Conceptual vs. Procedural Math at Mastery charters


“Maths” by Chris de Kok is licensed under CC BY 2.0

There was an interesting recent the74 piece on a Philadelphia charter organization, Mastery, which takes low performing schools and works to “turn them around.”


Embedded within this article is the implication that a shift to a focus on the teaching of conceptual math, rather than “rote” procedural teaching, led to a swift downturn in math scores.

“So this year, the network began reintroducing teaching techniques that had been a staple at Mastery schools for years, while seeking a middle ground between no excuses and restorative practices. It’s a ‘journey of trying to find out what’s the right mix,’ Gordon said.

Specifically, the network is reintroducing procedural math instruction, which focuses on rote instruction like memorization and repetition.”

It seems worth digging into this supposition a bit more.

Is Mastery’s downturn in math scores due to the failure of conceptual math in general as a pedagogical approach? Or is it a failure of the network to attract and train teachers who can teach this type of math more effectively?

Or is it a failure in the assessments that were used as a reference? Or was it that conceptual math takes longer to “stick” and pay dividends? Or was it a failure of the curriculum they used to move in a more conceptual direction? . . .

Low floor, high ceiling, wide walls in ELA classrooms

Have you ever heard of a “low floor (or threshold), high ceiling” task?

I’ve stumbled across it over the last few years in the math realm, such as in articles by Jo Boaler, or in tasks by Dan Meyer, and I found it intriguing as a general framework for lesson and unit planning. Finding ways to include both lower and higher performing students in rigorous academic instruction is something I think a lot about, and this seemed worth exploring. However, I work primarily in special education and ELA, not math, so I was having trouble generalizing.

So I did a little more digging. Here’s what I found:

The concept of low floor, high ceiling was first formulated in the 1970s by Seymour Papert, a professor at MIT heavily influenced by Piaget, as a design principle for a programming language called Logo. The idea was to make programming accessible to young children, while simultaneously being usable at a more complex level by adults.

A robot turtle was developed to provide concrete access to kids for using the programming language.

By Valiant Technology Ltd., CC BY-SA 3.0,
By Valiant Technology Ltd., CC BY-SA 3.0


Mitchel Resnick, another professor at MIT, added the useful concept of “wide walls” to the design metaphor of a room:


When discussing technologies to support learning and education, my mentor Seymour Papert (who, sadly, passed away last month) often emphasized the importance of “low floors” and “high ceilings.” For a technology to be effective, he said, it should provide easy ways for novices to get started (low floor) but also ways for them to work on increasingly sophisticated projects over time (high ceiling). With his Logo programming language, for example, kids could start by drawing simple squares and triangles, but gradually create more complex geometric patterns over time.

But the most important lesson that I learned from Seymour isn’t captured in the low-floor/high-ceiling metaphor. For a more complete picture, we need to add an extra dimension: wide walls. It’s not enough to provide a single path from low floor to high ceiling; we need to provide wide walls so that kids can explore multiple pathways from floor to ceiling.

Why are wide walls important? We know that kids will become most engaged, and learn the most, when they are working on projects that are personally meaningful to them. But no single project will be meaningful to all kids. So if we want to engage all kids—from many different backgrounds, with many different interests—we need to support a wide diversity of pathways and projects.

. . . Our ultimate goal is to help all kids develop their thinking, develop their voices, and develop their identities. None of that will happen unless we continually ask: Who are we including? Who are we excluding? And how can we provide everyone—everyone—with opportunities for exploring, experimenting, and expressing themselves?

Resnick offers some further advice for designers in an MIT paper, “Some Reflections on Designing Construction Kits for Kids” (bearing in mind this is for construction kits, not for academic content):

  • Design for Designers
  • Low Floor and Wide Walls
  • Make Powerful Ideas Salient – Not Forced
  • Support Many Paths, Many Styles
  • Make it as Simple as Possible – and Maybe Even Simpler
  • Give People What They Want – Not What They Ask For
    • “Often, designs with well-chosen parameters are more successful than designs with fully adjustable parameters” ← I like this quote. This connects to the idea of constraints.
  • Invent Things That You Would Want to Use Yourself
    • In ELA, this translates into assigning tasks that you would want to do yourself. For writing tasks, this most likely would result in something you’d actually enjoy reading.
  • Iterate, Iterate – then Iterate Again

This is all well and good if you’re designing a gadget or a programming language, and it kinda makes sense in math in the sense of a well-designed problem, but what does “low floor, high ceiling” mean in terms of designing lessons or units in ELA? This is where it gets murkier. Does a concept that applies to design have a translation to academic literacy instruction?

Here’s my thoughts on that question:

Usually in ELA we are engaged with texts. A rich text has multiple layers of meaning and ideas well-worth exploring, but the level of abstraction and demands of the language can be a barrier for many students. We can therefore think of the text itself as the “high ceiling” for many lessons (I think, in any case, I could certainly be off base on this).

In many cases, therefore,  the “high ceiling” aspect has already somewhat been defined in an ELA lesson (assuming you are studying rich texts together as a class).

So then, how you do you provide a “low floor” for all of your students to a complex text? And more abstractly, how do you support a wide diversity of pathways or perspectives?

