Tag Archives: how teachers teach

A Math Teacher Remembers Her Students (Education Realist)

 

This abridged post comes from the blog Education Realist. The teacher who writes this blog prefers to remain anonymous. I have observed this teacher teach math and social studies lessons; we have also met and had lunch discussing many issues in public schools.

In the fall of 2012, I began my first year at this school. I met a group of 29 freshmen in their first high school math class: geometry.  From the beginning, we all clicked. A new school didn’t seem quite so intimidating because every day of that first semester started with camaraderie and good times–and some learning, too.

Of the 26 who stayed the whole year, all but one passed. Nearly half Asians (from every part of the continent), over half the rest Hispanic, and seven whites, and one African American. Ten athletes, including two who turned their ability into scholarships. The eventual senior prom queen. All those who passed made it through trigonometry, at least. Most made it to pre-calculus. Only a few made it to Calculus or Advancement Placement Statistics.  They reflected the school’s population writ large: diverse, athletic, not overly focused on academics, but smart enough to get it done.

A few others were never in one of my classes again, but I saw them frequently; they’d always shout a greeting across the quad, identifying themselves because they know I never wear my glasses.

The remaining saw me in at least one subsequent math class. None seemed to mind.

When we talked, as we did often, we’d regularly refer to “that first geometry class”.  Our touchstone memory, kept alive through four years of their education.

One of my “three-timers”, a sweet, tentative young man who never had another math teacher until pre-calc, stopped by with his yearbook. As we thumbed through the senior pages, calling out familiar faces, he suddenly said, “Man, I bet you’ve taught most of the seniors at least once.”

We counted it together—of the 93 rows of four students each, I’d taught 288 of them, or roughly 75%. Many more than once.

In the face of that percentage, I decided it was time to work around my dislike of crowds, speeches, and heat in order to represent on their big night. So at 4:30, I showed up at the stadium to help assemble them for the procession.

At first, the seniors were gathered in informal groups outside the staging area, taking pictures, talking, dancing about impatiently. Many called me over or waved, shouting out their names.

As they moved into the cafeteria for the staging, I wandered around, touching base, asking about plans, saying goodbye. As I’d expected, they needed teachers to organize the alphabetized lines for the procession, so I took a list of twenty. Rounded them up, hollered them into line, while the fourteen students I’d taught before joked that in less than three hours they’d never have to listen to me again. “And that’s why you became a teacher!” a bunch of them chorused.

Finally, the graduation manager gave the sign for zero hour. Suddenly well-behaved and serious, they streamed out in order, paused for a few minutes at some inevitable delay, and then the music started. I stood about 15 feet away from them, put on my prescription glasses, even in the sun, the better not to miss any face.

Waved and cheered at brand new adults who waved and cheered back, glad I was there, happy to see me, happy that I was wearing my glasses and could see them.  And when the last student–one of mine–turned for one final smile, I decided that the graduation itself, the heat, the speeches, the names, would dull the joy I felt in this moment. Time to go.

As I walked back to where I’d parked my car, latecomers were hustling to the stadium, many holding signs and pictures. I saw pictures I knew, stopped to congratulate the parents and send them on their way.

And suddenly:

“Hey, it’s my geometry teacher!”

I smiled at the pretty, lively young woman holding a…toddler? infant? gurgling happily walking towards me, waving.  But I’ve only taught three geometry classes in those four years, and was coming up blank.

“You don’t remember me? I’m Annie!” and I gasped.

“Oh, my God. Annie! I thought…I haven’t run into you for so long…you didn’t go back to live with your mom? I don’t think I’ve seen you in..three years? I didn’t recognize you. You’re all grown up! ”

Annie was the only one in the geometry class that didn’t pass.

“How’s your dad? You look fantastic. And how’s this little guy? How old is he, fifteen months?”

“Nope, just nine months.”

“He’s gorgeous. How are you? Come to see the grad…well, duh, yes.”

She laughed, and hitched the baby to her other hip. “It’s great you came! I still think about that geometry class. It was so fun!”

“I wish I’d run into you more. Go, get going, you don’t want to be late. Take care of this adorable one. I’m happy to see you.”

“Me, too. Take care. Bye!” and off she went, striding confidently into her future.

I watched her, thinking of all the questions I wanted to ask: did she graduate? Go to our excellent alternative high school? Is the baby’s dad in the picture? What are your plans? and being so very glad I didn’t ask.

I resist presenting Annie as a tragedy. I didn’t feel guilt.  But I did feel…awareness, maybe? I’m good with unmotivated underachieving boys. Am I as good with girls?

Could I reach out more? Give them reasons to try, to play along?

I then remembered a saying from my ed school professor

“You should never be satisfied. You can always do better.”

