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? . . .

Smorgasbord: Some Important Stuff

Buffet Train Lunch

On the necessity for deliberate practice of foundational writing skills in classrooms.

“The idea behind progressive mastery is to protect students from what confuses them until they have mastered each individual component.”

Connect this to what I wrote about Hochman’s writing method.

Air pollution is damaging our nation’s children in the one place they spend some of the most time in and should be most protected in — our schools.

A critically important piece from The Center for Public Integrity on the invisible–and thus largely ignored–health risk of air pollution. Many schools, especially here in NYC, are built right next to busy roadways. The long-term health costs are incalculable, and all it would take would be a high grade air filter that can remove 90 percent of the pollution. And forcing old diesel trucks off of our roads. This may sound like a pipe dream, but California has already led the way.

Says one baffled Californian:

“The technology is well established, the installation is straightforward and the maintenance is simple,” said district spokesman Sam Atwood, who doesn’t recall officials from other states getting in touch to learn from his agency’s experience.

As in the office, so in the classroom. Empower students to design their spaces.

“When workers were empowered to design their own space, they had fun and worked hard and accurately, producing 30 per cent more work than in the minimalist office and 15 per cent more than in the decorated office. When workers were deliberately disempowered, their work suffered and of course, they hated it. “I wanted to hit you,” one participant later admitted to an experimenter.”

A special education teacher discovers the power in scheduling for effective collaboration.

“Most people struggle with the idea that medicine is all about probability”

An important ProPublica piece on the hit and miss nature of many medicinal and surgical interventions. Most will do no harm —a few may gain benefit—and some will be harmed. There’s some parallels to consider with education here.

“If we really wanted to make a big impact on a large number of people. . . we’d be doing a lot more diet and exercise and lifestyle stuff.”

Kevin Carey outlines the generally poor results on vouchers.

“while vouchers and charters are often grouped under the umbrella of ‘school choice,’ the best charters tend to be nonprofit public schools, open to all and accountable to public authorities. The less ‘private’ that school choice programs are, the better they seem to work.”

Interactional motivational scaffolds are more effective than other scaffolds.


“conversing with a child in an elaborative way could help them remember more about their lesson”

Need to remember something? Use weird visual cues to trigger your memory. Classroom teachers, take heed.

We blame a lot of problems on immigrants. But maybe it’s time to point the finger at the “longstanding native-born Americans” as the real source of the problem.

Daniel Kahneman comments on a blog post. The world changes.

Kahneman responds to a blog post, noting that he was overzealous in his interpretation of studies on social priming. This is important not only as an encapsulation of the “replication crisis,” but furthermore for those of us who have read and been heavily influenced by Thinking Fast and Slow.

Wind turbines inspired by insect wings are 35% more efficient.

Special Education: Inclusion or Specialized Intervention

“Street Crowd” by Théophile-Alexandre Steinlen (French (born Switzerland), Lausanne 1859–1923 Paris) via The Metropolitan Museum of Art is licensed under CC0 1.0

A fair amount of academic literature calls for clinical, evidence-based models of intensive intervention for students with disabilities in K-12. Yet in the field, there is limited effective implementations of such interventions.

Models such as Response to Intervention (RTI), multi-tiered support systems (MTSS), and standard, evidence-based protocols and programs all make complete sense when you learn about them. But there’s also a problem with these interventions: they are based on clinical frames of implementation, as in a trained clinician in the given model or protocol delivers the intervention in a prescribed manner.

The daily reality of a K-12 school, however, is far from clinical. Opportunities to deliver prescribed interventions, whether in a small group or in the ideal of a 1:1 setting, are few and far between. Moreover, opportunities to be trained in such interventions are few and far between. One is certainly not trained in any given intervention in any traditional education program.

The very model of a self-contained classroom, a class in which students with more severe disabilities are separated from their peers, relies upon this clinical ideal. And again, in isolation, as an ideal, it makes perfect sense. Let’s separate out the kids with greatest of needs so we can provide them with individualized, supportive instruction.