Designing Scaffolded Tasks and Activities

What comes first to mind are the tasks and activities that a teacher designs to prepare their students for understanding the text, for interacting with the text, and for responding to the text. For an exemplar of this type of scaffolding, I highly recommend taking a look at Lesson 2 from Stanford’s Understanding Language unit on persuasion, specifically at how they scaffold student understanding of the Gettysburg address through multiple readings that are even fun. Close reading instruction will readily fail when a teacher simply asks students to re-read a complex text multiple times with no varied and scaffolded forms of engagement.

Designing Provocative Questions

I think the most critical consideration for “wide walls” and spanning from low floor to high ceiling is what sort of questions you plan. For example, for an 8th grade unit I co-designed on the topic of segregation, we generated a series of questions, ascending from elemental (“What is segregation? What is integration?”) to provocative and open-ended: (“NYC schools are largely segregated by race and class. Is it possible to provide all children an excellent education in a segregated school system? If so, how? If not, why not and what steps must we take to fix this?”). That final question represents the cumulative question for the unit. There’s certainly room for different ways of expressing knowledge based on a student’s own perspective on the topic. This could be via an essay, an action plan, a presentation, or a socratic discussion, as a few possible examples.

A critical element to both “low floor” and “high ceiling” is designing units and lessons around a provocative question. For example, watch this video of master teacher Sarah Wessling Brown modeling a high school ELA lesson on monsters (Easter egg: see if you can spot me in the background). She asks the provocative question, “What do monsters teach us about human nature?” and then designs engaging activities to engage students in the texts and knowledge they need to explore it.

I think questions like these embody what LFHCWW design is all about. They provide both engagement, and therefore access, but have ample room for sophistication and complex thinking.

One mistake some teachers make is to assume that a “higher order” question is beyond the purview of their struggling students, and they try to dumb down their questions. My advice is to worry less about the “cognitive level” of a question, and more about the language that you use and the manner in which you phrase it. Language and phrasing can either present a barrier to understanding, or a scaffold. A precisely constructed question provides the initial direction and language that students will need.

We haven’t even really gotten started

But this post is getting overlong. How do you think the concept of a task with low floor, high ceiling, and wide walls can apply in ELA classrooms? Share, and let’s build a common understanding of what this might mean in our lesson and unit design.

Slouching Towards Progressivism


You would not likely mistake me for a Dewey eyed constructivist. I get kind of dogmatic against the teaching of skills over literary content, for example, though I’m not quite so hard line against progressive instructional precepts as some, such as Harry Webb (my favorite ed curmudgeon. Read his blog regularly). If you’re really bored, you can read some of my circuitous expositions against constructivism here or here for further confirmation of my anti-constructivism.

But I’m moving into my 6th year of teaching special education, and my thoughts on progressive instructional approaches have shifted. Let me explain why, then let’s examine three articles that might provide some corroboration of my reasoning.

Coro New York ELC: Experiential Learning at its Finest

I took part in the first cohort of Coro New York Education Leadership Collaborative last year. The Coro methodology is experiential based, and in this sense progressive. I’ll admit I was skeptical at first when I sniffed constructivist signifiers at the outset of the program in words such as “self-discovery” and “skills.”

But after experiencing how effective well structured experiential group learning could be, I shed some of my cynicism. My co-teacher and I later brought the methodology to our own students and planned what we called an “Inquiry Day” on the issue of segregation (you can see the full unit we developed here), providing our students an opportunity to learn directly from group-guided interviews with inspiring thought leaders and activists. This experience for my students was just as powerful as it had been for me as an adult on Coro ELC strategy days.

I work with students who are often so accustomed to failure that they have long given up putting forth effort. Finding methods to include and engage them are just as critical as providing them with essential domain-specific knowledge. This is why I have shifted in my thinking.

Supporting Ideas for Embracing Progressive Elements of Instruction

Idea #1: “You do, y’all do, we do”

Elizabeth Green, one of the sharpest minds in the realm of education journalism, recently published a book, “Building a Better Teacher.” In a controversial sample from the book on NY Times, “Why Do Americans Stink at Math?,” Green presents a challenge to the traditional lesson format many teachers use. The “I do, we do, you do” format (something I utilize in my own lesson plan template), stems from principles of direct and explicit teaching: the teacher models and demonstrates, the students practice with guidance and feedback, and then practice is conducted independently.

How could you teach math in school that mirrors the way children learn it in the world? That was the challenge Magdalene Lampert set for herself in the 1980s, when she began teaching elementary-school math in Cambridge, Mass. She grew up in Trenton, accompanying her father on his milk deliveries around town, solving the milk-related math problems he encountered. . . .

She knew there must be a way to tap into what students already understood and then build on it. In her classroom, she replaced “I, We, You” with a structure you might call “You, Y’all, We.” Rather than starting each lesson by introducing the main idea to be learned that day, she assigned a single “problem of the day,” designed to let students struggle toward it — first on their own (You), then in peer groups (Y’all) and finally as a whole class (We). The result was a process that replaced answer-getting with what Lampert called sense-making. By pushing students to talk about math, she invited them to share the misunderstandings most American students keep quiet until the test. In the process, she gave them an opportunity to realize, on their own, why their answers were wrong. . . .

