Counterfactual Reasoning, Black Swans, and Common Planning Conundrums

There are many nuts-and-bolts topics discussed (which is probably why you are here) in the name of counterfactual thinking and black swans.  All interesting, but you may by here for only one, so scroll down to what interest you.  In order, the topics are: Introduction, Configuration, Schedule, Placement, Last Thoughts.  Enjoy.

Counterfactual Reasoning and Black Swan Planning

A few weeks ago I wrote about counterfactual reasoning–that it is easier to prove something doesn’t work than it is that is does work.  For example, it is hard to prove that coming to school leads to learning, but we know truants fall behind.  This is important to remember as we plan–we can’t confirm much about the future, but we can plan with that blind spot in mind.

The idea becomes important when looking at the surprises we seem to encounter after we do a lot of planning for the next year (placement, schedule, resource allocation, etc.).  The theory of this is the “black swan“; that unexpected events have a major effect on plans.  Because of this, the theory goes, we should plan with the unexpected in mind.  The other half of the theory is that it is difficult to know what to plan for.  In short, just be ready for something.

Note: Much of this is inspired by  Nassim Nicholas Taleb’s Black Swan: The Impact of the Highly Improbable.  Much of this essay looks at the unexpected events that cause those disruptions every educator can relate to–nothing Earth shattering, but annoying nevertheless.

As educators, we tend to lock everything down–protocols, lessons, spaces, schedules, class lists–because we like to think we can predict everything.  For example, our school locked students into the three homerooms last June, but we did not take into account several unexpected developments.

The largest was we had asked students their World Language preference (French or Spanish).  Our students move through the school by classroom–Art, PE, Music and World Language.  During the summer we realized we could not honor most preferences because placement was based on a different criteria.  We punted.  But we also did not expect several students from one classroom to move away or that so many new families would move into our district.  We placed with insufficient information.  Then student preferences for WL created more turmoil, as parents demanded their kid get this or that language (they, of course, waiting for three weeks into September before doing so).  It also took a few weeks to figure out the WL/Tier II needs of new and leaving students.  Who knew?

As the old Yiddish proverb goes, “Man plans and God laughs.”

One of the mistakes people make is in trying to anticipate the black swan.  If we only anticipate more contingencies we think we can control it all.  No.  We certainly can straighten out many issues.  And we still have to make plans–schedules, room assignments, placement, etc.  How, though, can we plan while respecting the unknown?

Here are some examples of common issues facing schools.


A few weeks ago I shared a configuration idea for our middle school.  For forever they have been multi-age, but they are contemplating going straight-grade “just for next year” because class sizes are getting too large and students are falling through the cracks.  There are several challenges facing the team, but the main one will be the influx or exodus of students.  I argue maintaining multi-age classrooms is the best safeguard against student numbers changing.

They are adding a fifth teacher to a four person team.  The Core is responsible for Language Arts, Math, Science and Social Science.  Currently, two teachers are licensed to teach STEM and two Humanities.  To alleviate class sizes they plan to hire a Science teacher.  In theory, this lowers the class average from 28 students to 23.  Of course, because the new teacher can only teach Science it does nothing to help the Humanities classes .  In theory, one of the STEM teachers will shift some of her load towards Math, but Math being taught straight-grade and other elements conspire against such neat divisions.

Using the our middle school’s straight-grade plan as an example, three teachers for the 7th and two for the 8th creates an automatic imbalance.  Of course, these can be mitigated (supports, aides, schedule).  But, should five students leave the 7th, or five join the 8th (or both), there is suddenly a difficult situation with no easy fix.  We can’t know if that scenario will play out, or be worse.  The plan, though, is crafted with little wiggle room should any black swan appear.

Using counterfactual thinking, instead create a multi-age made up of two teams.  Each team has a Science and Humanities teacher.  A single Math teacher instructs all students–a big load, but she is relieved of other duties and the two teams can focus on social-emotional middle school programming.

Imagine, now, five students leave the seventh–the release would be divided between two teams, offering a slight relief of two or three on each team.  In the case of the five joining the 8th, a much more devastating event, that burden would be shared and only result in two or three each.  In fact, if both scenarios play out, much of the effect is a wash.  Multi-age benefits can mitigate the other effects of population bubbles.  For example, each year teachers move (with their classrooms) and they need to relearn new curriculum and start new team protocols, etc.  Multi-age allows multi-dimensional flex.