I told him that the two sentiments don’t follow. I am satisfied. I can try to do better.

Goodbye, class of 2016.

Goodbye, geometry class. I’ll miss you.

 

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The Perils of PBL’s Popularity (John Larmer)

Recently, I have published posts on Project-based Learning. A student and foundation official  have raised questions with and about PBL as an appropriate instructional approach. As this instructional reform, once the darling of early and mid-20th century Progressives, has surged again in practitioner and researcher circles, criticism of its implementation and use needs to be aired. For this post, I turn to John Larmer, a champion of PBL, who believes deeply in the instructional approach but shows concern over its potential faddishness and too easy acceptance. Former high school teacher of social studies and English, Larmer is Editor in Chief of publications at the Buck Institute for Education (BIE). He writes often about Project-Based Learning. This post originally appeared March 21, 2016

As readers of this blog well know, Project Based Learning is a hot topic in education these days. The progressive teaching method is being touted as one of the best ways to engage 21st-century students and develop a deeper understanding of content as well as build success skills such as critical thinking/problem-solving, collaboration, communication, and self-management.

At the Buck Institute for Education, we think PBL is even more than that; it can be absolutely transformative for students who experience enough high-quality PBL in their K-12 years. They gain not only understanding and success skills but also confidence in their ability as independent learners and a greater sense of their own efficacy and power.

PBL is transformative for teachers and schools, too, as they create real-world connections to learning, change school culture, and guide students to successfully complete high-quality projects. And teachers who use PBL regularly can experience  “the joy of teaching,” which they may not – make that likely will not – in a test-prep, drill-and-kill environment.

You’ll notice I use the term “high-quality” twice in the above, which points to a real concern we have at BIE. We don’t want PBL to become yesterday’s news, another education fad for which much is promised and little delivered. This is why BIE developed and promotes the Gold Standard PBL model: to help ensure PBL’s place as a permanent, regular feature of 21st century education for all students.

If it’s not done well, I see PBL facing three dangers:

1. Unprepared Teachers & Lack of Support
Teachers who are not prepared to design and implement projects effectively will see lackluster student performance and face daunting classroom management challenges. Shifting from traditional practice to PBL is not a simple matter of adding another tool to a teacher’s toolbox. PBL is not just another way to “cover standards” that’s a little more engaging for students. PBL represents a different philosophy about what and how students should learn in school, and many teachers and school leaders do not yet realize its implications. It was born in the progressive education movement associated with John Dewey, with more recent ties to constructivism and the work of Jean Piaget. Adding to this situation is the fact that most teachers teach the way they were taught, and did not experience PBL when they were students – so they don’t have a vision for what it can be.

Schools and districts need to provide teachers with opportunites for extensive and ongoing professional development, from workshops provided by experts (like BIE’s) to follow-up coaching, to work in their professional learning communities. Policies around grading, pacing guides, benchmark assessments, and more will need to be re-examined. It also means having longer class periods or blocks of time for project work, and rearranging how students are assigned to classrooms to allow for shared students for secondary-level multi-subject projects. And – I can’t stress this enough – teachers will need LOTS of time to plan projects and reflect on their practice. This means changing school schedules to create collaborative planning time, re-purposing staff meetings, perhaps providing (paid) time in the summer, and finding other creative solutions. All of this is a tall order, I realize, but these are the kinds of changes it will take for PBL to stick.

2. PBL-Lite
Many teachers and schools will create (or purchase from commercial vendors) lessons or activities that are called “project-based” and think they’re checking the box that says “we do PBL” – but find little change in student engagement or achievement, and certainly not a transformation. I’ve been seeing curriculum materials offered online and in catalogs that tout “inquiry” and “hands-on learning” that, while better than many traditional materials, are not really authentic and do not go very deep; they do not have the power of Gold Standard PBL. (For example, I’ve seen social studies “projects” from publishers that have kids writing pretend letters to government officials – instead of actually taking action to address a real-world issue – and math “projects” where students go through a set of worksheets to imagine themselves running a small business, instead of actually creating a business or at least an authentic proposal for one.)

With materials that are PBL-lite, we might see some gains in student engagement, and perhaps to some extent deeper learning; many of these materials are in fact better than the traditional alternatives for teaching the content. But the effects will be limited.

3. PBL Only for Special Occasions or Some Students
PBL might be relegated to special niches, instead of being used as a primary vehicle for teaching the curriculum – or being provided equitably for all students. I’ve heard about really cool projects that were done in “genius hours” or “maker spaces” or Gifted and Talented programs, or by A.P. students in May after the exams are over… but most students in the “regular program” did not experience PBL. Or schools might do powerful school-wide projects that do involve all students once a year or so, but the teaching of traditional academic subject matter remains unchanged. If this happens, the promise of PBL to build deeper understanding, build 21st century success skills, and transform the lives of all students, especially those furthest from educational opportunity, will remain unfulfilled.