Over the years, observers who have studied Lampert’s classroom have found that students learn an unusual amount of math. Rather than forgetting algorithms, they retain and even understand them [Bold added].

Definitely constructivist elements in play here, which set alarms ringing in anti-constructivists minds. Tom Loveless wrote a scathing rebuttal to combat these constructivist implications.

But this flip from “I do, we do, you do” to “You do, y’all do, we do” is an instructional approach I find very compelling.

The idea of allowing students to process and struggle with something based on their current level of understanding, then slowly unpack those misconceptions and insights via group discussion, is something that I’ve witnessed take place very powerfully in classrooms.

Idea #2: Foster Productive Confusion

In an article by Steve Kolowich, “Confuse Students to Help Them Learn,” there’s support for Magdalene Lampert’s approach to instruction:

“It seems that, if you just present the correct information, five things happen,” he said. “One, students think they know it. Two, they don’t pay their utmost attention. Three, they don’t recognize that what was presented differs from what they were already thinking. Four, they don’t learn a thing. And five, perhaps most troublingly, they get more confident in the ideas they were thinking before.”

“Common wisdom holds that confusion should be avoided during learning and rapidly resolved if and when it arises,” wrote a team of researchers in a paper published earlier this year. While this might be true when it comes to superficial tasks such as memorizing facts and figures, “Confusion is likely to promote learning at deeper levels of comprehension under appropriate conditions.”

In other words: If teachers want students to learn the really important stuff, like comprehending difficult texts and modeling complex systems, they should put their students in confusing situations.

This is where harnessing the power of confusion becomes difficult—and risky. Some students are likely to snap sooner than others. “We still don’t know how soon to rescue them from the confusion,” Mr. Graesser told The Chronicle in an interview, and the right answer undoubtedly varies from student to student. Researchers say that confusing students works only if instructors can track and moderate the confusion.

There’s the rub: Detecting confusion is hard, especially in the moment. So is controlling it. For an instructor standing before a sea of faces, it’s virtually impossible [Bold added].

This caveat at the end is important: it suggests that to balance confusion with success is extremely difficult to achieve. This can explain in part some reluctance to adopting such an approach wholesale for classroom pedagogy. Great teaching is hard. I’ve had the honor of working with some great teachers, and I’ve seen this approach work. I’ve also seen it fail miserably—most especially when I try to implement it with my own students in a self-contained setting.

With students who struggle the most in the classroom, achieving this balance is tricky. We want to “confuse” and challenge our students to unveil their misconceptions, but we also need to engage and motivate them. This is where our next idea comes in.

Idea #3: Make Your Audience Care

In a seemingly unrelated article about making films, some advice from Pixar’s Andrew Stanton stood out to me in relation to this:

Since we’re all natural problem solvers, it brings us great satisfaction to solve problems put in front of us. Contrary to what it might seem, we actually like to work for results rather than be given them, and this goes for watching films, too. Audiences don’t tend to enjoy films with a lot of exposition and over-explanation or over-simplification of plot and character motive, because it takes the fun out of putting the pieces together themselves; it denies them the chance to engage in the story, to participate in it, which, in the end, doesn’t inspire them to care [bold added].

In other words, engaging our students—making them care—could be viewed as part and parcel of allowing them struggle through something before we provide them with any answers. This beautiful struggle occurs when we figure things out on our own. But in a classroom, such struggle must be carefully designed: “The elements you provide and the order you place them in is crucial to whether you succeed or fail at engaging the audience.” It’s not something that just happens. “Discovery” learning must be rightly critiqued as BS. But a well-crafted problem, designed intentionally to surface deep-seated misconceptions and create productive confusion, can be simultaneously engaging and enlightening.

What do you think?

Free Range Children

“Which brings us to the inevitable issue of what will become of my boys. Of course, I cannot answer in full, because their childhoods are still unfolding.

But not infrequently I field questions from parents who seem skeptical that my sons will be exposed to particular fields of study or potential career paths. The assumption seems to be that by educating our children at home and letting them pursue their own interests, we are limiting their choices and perhaps even depriving them. The only honest answer is, Of course we are. But then, that’s true of every choice a parent makes: no matter what we choose for our children, we are by default not choosing something else.

I can report that Fin and Rye both learned to read and write with essentially zero instruction, albeit when they were about eight years old, a year or so later than is expected. They can add and subtract and multiply and divide. I can report that they do indeed have friends, some who attend school and some who don’t, and their social skills are on par with their peers. In fact, Penny and I often hear from other adults that our sons seem better socialized than like-aged schoolchildren. Fin and Rye participate in a weekly gathering of homeschooled and unschooled kids, and Fin attends a weekly wilderness-skills program. In truth, few of their peers are as smitten with bushcraft as they are, and sometimes they wish for more friends who share their love of the wild. But even this is OK; the world is a place of wondrous diversity, and they must learn that theirs is not the only way.”

–Ben Hewitt, “Unschooling: The Case for Setting Your Kids into the Wild” on Outside

Only One Road to Mastery

Statue of Bruce Lee | Chintunglee

A blog I recommend putting into your Feedly or NewsBlur lists (or sign up for the newsletter) is Barking Up the Wrong Tree. Eric Barker provides insights gleaned from research and experts on productivity, leadership, and life fulfillment that are often relevant to the classroom.