But the question to ask is why that plan will not work?  I have shown the problems of straight grade (there are more, unwritten here), but that does not mean multi-age is better.  The black swan, counterfactual advice is to take each option and poke at it–with some of the more outlandish variables–until it reveals its flaws.  Then, put down other ideas, too, and poke them.  One area to look at is which “losses” are most tolerable and which would be devastating.  The plan with the most resiliency is probably your best bet.


The difficulties of crafting a schedule are long and well known (we even know that we don’t know enough).  This is especially true in schools with many grades and diverse needs (we are a pre-K through 8).

I actually learned a lot recently on why crafting a schedule is so hard through an article on chaos theory (an article for later).  In short, such endeavors are dynamic and resetting course causes exponential problems down the path.   What we do know is that schedule craft works up to 80% of the elements are placed, but then conflicts trouble the last 20% of needs (that’s the dynamic nature of the process).  To fix it we begin to make compromises (which creates more conflict, exponentially).  Each year, someone (or many) is (are) unhappy.

Then, each year, we have a black swan surprise.  Last year, it was WL and everything that followed it.  Other grades had other emergencies.  Each fix seemed to bring more problems.  We live with it–we have no choice–but that 20% consumed a lot of resources and continues to create ripples (e.g., it is unclear if student preference for WL will be honored in 7th grade now that they have a year of one language under their belt.).

My solution is blocking out time instead of scheduling in time.  For example, one grade level figures four uninterrupted hours of seven school hours are needed for Core–90 minutes of Literacy, 60 minutes for Math, 60 for Science/Social Science and 30 for TA.  We demonstrate what’s important to an organization by the resources we put towards it (time, money) and four hours uninterrupted seems a reasonable commitment.  That leaves three hours for lunch, recess, Unified Arts (UA), band, mentor, counseling and any other non-Core activity.

How is a block resilient?  Let’s look at how our current system is not.  Predicting a seven hour day is hard; there are many variables.  It is also easy to be fooled by small numbers–three kids pulled out here, four there.  Currently, music lessons, mentor, speech and physical therapy, and other student needs are pulled from Core.  There are many reasons for this–part time employees and mentors have locked-in schedules, no one wants to deny a child their one Art class a week, and a few kids here or there are seen as non-disruptive.  But in my class of 20, one absence and three music lessons are 20% of the class.  Plus, recovery now becomes a negotiation not with two other Core teachers, but with three times that–pull from Art? PE? (And, because of the dynamics of the interwoven schedule, also lose 20% of their students and need recovery for them).  Again, here is the problem I am poking a hole in with our current schedule and how it was created.

By dividing the day into two blocks (4 hour, 3 hour) that do not overlap, students and teachers only have to negotiate within those blocks, with only those adults.  It is more likely I can flex with my Core teammate’s schedule because a) we have an aligned schedule, b) fewer pulls (classes) means fewer and smaller disruptions, c) fewer agents means less communication needed.  On Core, we can debate the virtues of Math vs. Science and time required to do it right, but with blocks we do not have to debate the death by a thousand cuts we currently face.  Four hours uninterrupted shows we value Literacy, Math, Science and Hive.  Three hours should be enough for others to negotiate what is best for students, among actors who have more in common (UA).  Or, to demonstrate that we want more for our students than the resources we have (or are willing) to give.  Again, this may be flawed.  Poke it.

Student Placement

Has there not been an issue with placement?  Do kids every come as advertised, stay friends (or enemies) with the kids from the previous year, or continue to need the same services?  Too often, we’ve even had to change the teacher assigned to the class (illness, pregnancy, number shifts).  For all the benefits we argue placement provides, those are the holes I poke in our locking kids in as we do.

Three years ago, the middle school wisely created two teams with a blank slate for placement.  First, Special Ed (SE) placed students on the two teams with a variety of rationales–service providers, friend/tormentor locations and the like.  This was open to debate/poking by the group, but we deferred to the experts.  Second, a small number of kids who do not receive services were separated or paired because of behavior or emotional needs.  Some kids need friendly peers, while others are a bit too friendly during class time.  All told, about 20% of placement was locked in like this.  That is an example of necessary planning with what is  known (at that time).  What’s important to note is what they did not do–lock in the remaining 80%.