Similarly, within an inclusive classroom, district leaders continually speak about and prescribe the need to move away from a one-teach, one assist model to a parallel, station, or team teaching model. Or they speak of the need to “differentiate” and “individualize” instruction.

Idealized models that make perfect sense and sound great, but that rarely play out that way on the ground.

A Division Between Inclusion and Specialized Intervention

There is some scholarly debate about this. Fuchs et al, in a 2010 paper, “The ‘Blurring’ of Special Education in a New Continuum of General Education Placements and Services,” provides a useful delineation into two camps they term IDEA and NCLB. The IDEA group advocates for a top-down (i.e., replicable), linear, and time-sensitive process with fewer tiers of instruction, which serves both prevention and a more valid method of disability identification. They believe in evidence-based programs at Tier 1, the strength of standard protocols in Tier 2 and Experimental Teaching for Tier 3 intervention. They believe in the importance of a distinct special education program.

On the other hand, the NCLB group focuses on a problem-solving approach based on standards. “Whereas special education remained a distinct entity in reform making in the 1980s and 1990s, many in the NCLB camp today are advocating for obscuring, smearing, dimming, and confusing special education by blurring it into general education. In their plans—however implicit—special education vanishes in all but name (and maybe in name as well).”

Research suggests that the standard-protocol approach is superior to problem solving in accelerating the progress of children with serious learning problems. However, the authors acknowledge that “because there are insufficient numbers of such protocols in many academic areas and in the higher grades, and because ‘the school bus arrives every morning,’ many practitioners may have little choice but to rely on some variant of problem solving.”

In a more recent paper in 2015, “Inclusion Versus Specialized Intervention for Very-Low-Performing Students: What Does Access Mean in an Era of Academic Challenge?“, Fuchs and other authors again examine the split between those who push for a problem-solving, inclusionary approach vs. that of “specialized intervention” approach and advocate for a focus on explicit, specialized intervention delivered in a separate setting.

Here’s a couple of provocative quotes from this paper that struck me:

“. . . access cannot be assumed even when inclusive instruction reflects state of-the-art accommodations and support. Instead, only evidence of adequate student outcomes demonstrates that access to the curriculum has been accomplished. In fact, the present analysis indicates that such access is sometimes more satisfactorily achieved under a service delivery arrangement that occurs outside the physical space of the inclusive program and using instructional methods that differ from the inclusive program. All this argues for a definition of access to the general educational curriculum that is based on empirical evidence of adequate learning— regardless of the setting in which or the instructional methods by which that learning is achieved.”

“…it is not possible to ignore students’ foundational skill deficits if progress toward CCSS is to be realized. For example, to demonstrate meaningful improvement with informational text, specialized intervention must address very low performers’ decoding, word recognition, and vocabulary deficits, and this often requires out-of-level foundational skills instruction. Therefore, although reconceptualizing access as empirical demonstration of learning, schools must also recognize that the access mandate often requires schools to provide out-of-level instruction to meet students’ needs for accessing the grade-level curriculum.”

Yet I don’t agree with the authors that putting in place explicit instructional intervention programs will solve all the problems they’ve identified with inclusionary practices. You can place my own professional stance as firmly within the “NCLB” camp outlined above. Schools are not clinics, and unfortunately, special education teachers and other personnel in school buildings are rarely, if ever, trained in the delivery of specific interventions.

In fact, I think the issue of either strong inclusionary instruction or specialized intervention comes down to the same fundamental issue: there is a general lack of instructional capacity and expertise in most schools, in addition to a general lack of curricular coherence and vision.

Either way, we certainly need to rethink how we are putting in place supports for students who struggle the most and assessing whether those supports are actually effective.

My argument, however, is to place our primary and immediate focus on establishing coherent and rigorous curriculum and expectations for all students. I thus argue for inclusion and a problem-solving approach.

A recent article in Education Next,”Reforming Remediation” neatly encapsulates the rationale for this inclusionary argument. Students placed directly in college-level statistics did far better than their counterparts in remedial classes.