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Project-based Learning Needs More Learning (Gisèle Huff)

Gisèle Huff is the executive director of the Jaquelin Hume Foundation. This post appeared on Flypaper, August 3, 2016

After almost eighteen years in the field of education, I have become convinced of the need to transform the way our children learn so that they can confront the unknowable challenges of the twenty-first century. I applaud any effort aimed at changing the mindset of those involved in the education system so that they can leave behind the traditional twentieth-century paradigm, which was (and in most places still is) an industrial model. Today’s enthusiasm for project-based learning (PBL) fits into the paradigm-shifting category, helpfully emphasizing that we learn best by doing. As a complete educational philosophy or strategy, however, it falls short on many fronts.

At some level, doing must be based on knowing. Yet in almost every PBL model that I’ve observed—Summit Public Schools being the main exception—little or nothing is said about the acquisition of knowledge. Instead, these models emphasize the completion of the project, and whatever knowledge students may actually acquire seems incidental and not clearly assessed. Of course, it’s true that knowledge alone is insufficient for today’s economy. Skills and dispositions must be developed in the learner for content to be relevant and engaging. But it is that “content” (a.k.a. knowledge) that students must master in order to apply it to hands-on projects. There is no need to sacrifice the rigor of content. Only its delivery and assessment must be changed to move from Carnegie units and seat time to competency-based learning.

The second problem with PBL as the main vehicle for students’ learning experience is that it is not nearly as personalized as its adherents would have us believe. One of the big problems that personalized learning seeks to solve is the “Swiss cheese” problem.  Because we all learn differently, moving along at a one-size-fits-all pace means that slower students are left with big gaps of knowledge and skills—gaps that will come back to haunt them later on. That is of particular concern when PBL occurs at the elementary level, when youngsters are building their knowledge base.

When PBL is deployed, knowledge acquisition is driven by the demands of a given project. The object may be “deeper learning,” but the outcome is definitely narrower, potentially excluding other critical knowledge and skills. This should be solvable, yet the PBL instructional models make no specific reference to mastery. In other words, students can complete a project without mastering the skills in that project or the knowledge underlying its successful completion.

PBL also suffers from a significant “free rider” problem. Because most PBL schools have students work in groups and do little tracking of individual performance, some students naturally coast on the work of others. In his five-minute “commencement speech” on the Getting Smart website, Tom Vander Ark encourages listeners to develop skills in team leadership and project management in order to succeed in the new economy. But each team has only one leader and one manager. Where does that leave the other members? In Most Likely to Succeed, a film focused on the largely PBL-based High Tech High, one of the two main students takes over a project that he has obsessed over and then fails to complete it in time. Somewhere along the line, the classmates who were once part of his group disappear. They seemingly abdicated their roles, and it is not clear how they benefited from the experience or how they were able to demonstrate their achievements in order to be assessed. The featured student himself doesn’t even master the knowledge and skills critical to the project! While embracing failure is an important part of a robust learning system, such setbacks should be used to help students revisit and master the requisite competencies. Kids should be provided with more insights into why they failed and what to do about it, so as to increase their likelihood of future success. Failure of core knowledge and skills is not an option in any effective learning environment.

Finally, PBL relies heavily on highly qualified teachers, so much so that High Tech High now trains its own. That’s well and good for High Tech High, but it isn’t a satisfactory formula for mass adoption of PBL. American public education faces an immense human capital problem that we have not been able to resolve since “A Nation at Risk” sounded the alarm in 1983. We cannot rely on extraordinary people to deliver a twenty-first-century education to all our children; not enough such people exist. We have to deploy strategies that empower the learners and teachers as they are, where they are. In its current form, PBL may work well for kids in boutique school settings. But it offers scant hope of solving education problems on the scale that America needs.

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Why I’m Unsure Project-based Learning Prepares Students for College (Ronnie Estoque)

“Ronnie Estoque is a junior at Seattle’s Cleveland High School. He is a staff writer for Cleveland Publications, an intern at The Seattle Globalist and is interested in pursuing a career in journalism.” This appeared in the Seattle Times, June 16, 2016.

As a junior attending Cleveland High School, I am slowly approaching the arduous process of college applications. This has led me to reflect on whether or not Cleveland has prepared me for college-level work.

In the fall of 2010, Cleveland became a STEM high school with a focus on project-based learning. The newly designed curriculum was meant to emulate a work environment for students while teaching them how to use technology in their school work. Cleveland classes revolve around group work and projects. This unique way of teaching helps students build group-work skills, but does it prepare students for college, where students mostly work independently?

