Lately, I’m working in two kinds of classrooms: ones where the teacher makes good use of digital devices and the other where the teacher makes good use of paper. I’m noticing the same challenge in both classrooms: students come to believe their effort doesn’t matter.

They know they can complete the next slide or not. They know they can answer the next workbook question or not. They know how to hide. Whether they’re working on screens or paper, they know how to look busy and when.

I’m watching the teacher circulate around the room. As she moves, every student inside a two-desk radius locks in on their page, brows furrowed, scribbling or typing, but when the teacher moves on they relax.

This is the challenge—making difficult cognitive work matter to kids. Teachers have lots of responses to that challenge, but most of them scale the time cost linearly with the number of students. Checking in with students in class. Grading each warmup. Grading each student for participation. Calling home. Grading all the essays. Double the students and you double the time cost for each of those interventions. This is burnout. Teachers need non-linear responses here, responses where doubling the students costs something far less than double the time.

“I have been struggling with this post-COVID,” veteran educator Nick Corley told me recently. “The number of students who only work when watched or for a grade has increased significantly. I’d love to hear what is working for others.”

Five Friends

Me too, Nick. So I pulled in five friends—veteran educators, coaches, total pros, and asked them:

What is a reliable way you can let a bunch of students—students who outnumber you 20 or 30 to 1—know that their effort, their work matters?

Zak Champagne taught elementary math for years and recently became Chief Content Officer at Flynn Education. He said the key to getting kids to sustain their effort with students was giving kids permission to stop sustaining their effort.

Now this might sound counterintuitive, right? Walking away from a math problem sounds like they don’t have to show effort. However, it was my experience that when the young people in my room knew they could walk away, they were less likely to do that. And they would spend more time working through the tough stuff. Sometimes just knowing you have the option to walk away from something is the very thing that keeps you going. And providing that option communicates to them that you trust them.

Katrine Bryan has been a secondary math teacher in San Luis Obispo County, CA, a math teacher coach, and I’ve showcased her teaching here before:

Moving away from a viewpoint focused on teacher knowledge to a stance that celebrates student voice and student actions will build the foundation, showcasing that what a student does matters: to the teacher, to their peers and ultimately, to themselves.

Pam Seda has held down jobs from classroom teacher to district math supervisor. She consults and recently co-authored the book Choosing to See: A Framework for Equity in the Math Classroom, which seemed relevant to my question.

Students learn that their work matters when the audience shifts from the teacher to their peers. When a classroom moves from a group of individuals to a community of learners — where anyone can be an expert and anyone can contribute to the group’s collective knowledge — the stakes become real.

One example: when students do group work, instead of asking each group to present their own process to the class, have the class speculate about how a group was thinking based solely on the work they see. No presentation, no narration — just the work, doing the talking. In this way, the phrase “make your thinking visible” becomes far more meaningful when students know their peers — not just their teacher — are the ones doing the reading.

Dylan Kane is one of the most thoughtful and discerning math educators around, one who teaches at a high level and still somehow has energy to share his thoughts at his newsletter:

I think really hard about the first things students do when we’re launching into a new activity to build momentum. I often start with a simple, straightforward question on relevant prior knowledge, and ask students to answer on mini whiteboards. Students are most likely to see their learning matters when I meet a few basic conditions: I build off of what they already know, I begin with something students can do successfully and that makes them feel smart, and I check to make sure students are learning and adjust when they are not. Mini whiteboards are the best tool I’ve found to help me meet students where they are, adjust on the fly, and build momentum at the start of class.

Tracy Zager is a former classroom teacher, current coach, author of Becoming the Math Teacher You Wish You’d Had, and perhaps most importantly, the editor of my book (still forthcoming):

I need to do the slow and careful and authentic work of creating a community where each student’s thinking and work really does matter–to the student, to their classmates, and to the learning of the class as a whole. My first thought is there are three big components:

• I need to choose curriculum and tasks that are worthy of my students’ time and thinking.

• I need to give a why behind everything we do–what is the purpose? If I don’t have a good purpose for a task, into the bin it goes.