While that example is focused on a higher education setting, we can find parallels in K-12 by looking at access to Advanced Placement (AP) or International Baccalaureate (IB) programs, or to difficult academic subjects such as Latin. Disadvantaged students rarely have the opportunity to experience such rigorous curriculum. Yet when they do, as Bronx Latin teacher Peter Dodington put it, “The combination of a difficult topic and a well-ordered, step-by-step curriculum allows even otherwise weak students to succeed, and gives them a new understanding of their own strengths and talents.”

If we raise our expectations and the rigor and coherency of our curriculum, then we will see more educational benefit for all students. The dire reality of poor teacher training and knowledge of the content they teach is a significant problem, but a stronger school-wide curricular program can help to assuage this.

I strongly believe in the need for specialized interventions for students who require the most support. But how can we put in place effective interventions when a strong and well-implemented core curriculum is not present?

Let’s address the foundations first before moving to the clouds.

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.

On Threshold Concepts and Experiences


In a recent post, “On Knowledge and Curriculum,” we reviewed a few disruptive ideas from cognitive psychologist Daniel Willingham, with the most incendiary implication being:

a school needs to come to a consensus on the topics, texts, vocabulary, and concepts that are most essential to know within and across each academic domain and carefully sequence and reinforce those concepts across classrooms and grades.

So how can a school embark upon this quest? In this post, I will attempt to provide some guiding ideas and protocols for this work.

How Do We Reinforce Knowledge?

First off, a few guiding documents to equip you with the cognitive principles of affirmative testing, which are essential to reinforcing knowledge over time:

—Annie Murphy Paul, “Affirmative Testing” (she has designed an entire e-course around these concepts!)

—Deans for Impact, “The Science of Learning


How Do We Determine the Knowledge that is ESSENTIAL?

Folks are going to disagree about this, including the “experts,” so ultimately, this determination should be made collaboratively within a school (and beyond). The key is that the school comes to a consensus on this essential knowledge, then teachers carefully sequence it across the curriculum and quiz it repeatedly in a low stakes manner.

There’s a useful frame, known as threshold concepts, for drilling down to this “essential knowledge” within a specific academic domain. Threshold concepts come out of higher ed academia, and it’s admittedly a bit esoteric in the literature, but I think it’s a useful lens with practical implications. Threshold concepts are very much related to Wiggins and McTighe’s “big ideas,” but with a few interesting twists.

I first stumbled over the threshold of these concepts in blogs from UK educators, to whom I’m indebted for starting me on this journey:

—Alex Quigley, “Designing a New Curriculum: What are your ‘Big Ideas?’

—Joe Kirby, “One scientific insight for curriculum design” (he also sums up research on affirmative testing really well here)

What we’re really trying to get here is that 20% of the knowledge that is most essential to understanding an academic domain in a specific grade. Here’s a frame for this:


How can threshold concepts help us to determine that 20% of essential knowledge within a specific academic domain? I decided to review some of the literature for further clues:

—Ray Land, Jan Meyer, and Jan Smith,”Threshold Concepts within the Disciplines” (Land and Meyer are the rockstars who originated the concept)


—James Rhem, “Before and after students “get it”: threshold concepts” (a useful overview)

This idea of a transformation of understanding that is essential for progressing deeper into the academic content is really interesting.


—James Atherton, “How do people ‘get it’?” (another useful overview)

There are many other characteristics that were identified, but they don’t all seem very useful in a practical sense for K-12. I think the three outlined above are the most relevant and applicable.

—Tracy Fortune, Priscilla Ennals, and Mary Kennedy-Jones, “The Hero’s Journey: Uncovering Threshold Barriers, Dispositions, and Practices Among Occupational Therapy Students


I love this idea of viewing a student’s passage through a threshold concept as akin to a hero’s journey. In considering this journey, what are the troublesome obstacles and bottlenecks that student will face? The idea of “bottlenecks” comes thanks for the link immediately below. In thinking through this, I also think we need to acknowledge that bottlenecks may not be purely conceptual — they can also be procedural, in the form of skills required to complete academic tasks, as well as social-emotional (this can be a tremendous and often unaddressed barrier for many kids).