Linda Chen graduated from Cleveland in 2015 and is a freshman at the University of Washington. She enjoyed her time at Cleveland, but now sees one major flaw of project-based learning.

“The one thing I hated was that they (teachers) didn’t enforce student accountability during projects,” Chen said. “Most of the time it was me just doing all the work and someone else taking the credit.”

Group projects, in other words, don’t accurately reflect students’ individual knowledge and, more often than not, the students who work hard and complete their portion of projects also have to do more work to make up for the students who aren’t pulling their weight.

Kiet Sam also graduated in 2015 and is a freshman at the University of Washington majoring in computer science. Sam describes in stark contrast his college-level and the project-based learning at Cleveland.

“In college, almost all my work is completed independently.” Sam said. “Depending on your major there may be more projects, but in general, college is mostly to measure a student’s individual ability to perform.”

Cleveland students are judged on their individual knowledge through tests, but not as frequently as other high schools that don’t use project-based learning. Catherine Brown, the School of Life Sciences principal at Cleveland, said she thinks project-based learning has been good for the school.

Before, there were small pockets of success among the student population,” Brown said. “Now success is the new norm.”

And there’s evidence that the changes at Cleveland have made a difference. According to the state Office of Superintendent of Public Instruction, only 17 percent of 10th-graders at Cleveland met state standards for math in the 2009-10 school year. During the 2013-14 school year, that number dramatically increased to more than 80 percent.

Cleveland teacher Steve Pratt, who has taught at the school for 10 years, said the implementation of STEM and project-based learning at Cleveland has also led to a drastic change in student culture. According to Pratt, before STEM and project-based learning, students weren’t as engaged and eager to learn in class. Now, he sees more students striving to take their work more seriously.

“It has done great things for Cleveland even though there are still some things that need to be improved,” Pratt said.

Pratt is one of the teachers who enforces student accountability. In his classes, students can “fire” their group members during projects. Pratt holds a high standard for his students’ group work contributions, but not all Cleveland teachers do the same. He also believes that it can be difficult for students to adjust to project-based learning if they’re coming from a conventional style of teaching, and students can quickly fall behind in the workload. I believe more teachers, like Pratt, should hold students to higher standards.

While project-based learning, along with STEM, has done great things for Cleveland as a whole, I worry that many students won’t be as prepared for college as they need to be. I believe that more teachers at Cleveland need to hold students more accountable for the roles they play in projects. By holding students to higher standards during group projects, teachers will be able to teach them more about responsibility, time management, and prioritization.

Students like Chen and Sam, who do their share of project work — and more — are doing fine in college, although Chen said the adjustment to individual work was tough at first. I am concerned about the students who are piggybacking their way through Cleveland’s system. Those are the ones who will suffer most when they get to college. This worries me, as I also have been a student who has had to do the work of peers who didn’t do their share.

What will happen to them?

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Hype on Steroids: Self-Driving Cars and School Technologies

A full week of mainstream and social media swept across the nation about the death of a Tesla car owner killed in Florida using the self-driving option. With the auto-pilot function turned on, the Tesla driver collided with a tractor-trailer and became the first known fatality in the industry’s surge to produce self-driving cars. Google and Tesla and 30 other companies (e.g., Honda, Ford, GM,Toyota) compete for what is hyped as the “next big thing”; such cars, they claim, will “disrupt” the century-old personal transportation market.

A Morgan Stanley Blue Paper announced in 2013:

Autonomous cars are no longer just the realm of science fiction.They are real and will be on roads sooner than you think. Cars with basic autonomous capability are in showrooms today, semi-autonomous cars are coming in 12-18 months, and completely autonomous cars are
set to be available before the end of the decade

Tesla’s founder, Elon Musk said the self-driving function on the Tesla meant that “[t]he probability of having an accident is 50 per cent lower if you have Autopilot on” …. “Even with our first version, it’s almost twice as good as a person.”

Skeptics have tossed in their two cents (see here and here; for rebutting skeptics, see here) but when it comes to questioning new technologies in U.S. culture, skeptics are alien creatures.

While the hype pumping up self-driving cars can lead to accidents and deaths, no such serious consequences accompany promoters of technological innovations who have promised increased teacher efficiency, improved student achievement, and the end of low-performing schools for the  past half-century.  Need I mention that Google has a “Chief Evangelist for Global Education?”

Nothing surprising about hype (even when  injected with steroids)  in a consumer-driven, highly commercial society committed to practicing democracy. Hype is hype either for self-driving cars or for school technologies. Parsing the hyped language and images becomes important because real-life consequences flow from these words and pictures.

 

Consider these advertisements championing new technologies since the 1950s.