In an interview with author Cal Newport about how to become an expert, for example, I found this particular passage interesting, especially in its relation to education:

I think when people want to get better at something the biggest mistake they make is seeking flow. It’s a very enjoyable state. It’s where you’re lost in what you’re doing, you’re applying your skills seamlessly and fluidly, and you feel like you have control. 
But we know from research on how people actually gain expert levels of performance that the actual state in which you’re getting better is one of strain, and that’s different than flow. It’s a state where you actually feel like you’re being stretched. It’s uncomfortable. You’re doing things beyond your current abilities. It’s not fluid. You’re not necessarily lost. Your mind might be saying, “This is terrible. This is terrible. Check your e-mail. This is terrible. What if there is something on Facebook?“ 
We avoid that for the most part, but we know that if you just keep doing what you know how to do already, you’ll hit a plateau almost immediately. So I think the avoidance of strain is the biggest mistake people make in trying to get better.

In terms of education, another way of saying this is that learning, with an eye towards mastery, is not always fun. It requires hard work and going beyond one’s comfort zone.

This is something I’ve written about before in relation to constructivism and the current edu babble about digital natives and 21st century skills. Teachers are under great pressure to magically instill mastery of rigorous academic content in students who may lack essential foundational skills, or don’t yet see any value in education. In general conversations about public education, we all too often infantilize students to the point of subtracting any burden for learning from their shoulders, thereby placing the burden entire on that of their parents or teachers when they fail.

The reality is that in order to go beyond superficial exposure to knowledge and edge towards applicable mastery, students must work hard. And they must not merely work hard in the confines of the classroom, but put in work on their own time.

A simple example of this is mastery of the utterly essential yet hugely complex ability to read. Students might read while in school, but some consider reading a burdensome task that they are unwilling to engage in when not “forced” to. Instead, they opt for activities that require little mental strain, such as Facebook, button mashing video games, facile Hollywood movies, and TV sitcoms. But to become more than a barely proficient reader, in order to become a masterful reader, with an understanding of the world beyond one’s own neighborhood, one must read constantly, one must devour books, sit focused for hours in place, immersed in the struggle with a narrative or informational structure that will, over time and across multiple books, cumulatively, broaden and challenge complacent interpretations and shallow stereotypes of the world.

A great teacher is a gateway to such expansion and challenge, but they cannot substitute for the effort and work which must ultimately come from the student themselves. There is no mastery without hard work.

Right now in the edu sphere there is much talk of instilling “grit” and providing students with the opportunity to learn to “fail.” Indeed. Yet parallel to this conversation, there hovers a mirage of innovative edtech gamification: this idea that if we design the perfect learning experience, students will learn without even knowing that they are learning. They will be fooled by gadgetry and wonder into learning, despite themselves.

Yet all that glitters is not gold. There is only one path to knowledge and mastery — and that is through hard work.

Disagree with me? Great! Provide your rebuttal in the comments, or write your own blog post and post the link! I’m always game for a good debate.

The Power of Edtech: Idolatry and Pragmatism

The Power of Edtech: Idolatry and Pragmatism

(Note: if you have any trouble viewing this post due to its formatting, you can click here to go to the published Google Doc version)
I’ve been thinking a bit lately about technology and social media in education[1], prompted by my attendance at the recent #140edu conference, and conversations I’ve had with other edtech enthusiasts.

I am most decidedly an avid computer user (though I can’t claim geekdom); I am passionate about using open source-based operating systems and believe strongly in self-empowerment through tinkering and problem-solving using command line and code[2]. I am a firm believer in the emerging power of social media to break through traditional barriers between governing entities, businesses, and civil society. I’ve written about developing curriculum using open source methods and the potential it holds for disrupting monopolies by publishing companies, and I believe that technology furthermore holds great potential to break through the isolation of classrooms and connect students and teachers to a more open, self-empowered, and collaborative world.

That said, I also have a healthy dose of skepticism when it comes to the wide-eyed championing of edtech as a panacea for public education and professional or personal development. Part of this is that I am just naturally cynical[3]. Another part is fueled by an instinctive caution towards fervour of any sort due to its unfortunate proximity to zealotry.

Here’s an outline of a few common threads that emerge from the missionary set of the edtech crowd that I’d like to lend a dour note to:
  1. School is boring to kids who are “digital natives”
  2. Learning is based on discovery and passion, not drill and kill
  3. Kids are unique individuals who should all have personalized learning paths
  4. Technology puts power into the hands of our students, teachers just need to get out of the way
These all sound great, don’t they? It’s like we’re on the cusp of a major breakthrough in transforming education by making lessons fun and interesting, personalizing content for every student based on their interests and needs, and letting the overburdened teacher sit back, finally, to coach and mentor individually rather than dictating and lecturing to a whole class.

Thing is, all of these points are essentially a regurgitation of unbridled constructivist theory. And while that’s not inherently a bad thing — I’m not completely opposed to constructivism and I’ll get deeper into that in a moment — I want to make it clear that the underlying approach here is nothing entirely new, disruptive, nor revolutionary; it also has little to do with what is truly disruptive in edtech itself. Which isn’t an argument specifically against any of the points. Let me get to that now.