In this sense, then, we can expand the notion of crossing a threshold to not solely refer to concepts, but furthermore experiences. As educators, we seek to design experiences in which students engage in an academic form of a hero’s journey, learning to overcome barriers and gain the intellectual accomplishment of mastering skills and knowledge.

—Joan Middendorf & David Pace, “Decoding the Disciplines: A Model for Helping Students Learn Disciplinary Ways of Thinking” (they offer a useful protocol that I’ve drawn from below)

OK, So How Do We Discover These Threshold Concepts and Experiences?

But we still need some kind of process for distilling away all the cruft and getting down that 20% of the most essential knowledge within a content and grade.

Here in the US, we have a general list of skills we use as guidance in the form of state standards. And as I’ve done with the Common Core standards, we can do a deeper analysis to begin unpacking what that knowledge might be.

But this can still be at a pretty abstract level, and we want this to be relevant to classroom teaching. By focusing on the topics and texts that will be studied, we can make this more concrete.

Because English Language Arts is my specific area of expertise, I’ve focused my efforts in this area, especially since this content area is probably the most difficult to pin down in terms of a progression of knowledge.


There’s two ways we could utilize this protocol: 1) unit of study, or 2) over the entire school year.

1) Consider the topics and/or texts that will be taught.

2) What will be the product or products that students will be expected to create that can demonstrate their mastery of learning? (This product could also be a performance).

3) What are the primary modalities that this product is focused upon? In literacy, of course we’re focused on all modalities, but it helps for a department to focus upon the one they consider most essential.

4) Now consider the standards that your district adheres to. For the Common Core, they are helpfully broken up by modality, so turn to that modality. Then, narrow down which specific, few standards you will primarily be targeting.

5) What are the bottlenecks, most especially those that are conceptual and specific to this content, that students will encounter?

6) Evaluate the list of items you have generated. Do they fit the criteria of a threshold concept or experience? Are they transformative, integrative, and troublesome? If not, they may not be essential.

7) You don’t have to do this, but I find that at this step it can be useful to phrase the threshold concept in the form of a message or lesson, akin to a theme statement.

For example, for an upcoming professional learning session I’m working on about supporting struggling middle school readers, I’ve identified the following threshold concepts:

  • Students that struggle with reading comprehension also often struggle with a lack of academic and world knowledge. An English Language Learner can also be understood as native English speakers that do not understand the language of math, science, social studies – i.e. academic, formal, domain specific language.
  • A teacher must work through a task/text in order to identify key takeaways, key vocabulary, and potential barriers to learning, regardless of whether a curriculum is provided.
  • All learners can be engaged in reading and comprehending complex academic texts through well-designed activities, tasks, and resources.
  • An environment in which a student feels safe to take risks in front of peers is a prerequisite for learning — most especially for struggling readers.
  • Learners should be explicitly equipped with strategies and mindsets for when they encounter challenging vocabulary on their own.

It’s important to note that threshold concepts will vary completely depending on any teacher’s specific set of knowledge, perspectives, and interest, and I think that’s OK. What’s most important is that once these most essential concepts and experiences have been identified and voiced, they will not only help to focus that teacher’s instruction on what they feel is most important, they will serve as a basis for arriving at a consensus as a department and as a school.

Here’s a few really basic examples at a unit level of study:

Now that threshold concepts and experiences have been identified, here’s the really hard part:


This is where the rubber hits the road. This is the part that is so very contrary and disruptive to the norms of public education.


I hope some of these resources in this post are useful to your work. The slides outlined above and the protocol are accessible and downloadable here:

On Knowledge and Curriculum


Forget the presidential debates, this is more important.

I attended a PD today that featured cognitive psychologist Daniel Willingham. It’s pretty rare that my employer, the NYCDOE, offers professional learning that has someone presenting from the academic research realm, so when I saw this was happening, I jumped on it.

I’ve been following Willingham’s articles in American Educator and have read Why Kids Don’t Like School, and I’ve been convinced of the importance of a strong curriculum and building knowledge for a while now, but it was nice to get a direct and clear reminder of what really matters in literacy, especially when that message is so very rare.