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Over-stated claims are  commonplace when it comes to pumping up the benefits of the “next big thing.” Early adopters of new technologies discover the bugs in new hardware and software soon enough.  Glitches, however, seldom dissuade this crowd from peering around the corner for its replacement.

Does hype serve any social and political purpose other than to stimulate consumers to buy the product? I believe it does.

1. Over-the-top statements strengthen the popular belief that change is “good” for individuals and society overall. Not only is change “good” for Americans but in the technology industry and culture of school reform, change morphs into improvement. In Silicon Valley argot, “making the world a better place,” means a new product, a new service, a new app will improve life (a parody of this oft-repeated phrase can be seen here)

Equating change with improvement is a cognitive error. Surely, an improvement implies a change has occurred but because the change has happened, improvement does not necessarily follow. A moment’s thought would quickly squelch equating change with improvement. Stepping on a scale and seeing that you have gained five pounds while on a low-carb diet is clearly a change but not, in your view, an improvement. Think of a divorce in a family. The spouse initiating the divorce sees the split as a change for the better but for the others involved including children, few would see it as an improvement with two homes, living with different parents or weekend visits. Change occurs constantly but improvement is in the mind of the beholder.

Consider whether a new app that has a “smart” button and zipper that alerts you if your fly is down or another app that locates rentable yachts are improvements to one’s life (see here). To those individuals who buy and download these apps they appear as improvements promising a better life but to others, they appear as trivial indulgences that hardly make the “world a better place.”

School reformers who believe that changes lead to improvements in teaching and learning, for example, often refer to gains in student test scores, increases in teacher productivity (i.e., less time to do routine tasks), and other measurable outcomes as evidence of  better schooling. Reformers holding divergent values (e.g., higher civic engagement, student well-being), however, would differ over whether test scores, et. al. are improvements. Quite often, then, the definition of improvement depends upon who does the defining and the values they prize.

2. Hype over new technologies raises questions about the existing institution’s quality.  Consider current health care where millions still lack health insurance, emergency rooms are over-crowded, wait time to see specialists physicians increases, and patients get less and less time when they do see their doctors. Hyping the “next big thing” in medical technology becomes a direct criticism of existing health care. Think of “hospital in a box,” or patient kiosks placed in pharmacies, where ill people go to the kiosk for video conferencing with one or more doctors about what ails them. Such new technologies raises implicit questions about access to adequate health care and to what degree the relationship between doctor and patient is important in improving health.

Or consider the thousands of lives lost on the nation’s roads to accidents and human error in driving. Self-driving cars, once prevalent on the nation’s highways will, promoters claim, dramatically reduce the 32,000 deaths in car accidents while increasing worker productivity since with self-driving cars owners can complete other tasks that heretofore would have not been done. Self-driving cars raises anew questions about the lack of adequate public transportation and a society committed to one-person-per car.

And hype for technological innovations in schools for “personalized” or “adaptive” learning pictures the existing system as factory-like  whole-class, age graded, teacher-dominated instruction that ignores, even neglects individualized lessons, student-centered learning, and reconfigured classrooms.

3. Hype shrinks the time to show results to immediately. Most software products in the educational arena, for example, take time for teachers and students to grasp, understand, and use them in lessons. Education proceeds by short not long steps. Hyping these products leave the distinct impression that unless the desired result hasn’t happened in a few months then someone (note the beginnings of blame) has failed to do it right. And it ain’t the software developer.

4. Software and hardware developers come to believe their own hype. The cliche of “drinking the Kool-Aid–applies here and such self-deception occurs. And when it does, CEOs of start-ups and other companies start making short-cuts to get products into schools and stores. Those short-cuts increase software glitches, highten arguments with consumers of the products, and diminish faith in the innovation.

These outcomes of hype are not justifications for its ubiquity. They  help me understand the role that it (and its cousin, “magical thinking”) perform in U.S. society.

 

 

 

 

 

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How To Do Adaptive Learning Right (Keith Devlin and Randy Weiner)

Keith Devlin is (@profkeithdevlin) Co-founder & Chief Scientist at BrainQuake and a mathematician in the Stanford University Graduate School of Education. Randy Weiner (@randybw15) is Co-founder & CEO at BrainQuake, a former teacher, & Co-founder and former Chair of the Board at Urban Montessori Charter School in Oakland, CA.

This opinion piece appeared in EdSurge, June 30, 2016.

As one variant of the saying goes, if your strength is using a hammer, everything can look like a nail. Examples abound in attempts to use new technologies to enhance (if not “transform”, or even “disrupt”) education. Technologists who have built successful systems in other domains—and who frequently view education as just another market in which to apply their expertise—often doom their project to fail at the start, by adopting a narrow and outdated educational model.

