My son Ben once taught me more about mathematics with five putts than most assessment systems ever could.

We were working with a new putting stroke, and I set up a ladder at roughly 10, 15, 20, 25 and 30 feet. The scoring was simple. Leave it short and you get nothing, because short putts don't go in. Hole it and you get two points. Get it past the hole but within two feet and you get one. Run it farther than two feet past and you can reclaim the point by making the comebacker. The goal was six points out of ten.

Ben holed the first three. He had already reached six points and accomplished the goal when he looked at me and said, “See? Three in a row.”

Something had changed. Nothing physical had changed. It was the same kid, the same putter and the same stroke, but now there was a streak. The fourth putt had become important.

It was longer and uphill. I watched him make a longer stroke and then, near impact, try to rescue it. There was a little steering, and he pulled it. The speed was still good enough to finish within two feet, so he earned another point, but his self-created goal of four in a row was gone.

Then came the fifth putt. He had already exceeded my original goal, and his new challenge of making four in a row had disappeared. This time he left it short.

Five putts had produced three different psychological states, and the final two misses came from almost opposite conditions. If all I recorded were the outcomes, I would have missed the most important information.

Sergio Garcia's Putt

At the 2007 Open Championship at Carnoustie, Sergio Garcia reached the 18th green on Sunday with a chance to win his first major. His par putt missed, and Pádraig Harrington eventually won the playoff.

When I watch Garcia's stroke, I see a tiny disruption, a little stab and a little steering. I cannot know exactly what was happening inside Garcia's head from television footage, but I recognize the performance pattern because I have seen versions of it in athletes I have coached and in myself.

The putt had become important.

Garcia was trying to win the Open Championship. Ben was trying to show his father that he could make four putts in a row. The stakes aren't remotely comparable, but the underlying performance problem can be. A movement you already know how to make can become harder to access when the outcome becomes emotionally important.

The same thing happens in mathematics. A kid gets three problems right, and suddenly the fourth one means an A, keeping the streak alive, proving something to the teacher or not disappointing Mom. The mathematics may be no more difficult than it was three minutes ago, but it is no longer the same performance.

Then Comes the Fifth Putt

Ben's fourth putt became too important. His fifth wasn't important enough.

That is ADHD performance in miniature. Sometimes the nervous system doesn't have enough interest, novelty, challenge, urgency, passion, competition or creative engagement to come fully online. Sometimes anxiety, shame, fear, disappointment or performance pressure creates so much emotional noise that access to an already-developed skill becomes harder.

After enough fourth putts, a kid can also discover the emotional protection of the fifth. The homework comes back covered in red, the quiz is another bad grade, and another benchmark confirms what everybody already seems to think. Eventually, “I can't do this” can become “This is stupid. School is stupid. Who cares?”

Sometimes indifference is the beginning of the story. Sometimes it is the end. The child may have cared enormously for a very long time, but caring hurt and checking out hurt less.

Then the ball doesn't reach the hole, and we record another deficit.

Pádraig Harrington Didn't Need the Scoreboard

There was another lesson unfolding at Carnoustie that day.

Before the final round, Harrington and his caddie, Ronan Flood, had discussed how they would play the 14th hole. If Harrington needed to chase, they could be aggressive. If he was in contention, the safer play was a five-wood that kept dangerous bunkers out of play.

Harrington deliberately avoided the leaderboards. When Flood suggested the five-wood on 14, Harrington understood what that meant: he was in contention. He played the shot, then hit a 4-iron close and made eagle.

The scoreboard mattered because Flood needed the information to manage strategy. Harrington didn't need to carry the scoreboard around in his head.

The caddie managed the scoreboard. The golfer played golf.

There is an enormous educational lesson hiding inside that distinction.

Assessment Is the Scoreboard

Everything in a mathematics classroom is performance. Classwork, homework, conversations with the teacher, quizzes, projects, presentations, mental math, board work and tests are all opportunities for a student to perform.

Assessment gives us information about those performances. That makes assessment useful, but it does not make assessment the game.

A golfer shoots 78. That's a real outcome, but 78 cannot tell you whether the golfer drove beautifully and putted terribly, made fourteen pars and exploded on two holes, became anxious coming down the stretch, chose bad targets, or repeatedly hit good shots that produced bad outcomes. Nobody who understands golf thinks 78 explains the golfer. You have to watch the golfer.

Yet a child scores 62 in mathematics and we are tempted to treat 62 as if it explains the child. It cannot partition knowledge from retrieval, confidence from anxiety, engagement from boredom, shame from misunderstanding, working-memory load from negative self-talk, or today's performance from years of accumulated emotional baggage.

The scoreboard tells us what happened. It cannot tell us why.

Sports Psychology Watches the Performer

This is one reason I think teacher preparation has something important to learn from sports psychology. Sports psychology lives close to performance. Work with the athlete, watch them perform, intervene, watch what happens next and adjust.

Performance >> observation >> intervention >> performance >> adjustment

Those short feedback loops create practical knowledge about confidence, attention, visualization, anxiety, motivation, regulation, recovery and what happens when a performance suddenly becomes important.

Education can build a very different loop. Find the error, circle it, score it, remediate it and test it again. If we aren't careful, we can make the error more emotionally memorable than the correction.

We can give a child a bag of shame and then wonder why it gets heavier every time they walk into mathematics.

Math Is a Performance Sport

Mathematics is also far more physical than we often acknowledge.