There were a lot of great ideas and takeaways on motivating children to read at home and on reading comprehension in general, but there were two main points that especially struck me during his presentation (the summary and phrasing is my own):

  1. Knowledge needs to be “in the mind” in order for reading comprehension to be effortless, rather than a problem-solving struggle to determine meaning.
  2. We can only build the broad, world knowledge required for literacy through a carefully sequenced and structured curriculum.

If you take these points to be accurate, then the implications are quite revolutionary in comparison to the regular practices of most schools and districts.

Let’s break down why this runs so counter to the norm.

Here’s what would need to happen:

  • If knowledge must be “in the mind” (rather than on Google) than that means the knowledge considered worth studying must be reinforced and revisited, tested, interleaved, sequenced, and spaced throughout a school’s curriculum.
  • That means across classrooms and across grades.
  • Therefore, a school needs to have come to a consensus on the topics, texts, vocabulary, and concepts that are most essential to know within and across each academic domain.
  • That means that each teacher (or at the very least, a department head or team) will have to have invested a substantial amount of time, both individually and collaboratively, into studying those texts and topics themselves in order to know how to design a learning environment, projects, activities, field trips, and interim assessments that will provide the access to and reinforce that knowledge for all students.
  • This would of course be accompanied by adjusting the curriculum periodically based on an analysis and reflection on interim assessment data and student work.

Sound pretty straightforward? No. Here’s the norm in most schools:

  • What most prioritizes a school’s focus are external assessments, such as state tests. ELA tests in this vein consist of random passages of text that are meant to focus on isolated reading skills devoid of knowledge. Therefore, what is taught and focused upon are the practice of skills devoid of knowledge.
  • That’s what constitutes an ELA curriculum for many schools.
  • A teacher is either not provided a curriculum, or is provided a curriculum but no support, or is provided a curriculum and support but the curriculum is not oriented around sequentially building knowledge.
  • Even when a curriculum might be provided and might be relatively well-crafted (this is a rarity, and if you know of such a curriculum, tell me. I can name two. Maybe three), I have yet to have seen any curriculum that still does not require a teacher to revise and adjust it substantially based on the needs of their students, the circumstances of their school or classroom, or their own particular style and knowledge.
  • Thus, in those rare schools where there is even a coherent curriculum “in place,” the point made above about investment of time still holds. A substantial amount of time needs to be spent in designing and continually molding the school around and in support of that knowledge embedded within the curriculum.
  • Most of what is taught in different classrooms in a school has little coherency across a school.
  • What is a taught in any given classroom is rarely reinforced via low stakes quizzing across an entire school year.

See the problem? From what I’ve seen in much of the professional development sessions and focus of schools and districts is a focus on individual teacher strategies and practices. But let’s get real. If a school does not come together to determine and design it’s mission around the knowledge and skills it will teach sequentially and systematically, then there will be little impact.

For ideas on how a school might begin to do this work, check out my next post on this topic: On Threshold Concepts & Experiences

Sunday Smorgasbord: Race, Pedagogy, Business, and Science



Andrew Rotherham, aka Eduwonk, advises us to “buckle up” and expect more of the sort of suburban bred “local control” fearmongering against diversity and federal intrusion seen in this op-ed.

For more context and history on the racism that underlies that brand of fear, as well as to understand how it relates to crusades for local control of public land, read this excellent longform piece.

Federal protections can backfire, however, such as in this sad irony of fair housing laws used to prevent “community preference” in lotteries for affordable housing in San Francisco.

Even in diverse schools, students of color can still be denied a quality education. The question seems to be: how do you “create a more equitable environment and also keep the most powerful parents happy”? It’s a sad question to have to ask, but finding a solution to it will determine the success of future efforts in increasing school diversity.

Diversity is worth it, though, at least when it comes to working on a team. The work feels harder, but the outcomes are better. (This parallels the idea of fostering “desirable difficulty” in classroom learning.)

Because we all want money.


The inimitable E.D. Hirsch, Jr., makes the case that “good teaching can often depend more reliably on the coherence of the wider system, and on the cooperation it brings, than on virtuoso performances.” Stop blaming the teachers, and start developing better systems and curriculum.