Namely, they see education as the provision of facts, techniques, and procedures to be delivered and explained by instruction and then practiced to mastery. Their role, then, is to bring their technological prowess to bear to make this process more efficient. In most cases they can indeed achieve this. But optimizing a flawed model of education is not in the best interests of our students, and from a learning outcomes perspective may make things worse than they already are.

In the case of adaptive learning, education commentator Audrey Watters gave examples of how things can go badly wrong on her blog. “Serendipity and curiosity are such important elements in learning,” she asks. “Why would we engineer those out of our systems and schools?” More recently, Alfie Kohn provided another summary of the numerous reasons to be skeptical of education technology solutions.

Watters’ bleak future will only come to pass if the algorithms continue to be both naïvely developed and naïvely applied, and moreover, in the case of mathematics learning (the area we both work in) applied to the wrong kind of learning tasks. Almost all the personalized math learning software systems we have seen fall into this category. But there is another way—as our work, and a thorough review by a third-party research organization—has shown.

We both work in the edtech industry and have a background in education. One of us is a university mathematician who spent several years on the US Mathematical Sciences Education Board and is now based in Stanford University’s Graduate School of Education, the other an edtech veteran who is a former teacher and who co-founded Urban Montessori Charter School.

We are both very familiar with the common “production line” model of education, and recognize that it not only appeals to many (perhaps most) technologists, but in fact is a system that they themselves did well in. But collectively, the two of us have many years of experience that indicates just how badly that approach works for the vast majority of students.

Last year, with funding from the Department of Education’s Institute for Educational Sciences, our company, BrainQuake, spent six months designing, testing and developing an adaptive engine to supply players of our launch product, Wuzzit Trouble, with challenges matched to their current ability level. We were delighted when classroom studies conducted by WestEd showed that the adaptive engine worked as intended (i.e., kept students in their zone of proximal development), straight out of the gate.

We developed the game based on a number of key insights accumulated over many years of research by mathematics education professionals that should be applicable to all edtech developers—even those who are not building math tools.

Experience Over Knowledge

First, the most effective way to view K-8 education is not in terms of “content” to be covered, acquired, mastered (and regurgitated in an exam) but as an experience. This is particularly (but not exclusively) true for K-8 mathematics learning. Mathematics is primarily something you do, not something you know.

To be sure, there is quite a lot to know in mathematics—there are facts, rules, and established procedures. Imagine the skills expected of a physician. None of us, we are sure, would want to be treated by someone who had read all the medical textbooks and passed the written tests but had no experience diagnosing and treating patients. And indeed, no medical school teaches future physicians solely by instruction, as any doctor who has gone through the mandatory, long, grueling internship can attest.

In the case of math, the inappropriateness of the classical, instruction-practice-testing dominated model of education has been made particularly acute as a result of the significant advances made in the very technology field we are working in. (Advances we wholeheartedly applaud. Our beef is not with technology—we love algorithms, after all—but with applying it poorly.) In today’s world, all of us carry around in our pockets a device that can execute almost any mathematical procedure, much faster and with greater accuracy than any human. Your smartphone, with its access to the cloud (in particular, Wolfram Alpha), can solve pretty well any university mathematics exam question.

What that device cannot do, however, is take a real world mathematical problem and solve it. To do that, you need the human brain. In order to do that, the human brain has to acquire two things, in particular: a rich and powerful set of general metacognitive problem solving skills, and a more specific ability known as mathematical thinking (a component of which is known as number sense, a term that crops up a lot in the K-8 math education world, since the development of number sense is the first key step toward mathematical thinking).

Human Adaptivity

Another key insight that guided the design of our adaptive engine is that the main adaptivity is provided by the user. After all, the human being is the most adaptive cognitive system on the planet! With good product design, it is possible to leverage that adaptivity.

Most “adaptive” math algorithms will monitor a student’s progress to select the next problem algorithmically. But it is important that these puzzles allow for a wide range of of solutions and a spectrum of “right answers,” leaving the student or teacher in full control of how to move forward and what degree of success to accept. (Of course, such an approach is not possible if the digital learning experiences are of the traditional math problem type, where the problem focuses on one particular formula or method and there is a single answer, with “right” or “wrong” the only possible outcomes.)

Indeed, students still need to grasp the basic concepts of arithmetic, understand what the various rules mean, and know when and how the different procedures can be applied. But what they do not need is to be able to execute the various procedures efficiently in a paper-and-pencil fashion on real world data.

Today’s mathematical learning apps can—and should—focus on the valuable 21st century skills of holistic thinking and creative problem solving. The mastery of specific procedures should be skills that a student acquires automatically, “along the way,” in a meaningful context of working on a complex performance task—an outcome every one of us knows works from our own experience as adults.