Then, the sending teachers made two “balanced” teams.  More poking.  But the most important part was that no one was locked in until mid-September.  Each week the middle school would observe interactions, listen to students and families, and shift kids around.  Then, they locked in all kids, creating permanent teams and focused on creating identities for those teams and bonds within.

They waited because kids change–they move, they mature and their allegiances shift.  Because services did not have much flexibility (the nature of Spec Ed and part-timers), and some kids need reassurances (i.e., not being placed with a bully or knowing an adult face before the first day of school), those 20% never shifted.  But, as things shook out, a flexibility was built in for the other 80% so that movement was possible.  By the third week, the two teams were as solid as one is going to get.  It was a successful year.

Compare that flexibility with what happened when we locked in the grade last year that suffered at the hands of WL.  For what was gained (a faint sense of knowing their homeroom) much was lost.  While we should be aware of the anxiety we create with some unknowns, it can be fleeting compared to the year-long stress of a bad fit created by the black swan.  Again, the above might not survive a good poke, but our current spring lock-in is troublesome in the long term.

A Note About Counterfactual Poking

It is easy to spot flaws.  The question is a) if that flaw is true in any viable model, b) if that flaw has a major effect.

For example, one argument I have heard against postponing placement until a few weeks into the year is anxiety and parental concern.  Yet, when we locked in the placement of kids, one or two parents would inevitably call with concerns (or be more forceful about it).  Sometimes, that brought a dam break of other requests as parents micromanaged.  In short, parents and kids worry regardless.  The former is easily dealt with because the concerning elements are often soothed with more information, and solutions can be shared (including locking in needs).  The latter upends a carefully planned order, with results (according to chaos theory) that can prove exponential.

So, caution is necessary when weighing options.  People need to be objective that all plans have downsides–sometimes the same downsides–but some recover better.


The idea is that the we don’t know what we don’t know, but we still have to plan.  We want to poke holes in things early, and be honest about defects, before we choose the model that is best for students.