Doug Lemov interviews Tim Shanahan, who articulates the nuance of teaching reading strategies, provides a sound definition of close reading, and dispels the myth that leveled reading is worth any teacher’s time.

At the Windward School in Manhattan, they are using gesture and movement to teach reading to students with disabilities, and having powerful results. There’s something to this connection between corporeal movement and conceptual understanding; in the math realm, research suggests the same area of our brain that counts on our fingers continues to be activated when we move to higher level problem-solving.


Speaking of bodies, traders who are more effective listen to their bodies when making decisions under stress, rather than their minds.

We always hear from business leaders about how we’re not equipping our kids enough in K-12 with the high-level skills they are trying to hire for. But the FiveThirtyEight argues that there’s less of a skills gap, and more of a lack of job-specific training provided by those businesses.

In the most positive and exciting news in this presidential campaign thus far, both Donald Trump and Hillary Clinton are strongly committed to investing in infrastructure.


Our brain’s connectivity and wiring may be determined by its physical structure, not simply by its chemistry.

It may be possible to predict life success from a test at birth. This has much to do with “education-linked genes.” Which is scary.

And an important reminder that context and nuance is much needed when discussing research.



Providing context for concepts may hinder transfer

“One implication of this pattern of results is that as an instructor designs their instructional materials, they should be asking themselves whether they are trying to optimize their students’ demonstrated mastery of the material itself or their ability to transfer their understanding to new materials. . . .

Simply adding richer meaningful content to in-class examples may make intuitive sense, and may have immediately obvious benefits in terms of student engagement and comprehension. But as the results of our experiments make clear, these short-term benefits seem to come at the cost of students’ long-term ability to apply their knowledge. If educators are to take advantage of these inherent benefits, they will need to give careful consideration to how such examples are designed and used together in order to plan the most effective instruction.”

—Samuel Day, Benjamin Motz, and Robert Goldstone, “The Cognitive Costs of Context: The Effects of Concreteness and Immersiveness in Instructional Examples” on frontiers in Psychology (H/T Greg Ashman)

How Would You Revise the Common Core Standards?


NY State will conduct a formal review of the Common Core State Standards. I welcome the opportunity for a review. In my opinion, the more people talk about what should be taught in classrooms, the better.

Too often, we discuss education as an abstraction, polarizing around political issues largely irrelevant to kids and teachers at the ground level. What most impacts us on a daily basis is what is taught, and how. So while I would prefer we discussed the curriculum and content itself, talking about standards is at least a step closer to the heart of the matter.

As you may know, I’m a proponent of the Common Core Standards. I’ve advocated for them publicly, and I work with the standards in my daily practice.*

I advocate for the standards because I believe strongly in the need for shared, rigorous, and coherent standards. But that doesn’t mean I believe the standards, as written, are perfect.

If I Could Revise the Standards

Here’s what I would suggest as major points for revision of the ELA standards:

  • Provide more explicit guidance within the literary standards for the study of poetry. (See Sandra Stotsky’s Curriculum Framework for a good model.)
  • Overhaul the writing standards to include literary analysis as a genre of writing.  Merge argumentative and informative/explanatory writing, as the distinction between those two is unclear and it’s of questionable value to distinguish them. Consider broadening the scope of narrative writing to that of creative writing, to include poetry.
  • Clarify the meaning of the idea that literacy extends across all content areas, while reducing the stress on the oft misunderstood recommended percentages between informational and literary text. It should be less about pushing informational texts into ELA, and more about pushing the teaching literacy across science, social studies, and other content areas.

Others have also been saying that the Kindergarten standards need much revision. This is an area I’m less knowledgeable about, but I assume there’s some tweaking that should be done there, as well.

What aspects of the Common Core standards would you revise?