Breaking the Symbol Barrier

Mastery of symbolic mathematics is a major goal of math education. But as has been shown by a great deal of research stretching back a quarter of a century, the symbolic representation is the most significant reason why most people have difficulty mastering K-8 grade level math—the all-important “basics.” Almost everyone can achieve a 98 percent success rate at K-8 math if it is presented in a natural-seeming fashion (for example, understanding and perhaps calculating stats at a baseball game), but their performance drops to a low 37 percent if presented with the same math problems expressed in textbook symbolic form.

Well-designed technologies that take advantage of some unique affordances of a computer or tablet can help obliterate this historical impediment to K-8 mathematics proficiency. Students should be able to explore problems on their own until they discover—for themselves—the solution. They don’t require instruction, and they don’t need anyone to evaluate their effort. Students should get instant feedback not in the form of “right” or “wrong,” but information about how their hypotheses varied from their actual experience and how they might revise their strategy accordingly.

An analogy we are particularly fond of is with learning to play a piano (or any other musical instrument). You may benefit greatly from a book, a human teacher, or even YouTube videos, but the bulk of the learning comes from sitting down at the keyboard and attempting to play.

What could be a better example of adaptive learning than that? Tune too easy? Try a harder piece. Too difficult? Back off and practice a bit more with easier ones, or break the harder one up into sections and master each one on its own at a slower pace, and then string them all together. The piano is not adapting. Rather, its design as an instrument makes it ideal for the learner to adapt.

A well-designed math tool should be an instrument on which you can learn mathematics, free from the Symbol Barrier. Now imagine we present a student with an orchestra of instruments.

We think this kind of approach is the future of adaptive learning in math and believe we, the edtech community, should choose to go beyond the “low hanging fruit” approaches to adaptive learning that the first movers adopted.

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Draining The Semantic Swamp of “Personalized Learning”–A View from Silicon Valley (Part 1)

No surprise that a catch-phrase like “personalized learning,” using technology to upend traditional whole group  lessons, has birthed a gaggle of different meanings. Is it  updated “competency-based learning?” Or “differentiated learning” in new clothes or “individualized learning” redecorated?  (see here, here and here). Such proliferation of school reforms into slogans is as familiar as photos of sunsets. “Blended learning,” “project-based teaching,” and “21st Century skills” are a few recent bumper stickers–how about “flipped classrooms?”– that have generated many meanings as they get converted by policymakers, marketeers, researchers, wannabe reformers, and, yes, teachers into daily lessons.

For decades, I have seen such phrases become semantic swamps where educational progressives and conservatives argue for their version of the “true” meaning of the words. As a researcher trained in history, since the early 1980s, I have tracked policies as they get put into practice in schools and classrooms.  After all, the first step in science is to observe systematically the phenomenon or as Yogi Berra put it: “You can observe a lot by watching.” The second step is to describe and tell others what was seen and explain it.

Over the past few months, I have visited eight schools and 17 teachers in “Silicon Valley,” that near-mythical stretch of the Bay area in Northern California encompassing San Jose, San Francisco, and Oakland and their environs. I went into schools and classrooms that administrators, policymakers, researchers, and others identified for me as “best cases,” or exemplars of integrating use of technology into daily lessons. Many, but not all, told me that they had integrated technology into their lessons to “personalize learning.”

The questions I asked myself while observing a class was simply: What are teachers and students doing when computer use is integrated into a lesson? Toward what ends is such use aimed?

Teachers and principals invited me to observe.  There were no tours or group visits. I went to each school and talked with principals, various teachers, and read online documents describing the school. I sat in 90-minute lessons, listened to students in and out of class–even shadowing a student at one school for a morning–and took copious notes.  I sent drafts of my classroom observations to teachers to correct any errors in facts that I made. Then I published accounts of my observations  in my blog in March, April, and May 2016.  Although I am far from finished in this project, now is the time for that second step (see above). I need to make sense of  what I saw at the epicenter of technological optimism. So this is an initial pass at figuring out what I saw as I sloshed through the semantic swamp of  “personalized learning.”

The “Personalized Learning” spectrum

When I visited the schools, administrators and most teachers told me that they were “personalizing learning.” What I saw, however, in classrooms and schools was a continuum of different approaches–which I call the “personalized learning spectrum”–that encompassed distinct ways of implementing technology in lessons to reach larger purposes for schooling. Let me be clear, I value no end of the spectrum (or the middle) more than the other. I have worked hard to strip away value-loaded words that suggest some kinds of “personalized learning” are better than others.

At one end of the continuum are teacher-centered lessons and programs within the traditional age-graded school using behavioral approaches that seek efficient and effective learning to make children into knowledgeable, skilled, and independent adults who can successfully enter the labor market, thrive, and become adults who help their communities. These approaches (and ultimate aims for public schools) have clear historical underpinnings dating back nearly a century.