• And I need to teach students how to listen and learn together.

Three of my five friends name the same solution—community development—the slow, halting process of investing one student into the presence and ideas of another. This strikes me as one of those non-linear responses. As the class size grows larger, so too does the size of the community, the number of people who are, potentially, vested in your work. It’s also a solution that runs counter to the prevailing wisdom that what these kids all need is their own individual AI tutor.

I’m trying not to be a reactionary here, complaining about Kids These Days and yelling at clouds, but there does seem to be a dramatic vibe shift post-COVID that I am sure is multi-faceted and I’m grateful to these five friends (and anyone in the comments) each working to understand that shift and work to change it.

Odds & Ends

¶ Tim Daly recently brought useful data to the question of what it takes to get kids to try hard.

What makes kids try harder? Teachers, mostly. Strong teachers motivate students to elevate their effort as the material gets more challenging. A positive school culture - the sum of many teachers and support staff aligned to the same standard - ensures consistency across classrooms and magnifies the effect.

¶ EdSurge reports on a perspective towards AI among teachers that I also find quite common—not optimism, not pessimism, just indifference.

When teachers consider introducing AI tools to students during class time, the calculations they make change. The relevant question becomes: What student learning problem does this tool solve? Many educators are still trying to answer this question, even after several years of exposure to generative AI in some capacity.

¶ Bill McCallum, a lead author of the Common Core State Standards and the Illustrative Mathematics curriculum, is publishing a newsletter. In a recent post, he re-opens a 20-year-old paper from Sweller, et al, celebrating direct instruction and criticizing discovery learning. McCallum checks the citations and finds something interesting in Sweller’s praise for worked examples:

Here is the irony. The strongest evidence-based use of worked examples—carefully designed, presented in contrasting pairs, with structured opportunities for analysis and discussion—looks a lot like the kind of instruction that Kirschner et al would dismiss as constructivist-based minimal guidance. It manages cognitive load, yes, but through thoughtful task design, not by eliminating the need for student reasoning. It is, in fact, a form of productive struggle.

¶ Just a bonkers survey out from RAND. Student use of AI for homework help is up 14%. The majority of those students use AI in spite of their belief that it’s hurting them:

As of December 2025, 67 percent of students endorsed the statement “The more students use AI for their schoolwork, the more it will harm their critical thinking skills” — up more than 10 percentage points from ten months earlier.

¶ Peps Mccrea writes about the ways lesson plan design and user interface design inform one another.

The principles behind great UI are often relevant to the classroom. We could even think of teaching as Learner Interface Design. Here’s what that looks like:

Teachers have to think ten steps ahead of 30 other people, imagining dozens of possible futures, many of them quite bad. It’s fantastic preparation for the work of designing technology.

Teaching is weird. More specifically, humans are weird, and teachers spend their days trapped in a room with a bunch of little humans. Weird things happen.

Fierce Feats of Problem Solving

I shared a classroom with an English teacher over a decade ago who did something he called “Fierce Fridays.” I don’t remember the details, it was some type of close reading routine. And to get students excited, each Friday he would show a picture of something “fierce.”

Fast forward to today.

I adapted the idea into what I call “Fierce Feats of Problem Solving.” I wrote a few months ago about how I incorporate math puzzles, games, and problem solving activities into my classes. Before we do these, I frame the activities as “Fierce Feats of Problem Solving” and show students a picture of something fierce.

The first fierce picture of the year is always this one:

I use all sorts of pictures. Humans, animals. Whatever. If it looks vaguely fierce, it’s in.

Over time, students started contributing. They send me pictures of their pets, or their younger siblings, or weird memes. I’ve accumulated a massive collection of fierce photos. Now I sometimes get stuff like this in my email inbox:

If You’re Not Cracking...

Like many teachers, I love lame little catchphrases. Something I say sometimes is “Let’s get cracking,” as in “Let’s get started.” I think that’s a pretty normal phrase. Check me for a second here. Am I right? Does “get cracking” mean “get started” in this context?

My students this year told me that “cracking” actually means “to do crack.”