9 Steps to Creating a Schedule for a Complex Organization: Part Two

Schools are not the only organizations with a host of constituents demanding varied needs be met, but they offer a great case study.  I have broken these steps into two distinct parts: Theoretical  and Building.  Both are essential to success over 180 days.
Warning: It is easy to skip steps, especially the theoretical.  This groundwork is essential for the building portion to work.  Otherwise, you’ve got a “Blind Men and the Elephant” scenario.  Check out Part One here.
Part Two: Building: The mistake here is to see this as blocks needing to be stacked.  It’s true, in a sense, but when that mental shift happens the schedule produced becomes a series of pounding square pegs into round holes; lots of edges feel the rub.  At the same time, the water metaphor no longer works because a rigid line is needed in order to truly understand what works and what only seems to work (but, in the details, things are lost).
5. Schedule Everything: The big things become clear, and often have minor compromises; nothing is harder to roll with than additional surprises.  Often, these surprises are more disruptive than the larger issues.  For example, the one grade level at our school had 4.5 hours a day with students, or 22.5 hours in a week.  Band and Chorus was scheduled for three 40 minute blocks, or 2 hours, for 2/3 of our students (the remaining 1/3 were left for the teachers to plan for).  That left 20.5 hours of instruction for all kids.  Seems reasonable, except instrument lessons pull an additional 4 hours, and those are small clumps of kids that come-and-go at odd, rotating times–very disruptive.  When you craft the schedule, and put in 6 plus hours of music, it paints a very different picture.
But the time culprits are many: Guidance, mentors, Tier II, Special Ed…..  Each needs to pencil in a projected time.  The guidance counselor, for example, knows a bunch of his caseload.  If a special 3-4th grade block was identified based on expected need and time outside of non-negotiable times, that service would have a solid place to start and flexibility moving into September.
6. Populate the Schedule: Without a dry run, the schedule is an estimate.  That leads to grey areas, but grey areas add up to black over the course of the process.  While you might not have placement, you do know how many kids get pulled for X, Y and Z and can make reasonable assumptions about where they go.  For several years, one grade level had two sections of World Language–one French and one Spanish.  Then, the population bumped up.  It was a surprise that there needed to be three WL classes, not two as there had been.  That meant one Spanish and two French, which drove the UA groups, that had been driven by the homerooms–see, dominoes.  With each grade picturing their day–if not walking through it–many of the unexpected bits come into play.  Account for every kid and location.
7. Dry Run the Schedule: Even if each grade level imagines the day instead of physically walking through it, that’s something.  Did you take into account transition time?  The time it takes to put on snowsuits and take them off is substantial, especially if UA proceeds and follows recess.  For example, one grade’s schedule has kids go from UA to recess, which works well, but when they need their Chromebooks for UA after recess they go to the room, undress, get Chromebooks and walk to UA–five to ten minutes lost in a 40 minutes class.  Run the schedule in winter and warmer months, or whatever demands change in your locale.
8. All Teachers Sign Off: Every year, groups are asked to look and report back on if it works.  Every year, most people do.  But some don’t.  A few yeas ago, no lunch was scheduled for UA in the frenzy of crafting something that works; adjusting for it made the schedule a kludge, but since it was June everyone just went with it.  These things were not caught until after the schedule was set.  Everyone was mad at the group all year for the compromises.  Pet Peeve: There is often a member of the staff that claims to be helpless, and the nurturing environment of a school bends over backwards to accommodate, even as that person is rigid in their not being proactive or bending in retrospect.  Ugh.  At least with a signature, there is no buck-passing and everyone is forced to take some ownership of their part in the process.
9. First Schedule Wins (Bad): We like to believe the process is open and cooperative, but in reality the first schedule that works for 3/4 of the school rules.  Even with compelling arguments against it, little more than tweaks occur.  For that reason, the first few rules above are essential.  They need to be concrete as possible, and drive planning.
One way to counter this is to present multiple, diverse schedules.  Presented with three very different ways of doing something, people will see the possibilities, even when the schedule just doesn’t work.  By then going and adapting the best of several, you not only get more good ideas, but everyone sees how what was chosen is not the first presented, but the best of otherwise flawed plans.  It is otherwise easy to find fault without being tasked with a solution.
Every group needs to feel empowered.  There are a few ways to do this.  For example, allow each group to have the power to veto at each step, but once a step is adopted they lose that power.  So, if 90 minutes of literacy is a non-negotiable and adopted, the schedule bends to that even if means other desires are compromised when the final schedule comes out.  Each group should also have the power to create an alternative schedule.  Whatever, but something needs to happen to counter the “First Schedule Wins” problem.

9 Steps to Creating a Schedule for a Complex Organization: Part One

Schools are not the only organizations with a host of constituents demanding varied needs be met, but they offer a great case study.  I have broken these steps into two distinct parts: Theoretical  and Building.  Both are essential to success over 180 days.
Warning: It is easy to skip steps, especially the theoretical.  This groundwork is essential for the building portion to work.  Otherwise, you’ve got a “Blind Men and the Elephant” scenario.  Still, you can check out Part 2 here.
Part One: Theoreticals: At this point of development, the schedule is like a river: Water is fluid, bends around anything and fills every crevice.  Much like time.  Here, you will begin to construct the vessel that contains it (beginning with Start and End times of the day) and identifying those impediments it needs to flow around.
1. Vision: The schedule is a physical manifestation of the vision.  For example, if you want certain people to collaborate they need the same preps.  Or, if starting the day with a Restorative Justice circle in homeroom is important, than the day cannot begin before 8:20, so teacher have at least 15 minutes to start the day right.  Make a list of the vision(s) in all respects and then figure what elements of the schedule facilitate that.
2. Recognize What’s Just Tradition: Much of the schedule is the remnants of old visions, initiatives and needs.  In keeping what worked this year, we often perpetuate other patterns that no longer drive the schedule.  For example, we had Art scheduled on a day that worked for the part-time Art teacher, who worked at other schools on other days–when her situation changed, no one thought of changing the day.  Spending time just messing with assumptions both helps question how things are done and opens up new possibilities.  Often, these are impediments to work around that people do not even realize they are accommodating for; removing them frees up possibilities.  Even those that are preferential may not be as non-negotiable as an issue that comes up later than is mission critical to members.
3. Plan for Two Years (at Least): The class sizes are clear–if the 3rd grade needs three teachers, the 4th grade will need it next year.  You should also account for what the 4th grade looks like the year after, too.  Which class sizes are close to a bust (so that three kids moving in in August requires an additional teacher, classroom and the like), or might not be sustainable (i.e., that teach could be moved to a grade that needs her more)?  Plan teams, room assignments and the like towards that.  Also, think how part time staff will be used over that time.  It may not seem directly related to the schedule, but a) planning two years makes you be realistic about next year, and b) most schedules go south because small, unexpected changes that happen before September 15.  Best be ready.
4. Define Non-negotiables: What are bedrock points, that no one can touch.  For example, at one point 60 minutes of Math and 90 minutes of Literacy a day were non-negotiable in the schedule.  For any grade level, I would advocate for 3 hours a day uninterrupted–no lessons, pull-outs or other distractions; we are guaranteed all of our kids for that period of time.  Class size might be another (Art can only hold 25 students physically in the room).
Part Two: Building: The mistake here is to see this as blocks needing to be stacked.  It’s true, in a sense, but when that mental shift happens the schedule produced becomes a series of pounding square pegs into round holes; lots of edges feel the rub.  At the same time, the water metaphor no longer works because a rigid line is needed in order to truly understand what works and what only seems to work (but, in the details, things are lost).