First, however, let me quickly address a question you may have while reading this:

Why am I bothering to critique the missionary zeal of some edtech proponents, if I generally support the need for innovation and creativity in education, and believe strongly in the overall power of edtech?

I am writing this not only to get these thoughts off my chest, but furthermore because there’s a lot of snake oil salesmen out there right now with dollar signs in their eyes and hymns of the promised land in their mouths. We must be vigilant.

1) School is boring to kids who are “digital natives”

Let me ask what may seem like a senseless question: is it the central purpose of schooling, or of any form of education at all, to entertain? I certainly believe that learning should be fun, but it’s not always fun. Sometimes it can be downright dreary. Come to think of it, even the educational activities that we think of as fun and creative are often in reality full of drudge work and extensive, mundane practice on the long road to mastery. Like art. Or music. Or writing stories or poems. Ever written a poem?  It’s not what most would call fun. It entails going back over it again. Then back over it again. Again. And again, and again,  each time slicing, shaping, rethinking each and every syllable and sound of every word and its placement on the page. Ever read a book on something you were really passionate about learning, like the history of Quidditch, or organizational behavior? Books with lots of information and facts in them, unfortunately, can frequently be rather tedious. Gee. Just makes you want to pick up a remote or Wii controller, don’t it?

Which leads me directly to my next question: does having been raised using tablets, smartphones, and gaming systems that have been produced specifically for the purpose of the swiftest and most convenient consumption of content possible mean that our children are “experts” in technology use?
I believe the term “digital native” is misleading. It implies that having been bred and groomed as consumers of digital goods means that our children are technological experts, possessing some intrinsic wisdom, some capacity for leveraging technology that their outmoded neanderthal parents don’t. But knowing how to swipe a screen to download the latest app, or how to swing a controller so you can accrue points, or walking crookedly  down the sidewalk hunched over your smartphone tweeting out your gastrointestinal state to the world doesn’t mean you are technologically literate. What makes for technological literacy (in my humble opinion, of course) is the capacity for diagnosing and fixing technical issues with software and hardware, in addition to modifying and creating new digital environments, with a firm grounding in “machine” language. Some kids can do this. You know, the geeks. The ones that invest a lot of time in tinkering, learning command line and code. Kinda like how some kids can fix cars; the ones that invest a lot of time tinkering, taking engines apart, changing the oil.

But talking about kids tinkering with real things is taking me towards an argument FOR constructivism that I’m not ready to delve into just yet. We’ll come back to this idea later. For now, suffice it to say that kids — and adults — don’t necessarily know much about technology simply because they consume digital content.

I, for one,  don’t want our kids to be digital natives. I want them to be life-long learners capable of manipulating existing systems and creating new ones. In other words: hackers.

Let’s return to the original point I began with here: learning facts and gaining skills can sometimes be boring, even arduous. Without domain specific background knowledge (e.g. science and history), then kids are much more liable to turn into gullible, superstitious, ill-informed adults little able to participate meaningfully in a democracy[4]. Which is more or less the issue with our body politic at the moment, in my cynical opinion — we’ve got a nation full of debt-ridden, gullible, superstitious,  ill-informed adults, run by a coterie of sheltered, short-sighted, non-empathetic  adults operating on questionable assumptions and data. The fact that in 2012 those who govern us are still debating whether climate change is even a reality or not speaks directly to this point. If all of those adults were a bit more literate in a shared knowledge and understanding of history and science, we might have a better functioning nation.

Beyond acquiring domain specific facts and background knowledge, gaining fluency and mastery of any skill can sometimes be boring, too. And that leads us directly to the next point on the agenda.

2) Learning is based on discovery and passion, not drill and kill

Yes. . . but. In order to gain fluency, let alone mastery, practice is required. Stop calling it “drill and kill”and call it “practice and application[5]” instead, and it doesn’t sound so evil. Any musician worth their salt has spent countless hours practicing boring things like scales. You don’t gain automaticity in recall of your times tables through discovery and passion[6]. What makes the process of learning through practice different than drilling, according to Daniel T. Willingham, is that it is “executed for the purpose of improvement.”

Discovery and passion are fundamental and beautiful aspects of life and learning. It’s what drives us to put in countless hours of practice. It’s what drives researchers to spend years squinting at fruit flies mating or maimed rats eating. But discovery and passion don’t infuse every day, every minute unless the learner has the self-control, persistence, and wherewithal to see learning through. In the absence of these qualities and means, discovery and passion may simply mean chasing after fleeting pleasures.[7]

Look, I’m not trying to make an argument that learning should be boring. But I believe that real learning takes a lot of hard work, and that we need to be forthright about that.  Learning activities in school should certainly be engaging, but this engagement must be derived from the richness of the content itself, not from clever tricks with iPads and tapdancing by teachers. In my opinion, part of the reason[8] why education is such a failure for so many kids is not because teachers aren’t doing a nifty song and dance with fancy tools, but because teachers and schools are failing to provide content that is sequenced, structured, and steeped in a deeper understanding of the foundations of that specific academic domain. Which brings me to our next point.