Now let’s be clear. My students are wrong. That is not what “cracking” means. I will not let a bunch of 12-year-olds change the meaning of a cherished phrase.

So I turned it into a little call-and-response. As class starts and students sit down to begin their Do Now, I say, “Let’s get cracking! If you’re not cracking...” and students (reluctantly) respond, “you’re lacking!”

Bootytickled

Ok this one is really weird. Brace yourself.

My students recently started saying “bootytickled.” Bootytickled seems to be a synonym for “bothered,” so “Bro why you so bootytickled” would mean something similar to,“Hello friend, why is this bothering you so much?”

Anyway, students started saying that word. I requested they not say it. Seems reasonable, right? This is math class. We should be talking about math, not booties.

A student wondered aloud why I was so bootytickled by the word bootytickled. I observed that it was, in fact, a bit ironic. Turns out many of my students don’t know what “ironic” means, so I taught a little impromptu lesson about irony. I thought I was being clever. Teachable moment, amirite?

This was a mistake. By engaging sincerely with the idea of being bootytickled, I gave the word legitimacy. Now I can’t eradicate it.

Like many teachers I get frustrated or annoyed on a pretty regular basis. Word has spread. When Mr. Kane gets annoyed, make a joke about him being bootytickled.

Happily, this faded after a few weeks and students went back to making 6-7 jokes. But for a while, any time I was visibly annoyed with something, a student would comment that I was bootytickled. For me, it became a kindof weird little reminder. I would get annoyed at someone flipping their water bottle. A student would say, “Mister why you so bootytickled?” And I would say to myself, “Hey, I’m not going to let this bother me.” I would take a little moment to find serenity, push down the annoyance, take the water bottle, and keep teaching.

Be Weird

I don’t recommend copying what I do. Every teacher is weird in their own way. Let your personality shine through in whatever way works for you.

I do think there’s a lesson here. Lean into weirdness. Be human.

One of my perpetually unpopular opinions is that school is good. Age-graded classrooms, one-size-fits-all curriculum, and factory-model schools are easy to hate. Hate them if you like! School is far from perfect, but it’s the best we have. It’s the worst way of educating ever invented…except for all the others.

I think one key reason is the weirdness. A bunch of kids are required to come to my class every day and I give them some math to do. For 50 minutes they’re stuck with me and I’m stuck with them. All the inside jokes and weird little moments are what change an obligation into a ritual. Am I a complete loser in my students’ minds? Absolutely. But I’m a complete loser who students are, more often than not, willing to work hard for. That sounds pretty cool to me.

I want to argue that AI models will write good code because of economic incentives. Good code is cheaper to generate and maintain. Competition is high between the AI models right now, and the ones that win will help developers ship reliable features fastest, which requires simple, maintainable code. Good code will prevail, not only because we want it to (though we do!), but because economic forces demand it. Markets will not reward slop in coding, in the long-term.

— Soohoon Choi, Slop Is Not Necessarily The Future

Tags: slop, ai-assisted-programming, generative-ai, agentic-engineering, ai, llms

Idea

One of the most common worries I hear from parents and see on online forums is:

“My kid didn’t fully understand this concept. Should we slow down? Should I be worried?”

The truth:

• Understanding in math almost never happens the first time or second time.

In fact, many mathematicians would say it takes three to five exposures to really understand something.

• The first time: you get the shape of the idea

• The second time: you notice what you missed

• The third time: it starts to click

• The fourth and fifth time: you can actually use it

So if your kid does not fully understand a concept the first time they see it, that’s not a problem.

It’s natural and expected.

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This is not a flaw in your child, nor is it a flaw in the material.

It’s just how learning math works.

Even if they are a “math-y” kid.

Story

There’s a wonderful (and very human) story about two famous mathematicians: Hermann Weyl and David Hilbert.

Hermann Weyl and David Hilbert are discussing this very topic.

For some context, a quick snapshot of their background.

Hermann Weyl was a German mathematician whose research was in theoretical physics and number theory, and he had been described as one of the “last great universal mathematicians of the nineteenth century.”