*I work (or have worked) with the standards in some of the following ways:

  1. my daily work as a special education ELA teacher, using them to develop and align my school’s curriculum and assessments, as well as to develop IEP goals (I began analyzing them more closely to break down the relevant knowledge, skills, and products for grades 6-8 to guide this work)
  2. my work with NYCDOE as a Common Core Fellow to assess teacher team submitted performance assessment tasks
  3. my work with LearnZillion to develop online videos, lessons, and resources aligned to the Common Core

The Mirage of a Mirage: On the New TNTP Report on PD


Today I went down to DC* for TNTP’s release of their Mirage report on the (non)impact of professional development on teacher effectiveness. TNTP presented an overview of the findings, then journalist Amanda Ripley facilitated an interesting panel with USED’s John King, teacher Jennifer Corroy Parras, DC’s Kaya Henderson, and AIR researcher Dr. Michael Garet.

The big story is that teacher PD is 1) enormously expensive, yet 2) there’s no silver bullet. In other words, teaching is complex (glad ed reform world is beginning to acknowledge this), so we still are very far from knowing what improves teacher practice at scale, yet we’re investing a lot of time, energy, and money in it willy nilly.

There are a lot of aspects to explore, and the panel touched on a number of them. Ripley provided some nice framing of the systemic issues, such as that most PD (and US system of ed at large) is disjointed and incoherent, and that there is a general lack of clarity around what effective teaching looks like, accompanied by high expectations. She noted that this lack of clarity and high expectations for teachers parallels student experiences in our educational system, with both teachers and students leveling off in performance after an initial 5 years.

Both John King and Kaya Henderson pointed out that an oft missing link in PD is a focus on curriculum, a point on which I strongly concur. Curriculum provides the frame, the backbone, the structure that daily guides student and teacher experiences in the classroom. Without that structure and purpose, we are left with the incoherent gloop that Ripley first referred to.

TNTP’s report is incredibly insightful and useful–if enervating–material. I feel like it’s also important to define the kind of PD which the report mainly seems to abide by. I’ll admit that I haven’t yet dived too deep into the report, but from an initial scan of the survey questions and findings, I obtained the distinct impression that they mostly mean “PD” as in a specific dosage or frequency of a prescribed intervention that results in a change in an individual’s teacher practice within the classroom (and which should then ideally translate into improved student outcomes).

When I think of PD, I think of teachers sitting together around a table and collaborating to design common assessments, curriculum, resources, and examining student work and data. This was a component of TNTP’s teacher survey (noted as informal & formal collaboration, and peer time), but the report notes that an equal amount of such time was dedicated to this in both “improvers” and “non-improvers.” But I think there’s one key aspect of such collaborative time that we need to delineate, and which I believe could distinguish between those two populations: how teacher collaboration and planning time connects to a school-wide system.

Let me give some specific examples of what I mean to make this tangible:

  • A bi-weekly 8th grade-level team meeting working to horizontally (within the grade) align curriculum and assessments and strategically build  and reinforce content knowledge and skills
  • A weekly ELA department team meeting working to vertically align curriculum and assessments (and strategically build  and reinforce content knowledge and skills)
  • A PBIS system of agreed upon (developed both school-wide and via grade-level teams) infractions, consequences, and rewards
  • An established vision for utilizing advisory time to provide social-psychological interventions, accompanied by planning time to design these interventions, and time to analyze and assess their impact

You could go into both an effective and ineffective school and witness such use of collaborative time–but the key is how that teacher collaboration ties into a coherent, school-wide system.**

Admittedly, though, this all goes back to the great complexity not only of teaching, but of working in a school. There are so many variables behind what goes into anything remotely approximating either “PD” or “teacher practice” that it is difficult to define what we’re looking for, and even more difficult to do well consistently and to replicate and scale across different contexts.

I came back to NYC with three takeaways that best summarize my thoughts from the TNTP report . We would do well to consider the following in education reform:

  1. Coherency (in curriculum & assessment, first and foremost)
  2. Clarity (in expectations, feedback, and roles for teachers and students)
  3. Hard work (and more hard work)

*Thanks to Educators 4 Excellence for this opportunity

**I think this is what may have contributed to the differences between the charter and district schools in this study. The charter network was more effective in supporting their teachers effectiveness and growth over time. Charter schools often have much tighter and coherent school-wide structures and systems tied to assessment, curriculum, teacher practice, and observation.