3) Kids are unique individuals who should all have personalized learning paths

Well, sure. Every individual has a completely unique set of whorls chiseled into their fingertips. We are all amazingly singular variations on a common set of genes, living divergent experiences in widely variable sets of circumstances. But does this entail that each and every human being needs a specifically tailored suite of content from their public schools, delivered just so to meet their utterly  unique learning styles and abilities? Let’s exercise some caution.

I am a special education teacher, so I’m well aware that there are real differences in some children’s cognitive development that have real differences in outcomes. Developing personalized learning paths is critical to ensuring that students with learning disabilities are given an education that adapts and modifies the curriculum to enable them to access it alongside their peers to the fullest extent possible.

But I chafe against the idea that all kids require personalized learning paths in our public schools for a couple of reasons. First, our nation can barely even agree to common standards — forget about a nationally agreed upon curriculum that establishes a least a basic guide to just half of what a teacher is expected to cover. So how is one supposed to personalize something that hasn’t ever been formalized in the first place? Second, as a result of this soupy conundrum, the call to “personalized learning paths” ends up, in our edtech age, as a sales pitch for the latest software package from a for-profit vendor, who will then get to determine what that curriculum to be adapted shall be.

That said, I don’t want it to seem like I am against student-centered teaching or differentiation — I’m not. But I also think this notion of differences in learning can become so dramatically overplayed that it distracts from far more important concerns, such as developing or following the backbone of a solid curriculum in the first place. Which requires us adults to develop a backbone ourselves and provide some guidance and direction to children.

Which leads me to our final point.

4) Technology puts power into the hands of our students, teachers just need to get out of the way

I vibe with the liberating sentiment expressed here. I agree fully that we must shift from teacher-centered instruction to student-centered instruction, and that students need access to tools that will empower them to collaborate beyond the classroom, and develop and create meaningful student products. But my caution here is that this process of empowerment still benefits from clear and explicit adult guidance, as content experts[9], in the domain specific knowledge that will enable students to commence a more independent exploration of a topic, as well provide the school environment and structures that will best support and empower them in their journey.

However, I will readily acknowledge that indeed, if we hand over tools to students with little guidance, they can and will do and learn amazing things. Watch this TED talk from Sugata Mitra on children in India teaching themselves and each other using a “hole in the wall” computer on the street, and you’ll see that this form of technological empowerment can be convincing.

Take this idea to its logical extension, and it indeed has the potential to be truly revolutionary. The concept of teachers as a guide-on-the-side rather than sage-on-the-stage has been around for a while, but the levels of instantaneous connectivity we now possess finally offers the opportunity to realize that potential.

In his presentation at #140edu, Deven Black took this idea of self-discovery and self-teaching to its fullest logical extent, and advised students to drop out of school. Why do we keep these bumbling, oppressive, dinosaur adults around at all, anyway?

While I deeply appreciate the rebellious spirit underlying this idea, I think that there’s a serious problem with the suggestion that children can teach themselves, and it has little to do with academic content (some kids, after all, know much more than their would-be teachers[10]). I fully believe that students can teach themselves quite a bit once given some free reign. My concern has more to do with the broader idea of adults abstaining from providing the social, moral, and emotional guidance that children will need as they struggle through the stress and confusion of adolescence. By believing that children will teach themselves how to navigate the treacherous waters of the world excuses, in effect, adults from responsibility. And I think that our world is just a little too full of adults who have excused themselves from responsibility already. This applies to parents, this applies to educators and administrators, this applies to businesses, and this applies to those would govern. When we relinquish our roles as mentors and leaders, then we strand kids without the positive community of role models they desperately need.

In a school, therefore, I believe that it is the duty of the adults to provide that social, moral, and emotional guidance, in addition to academic content knowledge and expertise. And that doesn’t mean that we can’t empower students with technology and step out of the way. But we must be clear that as adults, we’ve first got to equip students with the academic knowledge they need, and provide the structures and environment that will enable them to explore and persist in their activities and learning.

OK, so what then? Would you have us return to to the Dark Ages of Catholic nuns rapping our children’s knuckles with rulers, desks in rows, and rote memorization of facts we can Google in milliseconds?

Well, actually, Catholic schools did a pretty darn good job of providing guidance (other than the rapping on the knuckles), and I’m OK with desks in rows[11] . . . But really what it comes down to is a few simple questions: what is the real purpose of school? Is it a place to find yourself? Or it it a place to discover common ground with others? Or is it both?

These are big questions, and I think I need to make something clear that I haven’t thus far in my critique: how we structure our schools must be dependent on the developmental needs of children. Many of the critiques I have been forwarding may not apply to high school, for example. In high school, I think kids are really ready to embark on their own individual pursuits based on passion and discovery — with the proper guidance and support from adults, of course. In high school, I don’t think curriculum should be as structured as I’ve been suggesting, and I think kids should be able to begin structuring their own learning paths by that point, if not earlier. But in elementary school, I believe that curriculum must be very structured in order to establish a strong academic and social foundation.

