift

Mia Christopher
Mia Christopher

The following is an excerpt from “Deeper Learning How Eight Innovative Public Schools Are Transforming Education in the Twenty-First Century,” by Monica R. Martinez and Dennis McGrath.

A particularly vivid example of putting students in the driver’s seat of their own education is the way they handle what traditional schools refer to as parent-teacher conferences. At these time-honored encounters, it’s not uncommon for students to stay home while the adults discuss their progress or lack thereof. But at schools built on Deeper Learning principles, the meetings are often turned into student-led conferences, with students presenting their schoolwork, while their teachers, having helped them prepare, sit across the table, or even off to the side. The triad then sits together to review and discuss the work and the student’s progress. The message, once again, is that the students are responsible for their own success.

The specific dynamics of these conferences vary widely. At California’s Impact Academy, three or four different sets of students and their families meet simultaneously, as teachers circulate through the room, making sure parents are getting their questions answered, and only intervening if the student is struggling. Yet in all cases, the basic spirit is the same: this is the student’s moment to share his or her reflections on achievements and challenges.

At King Middle School, the twice-yearly student-led conferences are “one of the most important things we do to have students own their own learning,” says Peter Hill, who helps prepare kids in his advisory class, or crew, for their meetings. “And yet, the students’ first impulse is to tear through their folders to find every best thing that they have done to show their parents.”

Instead, Hill encourages students to reflect on the connection between the effort they have made and the quality of their work. To this end, he asks them to choose three examples that help them tell their parents a deeper story: one that shows they have recognized both a personal strength and an area in which they are struggling. Most students, he says, have never thought about their learning in this way. Nor have most of their parents.

Indeed, many parents need some time to adjust to the new format, Hill acknowledges. Often, he says, a mother or father “just wants to ask me about how their child is doing, or how they are behaving. Sometimes I have to nudge the conversation back to let the child lead. We also have to teach the parents how to be reflective about their kids’ work and how best to help.”

Eventually, however, most if not all parents appreciate the new process, teachers told us. “They come to realize that report cards don’t tell them anything very useful,” says Gus Goodwin, Hill’s colleague. “And over time, the parents begin to set a higher bar for their students at these conferences.”

As crew leader, Hill has his students practice how they’ll discuss their work products with their parents. We watched as he spoke with one eighth-grade boy who initially shyly lowered his head as he confessed that he felt uncomfortable showing his work to anyone, including his mother and father. Hill told the boy he understood how he felt, and then offered some strategies for discussing his work in math, which both of them knew was a problem area. “You have done some good work of which you should be proud,” he told him. Together, they then picked out a paper that demonstrated the boy’s effort, after which Hill suggested: “When we have the conference, why don’t you use this assignment and begin by saying, ‘I have done a good job in math when I . . . .’ ” The boy wrote the phrase in his notebook, and visibly began to relax, after which Hill used the rest of the advisory period to find more examples of work that showed his effort.

As kids learn to advocate for themselves in this way, they discover how to let their parents know more specifically how to support them. Hill tells the story of one student who was clearly intelligent, but struggling with his independent reading. Rambunctious in class, the boy surprised Hill by sitting straight and quietly in his chair when his father, a seemingly stern man, walked into the room. But what surprised him even more was when the boy spoke up for himself during the conference, telling his father: “I realize now that I need to spend more time reading on my own and I need your help with that. I need my three brothers out of the room at night so I can read in silence.”

Such exchanges empower both students and their parents, Hill noted, adding: “When I checked in on the student a few weeks later, he was very pleased that his dad was keeping his brothers out of his room so he could do his silent reading.”

At Science Leadership Academy, health educator Pia Martin coaches her students in how to communicate with parents about difficult topics, such as why they might have received a C in a class. “How will your parents respond?” she asks. “What are the things that will trigger your parents and how will that play out? Will this lead to lost privileges or other forms of punishment? How do we minimize this?”

“In conference, I’m your advocate,” she always reminds them. Like Hill and several other teachers we spoke with, Martin said she usually helps begin conferences by encouraging students to talk about what they are good at, to prevent meetings from turning into blame-fests. She tells the students to start the meeting with two questions: “What do I do well?” and “How can I build on this?”

“I always tell them, ‘Own what you got,’ ” Martin says. Only after students spend a moment to recognize what they’re doing right does she encourage them to tackle the challenges, with the following questions: “What have I not done well?” and “How can I improve this?”

Copyright ©2014 by Monica R. Martinez and Dennis McGrath. This excerpt originally appeared in “Deeper Learning How Eight Innovative Public Schools Are Transforming Education in the Twenty-First Century,” published by The New Press Reprinted here with permission.