By Derrick Brown (follow on Twitter @dbrowndbrown)
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Boundary Value Problems (778
Words)
By Derrick Brown (Join Our Mailing List!)
In mathematics, a boundary value problem describes a system whose solution depends on what happens at the edges ... the limits that frame everything inside. Teaching, it turns out, works the same way.
Friday’s chaos taught me that I had to do a better job defining edges.
Not to build walls, but to mark where grace ends and foolishness begins.
Defining the Problem
Students were “weaponizing” bathroom pass requests … perhaps to register their displeasure with what (and how they) were being taught … and the resulting boredom.
Every “Can I go?” might have really been “Can I escape?”
So I designed a quiet counter-move.
Before second block began, I pre-wrote passes for the 2 most frequent “fleers” …
and handed them out at the door.
“You don’t have to ask anymore,” I said. “Go when you need to.”
It was both permission and pre-emption ... a neutral (and neutralizing) way of
saying I see how you move … and I
still trust you … but “check mate.”.
Only one of them used the pass.
Quietly.
Respectfully.
The other “did not need to go” … and perhaps never “needs” to go.
And just like that, the tension was diffused.
Boundaries, it turns out, are not just about control.
They are about clarity ... the invisible architecture that lets relationships breathe.
Logic
and Limits
In 1B, my strongest group, I introduced a new kind of challenge … moving away from plugging numbers into calculators … toward visible thinking ... seeing, saying, and showing geometric truths.
Gone were the “solve-for-x” shortcuts. In their place: congruence statements, logic chains, and disciplined reasoning.
There was some “kicking and screaming.”
Leaving the “temple of the familiar” is hard.
But by the end, I could see understanding flicker behind the resistance.
They were learning that mathematics, like maturity, requires structure.
The Village Principle
In 2B, the pre-written passes were only half the story.
The other half was collaboration ... the kind of village work that makes
boundaries sustainable.
KP, one of my toughest students, came in quiet after a conversation with our
resident mentor (a former football coach).
“I know,” I told him. “Coach and I talked before you did.”
He smiled ... half-sheepish, half-relieved.
We had “cornered” him … not with punishment … but with alignment.
When adults echo each other’s expectations, kids stop performing for
sympathy … and division.
They start respecting and practicing accountability.
That is the difference between a rule and a relationship.
When the Line Is Crossed
Then came 3B ... the real test of the system.
MM2 had been moved to a new seat after several weeks of subtle defiance.
I had warned her that sitting in the old spot again would mean she was choosing disrespect.
She walked in, dropped her backpack ... and sat in the old seat.
“Forgot,” she said.
I gestured to the new seat … and said nothing.
Sometimes firmness needs no words.
Boundaries only work when you enforce them as calmly as you draw them.
Grace in Practice
Each class taught a different boundary condition:
· 1B ... Logic. Discipline as intellectual honesty.
· 2B ... Structure. Restoration through trust and teamwork.
· 3B ... Clarity. Consequences without cruelty.
Even my hallway exchanges reflected the lesson.
I told AB and TA about “Lizard
Liabilities” ... the essay about control, compassion, and the student who saved
a gecko.
AW, that gecko-saving student, smiled when I mentioned it.
JS, once distant, now confided about cheerleading drama ... a sign that respect
had returned … where resentment once lived.
Every interaction, from the bathroom pass to the lizard story, traced the
same equation:
Grace × Consistency = Peace.
The Deeper Math
In geometry, a figure under rigid transformation moves without changing size
or shape.
In teaching, the challenge is similar: to move with compassion without
shrinking your standards.
Boundaries multiply grace and divide chaos.
They are the denominators that stabilize every human equation.
And like all math problems, they require visible work ... writing the steps, not just the answer.
Last Days, Lasting Lessons
I know I am in my “last days” as a classroom teacher.
But that awareness sharpens my sense of purpose.
These aren’t just lessons in congruence and coordinate planes.
They’re living experiments in how authority and empathy coexist ... how to
teach kids to “solve for x” without losing sight of why.
Some days I feel like the variable in everyone else’s equation ... an
unknown to be “managed, tolerated, or replaced.”
Yet moments like today remind me that the work still matters …
… when a student honors a boundary you drew with care,
… when another finds calm after being held accountable,
… when logic replaces noise.
Selah
Boundaries are not barriers.
They are the grace lines that give freedom its shape.
They teach both teacher and student that love without structure is chaos …
… and structure without love is cruelty.
The art of teaching ... and maybe of living ... is learning how to draw those lines with mercy … and to redraw them … daily … in peace.
Selah.
(The "Follow The Leader (changED - Volume 2)" Audio and Video Album / Mixtape is also available at TeachersPayTeachers.com)
(The "changED (Volume 1)" Audio and Video Album / Mixtape is also available at TeachersPayTeachers.com)
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I am a “standup storyteller.”
I fuse rap, spoken word (poetry), oration (traditional public speaking), singing, and teaching into messages of hope, healing, and change that I write, direct, and produce to help people who help people.
Everything must change - and stay changED.
Tradition begins and ends with change.
Change begins with me and the renewing of my mind ... then continues through efforts to effect small-group discipleship (equipping others to equip others) with audiences that respect and embrace mentoring, mediation, and problem solving as tools of change.
I am the product of my mentoring relationships, peacemaking (and peacekeeping), and problem-solving ability.
My education began when I finished school.
After school, I enrolled in a lifelong curriculum that includes classes in ministry, entrepreneurship, stewardship, literacy, numeracy, language, self-identity, self-expression, and analysis / synthesis.
My projects execute a ministry that has evolved from wisdom earned through lessons learned.
I want to share this wisdom to build teams of "triple threat" fellows - mentors, mediators, and problem solvers.
We will collaborate in simple, powerful ways that allow us to help people who help people.
I now know that power is work done efficiently (with wise and skillful use of resources, interests, communication, and expertise).
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