When You Choose Something, You Are Also Choosing Not

Too many people forget that in choosing a path, another is passed by.  Robert Frost understood this.  One of the most powerful themes of his poem “Road Not Taken” is that the titular path was “just as fair.”  In the end, what made all the difference was not that this or that path was less traveled, but that he made the choice.  That choice made all of the difference.

All of this comes into play when making a schedule.

For every education decision, the path taken is weighed against what is not.  Creating a schedule lays this bare each year.  If you give math more time, it will come from something else. As the parties vie for what they need to honor their subject, two things become clear: What the community as a whole values, and what each stakeholder values about themselves.

I have seen many different ways to craft a schedule. At a K-8 school different grade levels have different needs, so simply creating blocks and doling out portions is not the straightforward affair it tends to be at a straight elementary, middle or high school. Recently, each unit without our school has been sending representatives to a committee and, like the blind men and the elephant, we put something together. A look at the experience of our Unified Arts teachers is instructive for all.

The various parties who came to our scheduling brainstorm all had clear wants and needs.  Our Unified Arts faculty had a simple request–smaller classes.

This was understandable, as some of the rooms only held twenty students comfortably.  Our Family and Consumer Science room had cooktops for eighteen, and more than twenty middle school students in the Art room meant too many bodies.  In addition, Phys. Ed. was managing a combined class, which had over forty students.  Although they had two teachers, that many bodies meant for slow transitions and a lot of chaos.

Of course, if the student body and number of teachers remains the same year after year, creating smaller classes results in more classes overall.  If you have 100 students, for example, classes of twenty students are going to require five sections.  Smaller classes will require six, or more.

What the UA teachers did not realize at the time was that those extra sections would cause them to teach during their extra prep periods.  Our contract calls for a lunch and a prep totaling 70 minutes, but not necessarily a solid block. Typically, it plays out as having two forty minute blocks–one prep, and one lunch. All of the core classroom teachers are already at that threshold, but because the UA takes batches of students throughout the day they have been left with an uneven prep schedule.  On some days, they have four preps, while on others two.

When the beta version of the schedule, with smaller classes, was released they soon realized the trade-off.  Two teachers found they did not have lunch at any time that resembled lunch, and they had six block classes in a row. While long stretches of classes are not unusual for Core, the influx of varying grades–first grade one block, seventh the next–making it mentally and physically challenging. For Art, just managing the materials was near impossible. They had also lost their common planning time, which they often used for lunch and it kept them unified–and sane.

Suddenly, the larger classes were no longer an issue.

Unfortunately for them, a number of other needs had rushed into the vacuum and made a return to the old impossible.  They were given time to remake the schedule, but could never get it to work with all of the new services that had been added as UA covered more blocks. It was a rough year.

Lesson: Make sure all parties understand that choice comes with a price.  Eyes wide open.