At the other end of the continuum are student-centered lessons and programs that seek student agency and shape how children grow cognitively, psychologically, emotionally, and physically. They avoid the traditional age-graded arrangements that they believe have deadened learning for over a century. Their overall goals of schooling are to convert children into adults who are creative thinkers, help out in their communities, enter jobs and succeed in careers, and become thoughtful, mindful adults. Like the other end of the spectrum, these approaches have a century-old history as well.

And, of course, on this spectrum hugging the middle are hybrids mixing behavioral and cognitive approaches aimed at turning children into adults who engage in their communities, are creative, thoughtful individuals who succeed in the workplace.

Such a spectrum has been around for many decades with different names such as “Progressive-to-Traditional,” “Teacher-centered to Student-centered, etc. A glance at the rear-view mirror about the history of these continua helps me make sense of what I saw in my observations..

Looking back a century

What today’s reformers promoting “personalized learning” have to remember are their yesteryear cousins among Progressive reformers a century ago. Then, these reformers wanted public schools to turn children and youth into thoughtful, civically engaged, whole adults. Those early Progressives drank deeply from the well of John Dewey but ended up following the ideas of fellow Progressive Edward Thorndike, an early behaviorist psychologist and expert in testing.*

If one wing of these early progressives were pedagogical pioneers advocating project-based learning, student-centered activities, and connections to the world outside of the classroom, another wing of the same movement were efficiency-minded, “administrative progressives,” who admired the then corporate leaders of large organizations committed to both efficiency and effectiveness–Standard Oil, U.S. Steel, General Motors. Thorndike at Columbia University’s Teachers College, Ellwood P. Cubberley at Stanford and other academics, in alliance with the new field of educational psychology, borrowed heavily from business leaders. They counted and measured everything in schools and classrooms under the flag of “scientific management.” They reduced complex skills and knowledge to small chunks that students could learn and practice. They wanted to make teachers efficient in delivering lessons to 40-plus students with the newest technologies of the time: testing, film, radio. They created checklists for teachers to follow in getting students to learn and behave. They created checklists for principals to evaluate teachers and checklists for superintendents to gauge district performance including where every penny was spent.

A century ago, this efficiency-minded, behaviorist wing of the progressive movement overwhelmed the pedagogical progressives passionate about students developing and using a range of cognitive and social skills. Thorndike trumped Dewey.

Now in 2016 behaviorists and believers in the “whole child” wear the clothes of school reformers and educational entrepreneurs. They tout scientific studies showing lessons tailored for individual students produce higher test scores than before, or that project-based learning creates independent, creative, and smart students.

What exists now is a re-emergence of the efficiency-minded “administrative progressives” from a century ago who now, as entrepreneurs and practical reformers want public schools to be more market-like where supply and demand reign, and more realistic in preparing students for a competitive job market. Opposed are those who see schools as places to create whole, knowledgeable human beings capable of entering and succeeding in a world far different than their parents faced. The struggle today is between re-emergent, century-old wings of educational progressives. It is, then, again a family fight.

Part 2 will place some of the classroom lessons and schools I observed and have documented elsewhere along that continuum.

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*A current dust-up between Progressives and Conservatives over school reform (see Rick Hess’s summary of back-and-forth bloggers here) misses entirely the intra-reformer struggle among Progressives a century ago and how the conservative, efficiency-driven wing (e.g., Edward Thorndike, et. al.) of those early Progressives triumphed over the liberal, student-centered, reconstructionist wing (e.g., John Dewey, George Counts, et. al.) who sought to make  schools student-centered and agents of societal reform. David Tyack tracked this split fully in The One Best System and with co-author Elisabeth Hansot in Managers of Virtue. The split that Hess and others see today is hardly new. It is a resurgence of that old struggle among Progressives but now reincarnated in an age of standards, testing, and accountability. The  split among current school reformers is over  both equity and efficiency with one wing labeled “Progressives” and the other “Conservatives.” Current “Progressives,” imbued with social justice, want schools to be agents of social and political change and student-centered. They use both behaviorist and cognitive approaches to “personalize learning.”  “Conservatives” want contemporary reform policies (e.g., charters, standards and accountability) to be sustained because they advance equity and blend technology to create both student- and teacher-centered experiences. They, too, want learning to be “personalized” and create  both behaviorist- and cognitive-driven lessons.  Such clashes  track earlier differences among reformers a century ago. The conflict today, as then, tries to answer the age-old question: Is the job of public schools in a democratic and capitalist-driven society to solve larger economic, social, and political problems that the nation faces or focus on building whole human beings who can thrive and succeed in a highly competitive society?

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Filed under how teachers teach, technology use