David Hilbert was a German mathematician described as “one of the most influential mathematicians of his time,” and in 1900 presented a collection of 23 problems known as “Hilbert’s problems” that have helped drive mathematical research ever since (note: many of them are still unsolved!).

Weyl asked Hilbert:

“How many times do you have to explain something to your students before they understand it?”

Hilbert replied:

“Five times, Hermann, five times. But for very talented students like you, three times is enough.”

Even among the greatest mathematicians, understanding wasn’t expected to happen instantly.

It took repetition.

Personal Example

A few months ago, one of my kids was learning a new concept in geometry.

They followed the lesson and could do some of the homework.

But there were some problems they couldn’t solve because they couldn’t quite grasp how the lesson topic related to the problem.

Instead of stopping everything, we kept going.

As a rule of thumb, if they’re getting about 60–80% of the material, we move forward, trusting we’ll see it again.

A week later, the same idea showed up again, only this time inside a new type of problem.

And suddenly:

“Ohhh… that’s why we did that.”

The problems that once felt impossible became solvable (and were!).

This has happened to us so many times that we now expect it to happen

Which is why we don’t aim for 100% mastery the first time.

Getting to 100% is nearly impossible the first (or even second) time, so we keep going, knowing eventually they’ll get it.

Each time they revisit the concept, their understanding deepens, not because they stayed longer, but because they saw it from a new angle.

What at first looked like confusion was actually the beginning of understanding.

Why it matters

If we expect children to “get it” the first time, two things happen:

1. Kids feel like they’re failing when they’re not

2. Parents feel like they need to intervene too early

Real understanding of math is layered and takes time.

This is why many math curricula (even traditional ones) are designed to spiral:

• Concepts come back again and again

• Each time with slightly more depth

• Each time making more sense

• With space in between, so the idea feels “new” again

There’s also another important piece:

Sometimes a child doesn’t understand something because they don’t yet see why they need it.

For example, many students struggle with high school algebra, not because algebra is too hard, but because they haven’t yet seen why it matters.

Then they encounter calculus or physics, and suddenly those same algebra rules become essential.

When I’ve spoken with (high school and college) calculus teachers, they often say:

It’s not the calculus that students struggle with; it’s the algebra.

In many cases, a student’s real understanding of algebra arrives during calculus.

There’s even a saying:

“You don’t understand a class until you’ve taken the class that depends on it.”

That is, understanding often arises when the context for why and how it’s used emerges.

Practical tip

Instead of asking:

“Do they fully understand this?”

Try asking:

“Have they seen this enough times to be familiar with it?”

And if they haven’t seen it enough times, you don’t need to:

• re-teach everything

• slow everything down

• or find the “perfect” explanation

You can simply:

• Keep moving forward

• Mark the concept mentally (“we’ll see this again”)

• Revisit it later from a different source

One of the advantages of learning today is that “another source” is easy to find:

• a different book

• a YouTube video

• a new type of problem

• or even explaining it to someone else

Different explanations unlock different insights.

Takeaway

Your child does not need to understand a concept the first time they see it.

They need to see it multiple times, in multiple ways, over time.

The key to getting good at math is to keep doing math.

So if frustration creeps in (for them or for you(!)), take a breath and keep going.

That’s how deep understanding is built.

How to practice

Try this small shift the next time your kid says:

“I don’t get this.”

Say:

“That’s okay. You might not have seen it enough times yet.”

Then:

• Let them try a few problems

• Move on if needed

• Revisit the idea later in the week

You can even make it explicit:

“You’re going to have to see this idea a few more times before it clicks.”

Over time, your child will internalize the incredibly powerful lesson:

• Understanding is a process that happens over time

Really, truly believing this lesson will help them not only in math, but in anything else they choose to learn.

That’s all for today :) For more Kids Who Love Math treats, check out our archives.

Stay Mathy!

Talk soon,
Sebastian

There’s a reason it’s a popular aphorism

The post The Students Who Believe Practice Makes Perfect Get Pretty Perfect Grades appeared first on Nautilus.