I want to close this overlong piece on edtech already, so to begin to wrap this thing up, let me outline what I feel are important things to consider in the realm of edtech:

  • The power of technology and social media lies not in the tools themselves

What is revolutionary about technology and social media is not how well-designed and amazingly small and speedy tools are, but the level of connectivity that is established between individuals. The power, in other words, is not that technology can supplant relationships or individual ability, but that it can enhance them. These tech tools are connecting us to one another in ways that we have never seen before. It’s empowering — but it’s also dangerous. Our children must understand that everything they do online leaves a footprint, and that the seeming anonymity and informality of communication can still wreak terrible effects on other people’s lives. They must also understand that if they are unable to intelligently navigate online spaces, they may well be at the mercy of political propaganda, unscrupulous profit interests, and individuals with ill intent.

Navigating this new world of hyperconnectivity, therefore, still requires the social, moral, and emotional guidance that communities and schools must be expected to provide. Schools, as I have pointed out before, are all about relationships. No matter how we leverage and scale edtech, this will continue to be true.

Thus, we must be careful to not worship edtech as a saviour — if we don’t first build the human capital and capacity within a school, edtech will do little to empower anyone.

  • The skills that children need to navigate this new world are still founded in literacy, science, history, and math

It bothers me a bit when people keep on about “21st century skills,” saying that we don’t know what jobs will look like in X many years[12]. I would argue that the gap that is occurring between what employers are looking for and the skills people on the market possess[13] has much less to do with their ability for creativity and innovation, and much more to do with the fact that many can’t write a basic paper, conduct basic research, or do any of the things that they would be able to do and understand if they had a strong foundation in literacy, science, history, and math.

As I discussed earlier, calling kids “digital natives” is a misnomer. Knowing how to swipe a screen doesn’t translate into knowing how to target a Google search to find relevant information. I took the Google power search class I just linked to, and I was struck by how the most fundamental skills of effective search are based on the nature of literacy and deeper content specific knowledge.

In Summation. Finally.

My overall point in this piece is that we must be cautious about letting what is truly revolutionary about edtech sweep us over into unbridled constructivism and the idealistic expectation that our human and social capital problems will be solved.

As I mentioned earlier, I’m not wholly opposed to constructivism. The argument that I and my colleague Will Johnson have been making here on our blog Schools as Ecosystems — that schools should be viewed more holistically as complex adaptive systems — is fundamentally constructivist in its concern with the impact of learning environments and relationships on learning.

But I also believe, as I’ve argued here and elsewhere, that adults must commit to serve their natural roles as guides and leaders, and that we must approach this guidance systematically. So I am cautious about constructivism because in the jubilation and zeal for edtech, some folks are advising that adults should step aside and relinquish our leadership on content and structured learning. We should not step aside. Rather, we should step up and develop our professional  capacity for leveraging technology and social media positively and systematically.

At the #140edu conference, Principal Chris Lehmann made some great points about how the constructivist approach can be leveraged by edtech, and the one that most stuck with me was the call to let kids “build things that matter.” As I mentioned earlier, tinkering and exploring and messing around with things is how we gain expertise. This form of project-based learning, structured with the requisite domain specific background knowledge, in  a school that builds systems and structures with the proper tools to empower teachers and students to do this form of learning, I believe holds tremendous power for engaging learning that can be steeped in a foundation of content knowledge.

Another great point he made was that we must stop focusing so much on 21st century skills and focus instead on community. Unsurprisingly, this resonated strongly with me, given the skepticism I evidenced earlier about 21st century skills, but also because Will Johnson and I have been focusing heavily on the central concept of community in schools in our framework of Schools as Ecosystems. I believe that building stronger communities is central to the purpose of public education.

To close, I want to leave you with the idea that we can blend progressive and conservative ideals; constructivist and objectivist theories; visionary and pragmatic applications; and what is truly transformative in edtech, with what works in traditional schooling. It doesn’t have to be one ideal at the expense of another. We can blend these ideals together to form an evolutionary reality that works better for the ones who are our future.

Larry Cuban wrote a great series of posts recently about the power of teachers working with other teachers in a professional learning community. I’d like to close this piece with a quotation from one of those posts, in which he makes the point that there is no such thing as a “single one-best way of teaching,” but rather that effective teaching is the result of flexible yet disciplined structures of teams of teachers working together to problem solve based on the needs of their students:

When teachers work together to examine student work and analyze classroom lessons, they figure out collectively what works and doesn’t work and they build a culture of learning across grade levels in elementary schools and within departments in secondary schools. They build trusting relationships with peers  and learn from one another — a scarce resource because isolation is endemic across age-graded schools. The resulting pedagogical capital blends ambitious lessons and traditional ones of teacher- and student-centered practices, rather than a single one-best way of teaching. Such hybrids of teaching, working within adaptable structures of professional development and site-based learning communities, are tailored for complex, web-like systems like schools.”

[1] from here on out in this piece, “edtech” will serve as the all encompassing signifier for “technology and social media”
[2] though I don’t code myself–hence unable to label myself a true geek–I just ride on the coat-tails of those who do. I’m a “copy-n-paster,” not a “hacker”
[3] which made me quite the morose youngster, by the way. I’m trying to make up for it as an adult
[4] Though they will, of course, be consummate consumers
[5] I’m deliberately ignoring for the moment that practice and application can be done in innovative ways that are far more engaging and meaningful than worksheets and other rote forms of learning
[6] At least, I sure didn’t. I would certainly be interested in hearing otherwise
[7] Chasing after fleeting pleasures. . . that sure sounds like the defining pastime of a lot of Estadounidenses
[8] The other part is a failure to provide the social, moral, and emotional guidance and support kids need. More on this further down
[9] I say this knowing full well that some teachers are hardly experts, but that’s part of the REAL problem, don’t you think? We don’t value teachers enough in this country to ensure that they are picked competitively and trained extensively
[10] One student panelist and presenter at #140edu, Nikhil Goyal, memorably stated, “I learn more through Twitter than I do in class, and that’s a problem, I think.”
[11] This charade of pretending that teaching is progressive just because you force kids to sit in groups is preposterous. Some activities are best in groups, some are not. It also depends on the style of the teacher and the needs of the students
[12] Heck, with the way things are going, we don’t even know if there will BE any jobs
[13] I also think that we should be talking a lot more about getting students out of school and into workplace internships for hands-on experience and skills during high school

The Pre/Trans Fallacy in Public Education

In a post a while back reflecting on teaching the whole child, Will made an observation on what it means to teach the whole child that really resonated with me:

When we talk about teaching the whole child, we’re talking in part about teaching with an understanding that children are fluid beings who grow and develop constantly. In some way, then, the whole child includes who the student was, who they are, and who they will become. 

When politicians use “students first” language, pitting our students against the adults they will become, they negate the whole child, fetishizing students’ youthful selves and devaluing their grown-up selves. In environmental terms, it’s like saying we must prioritize acorns over trees. Shouldn’t we just take care of the whole forest, and defend it against those who want to slash, burn, and subdivide?

This idea of “fetishizing” youth reminded me of something completely tangential, but perhaps bearing some relevance to the broader concern here with holding up children as idealized pawns in ideological warfare. Ken Wilber, a controversial contemporary philosopher, has written about what he calls the “pre/trans fallacy,” in which he points out a potential pitfall in our thinking on nonrational states of being. He delineates nonrational states into “prerational,” such as infancy, Freudian drives, and myths, and “transrational,” which refers to spiritual, metaphysical states beyond rationality. He believes that the danger lies in confusing these two states, such as Jung elevates prerational mysticism to divine insight. Conversely, Freud portrayed transrational spiritual states as a regression to infancy. In other words, according to Wilber, in much of our thought there is little distinguishing between truly elevated states of consciousness (such as those states discussed by Sufi poets and Zen masters) and those states that precede the development of intelligence, or that operate at a minimal level of intelligence. When discussing spirituality, Wilber cautions against distortions of both “reductionism” (such as Freud’s take on religion in The Future of an Illusion) and “elevationism” of spiritual understanding (much of Romantic thought, the New Age movement et al).

At some level, this conflicted ideation of nonrational states can be viewed in the manner we talk about children, as Will pointed out. By prioritizing “acorns over trees,” and ideologically putting “students first” at all costs, we imply that childhood is an elevated state of being, rather than a developmental stage prior to adulthood that requires guidance and nurturing. Though this may seem like quibbling, the way we talk about children and childhood can reveal a deep problem in the manner in which we approach education.

Children require nurturing and guidance in developing sound of body and of mind and with the character and knowledge to face the problems and challenges of their society. It is our job as adults to provide that direction, nurturing, and guidance. Furthermore, it is our job to provide healthy eating options, and create positive learning spaces in which children are exposed to diverse experiences, access to abundant light and green spaces, and ensure students are provided with the academic and social knowledge they require to comprehend their world and make informed choices. Yet if we were to believe that childhood is some elevated state of being, we may instead allow children to do whatever it is that they so choose, as if all they require are boundless options, such that they could direct their own learning and “discover” all that there is to know. Though this may seem like a straw man argument, this sort of mystical thinking about childhood is evident in more extreme strands of inquiry-based learning, constructivism, and ideas about schools in which children are on completely individualized tracks, sift through activities and discover underlying concepts, or interact randomly with different resources.

Teaching is a craft that requires careful channeling of childrens’ innate talent, curiosity, and will towards planned and sequenced targets of learning. The best inquiry-based lessons are grounded in a deep understanding and mastery of the content by the teacher, who has carefully modeled, planned and structured the activities. It is this deep understanding and mastery that is often most obstructed by the policies, structures and schedules of our public schools (such as an unconscionable lack of paid planning time), and most ignored by education reformers who focus on external mechanisms rather than upon curriculum and school and community contexts.

Successful schools that nurture children and provide a strong curriculum are not harsh, militaristic environments. On the contrary, they are environments that abound in niches for sharing, learning, and positive social interactions.

As adults, we have for far too long absconded from our duty to provide warm nurturing and clear guidance and direction to children, and hidden behind political or theoretical abstractions that result, in the end, in the anemic drivel that is the typical curriculum of public schools, and the cold, alienating environment that constitutes many school contexts.

Perhaps if we recognize that we must “take care of the whole forest,” as Will suggested before, rather than reducing or elevating any one component of a school ecosystem, we can resist the urge to fetishize children and focus instead on how to best support those children that have been given unto our care to love and educate.