Put a pencil in a student's hand. They write an equation, make a mark, cross something out, move underneath it, draw an auxiliary line, sketch a graph, circle a relationship or rearrange something. The visual landscape changes, and that changed landscape suggests another move.

See >> move >> changed picture >> infer >> move >> changed picture >> infer

The pencil is not merely recording thinking that has already happened. Sometimes the movement helps create the thought.

Jeff Hawkins' work on sensorimotor models of intelligence has helped me think more deeply about this. Perception, movement and location interact as we construct models of the world. That is much richer than simply saying somebody is a “kinesthetic learner.”

When I work mathematics with a pencil, I am creating a visual map and a kinetic sequence together. In plain English, I have “doubled my chances” of finding my way home, not as a statistical claim but as a description of having another pathway available for retracing the thought. Sometimes the picture retrieves the movement, and sometimes the movement retrieves the picture.

Construction is simply multidimensional retracing.

Why a Keyboard Is Different

Typing is obviously kinetic too, but the relationship between the movement and the mathematical object is different.

A keypress is largely generic. Writing an equation, extending a line, circling a factor, sketching a parabola or moving through a derivation creates movements spatially coupled to the representation itself.

Recent handwriting research using high-density EEG has found broader patterns of brain connectivity during handwriting than typing, although that work did not directly demonstrate better mathematics learning and should not be stretched beyond what it measured.

We don't need handwriting to be magic. The better question is how many meaningful pathways back to the idea we are giving the learner.

The Post Is Doing the Teaching

I didn't learn this way of teaching from golf instructor Shawn Clement. I recognized myself in the way Clement teaches because I learn sports by feel.

Don't give me twelve positions to remember, six mechanical checkpoints and a process for consciously assembling the movement. Show me what we're trying to accomplish, give me an experience that lets me feel it, and then get out of the way. I'll find my version of it.

Long before I encountered Clement, I was doing something similar while coaching soccer one-on-one. To teach a side volley, I would put a soccer ball against the goalpost and have the player strike through the center of it with the thick part of the foot. Hit it squarely and the foot recoils straight back. You can feel that.

The post is doing the teaching.

Then I would hold the ball against the post, occasionally risking a broken hand in service of education, and progressively raise it. Two feet, three feet, waist high, depending on the player.

Something fascinating happens as the ball gets higher. A player unfamiliar with the side volley initially tends to stand too upright. As the striking leg rises toward parallel with the hips, that leg begins threatening the player's balance. The body has to solve the problem. To preserve the square-contact feeling while staying balanced, the player begins tilting back.

I don't have to prescribe an exact torso angle because the progression itself teaches the counterbalance.

Once the player owns the feeling, I toss the ball and timing enters. If the moving ball causes enough frustration that the player loses the feel, we don't respond with six new instructions. We go back to the post, recover the feeling and return to the moving ball.

I once did this with a club soccer player whose left foot was weak. Within a couple of minutes he was hitting left-footed side volleys. When he nailed one, he looked at me and said, “How is this happening?”

He hadn't memorized the positions. He had discovered the feel.

Structured Experimental Learning

That's what I call structured experimental learning.

Create a task, let the learner move through it, provide immediate feedback, adjust the challenge, introduce variation and let the learner discover a functional version that belongs to them.

Structured experiment >> movement >> immediate feedback >> adjustment >> variation >> ownership

Feel is not the absence of understanding. The “why” can emerge inside the experimentation. That matters because I don't want to confuse telling somebody how something works with teaching their brain how to do it.

The same architecture shows up when I tutor mathematics.

Teaching Students to See

One of the most common things I hear from an anxious student is some version of, “I can't do math in my head.”

I am not particularly interested in turning them into human calculators. I want them to develop a feel for numbers and symbols.

So we work with relationships. Threes, fives, sixes, nines, tens, elevens and twenty-fives become familiar enough that numbers begin to have texture. I want the student to look at a number and have it start talking to them.

If I see 475, I can see the 75 on the end and recognize that 25 may be sitting inside it. If I see √475, that ending gives me a doorway. Since 475 = 25 × 19, √475 becomes 5√19.

With 675, I don't need to start formal division to see 25. I think in quarters. How many quarters are in six dollars? Twenty-four. Then there is 75 cents left, which is three more quarters. Twenty-seven. Done.

So 675 = 25 × 27.

That isn't a procedure for factoring 675. It's a way of seeing it.

If I see:

x² − 4x − 140

I need two numbers whose product is −140 and whose sum is −4. Ten is staring at me. Ten and fourteen differ by four. Because the product is negative, the signs must differ, and because the sum is negative, the larger-magnitude number must be negative.

So −14 and 10 give me:

(x − 14)(x + 10)

The student begins seeing relationships instead of waiting for me to tell them which process to execute.

Can You See It Now?

Then I start moving quickly. I give them an easier quadratic, then another one, then something slightly more complicated, followed by something that uses a relationship we just discovered in a different way.

“Can you see it now?”

Then another.

“Can you see it?”

It becomes almost a rapid-fire mathematical version of Socratic learning, the math-athletic version of the ladder drill.

Mathematics, however, is a nonlinear ladder. Every step is built from something that came before, while the pathways continually branch and recombine.

See something >> use it >> vary it >> combine it >> recognize it somewhere else >> see more

Take 374. Three plus four is seven, which tells me 11 may be hiding inside the number. Why?

I don't need to begin by giving the kid an algebraic proof. Let them see it:

Plaintext

  340
+  34
-------
  374

The 3 remains on the outside, the 4 remains on the outside, and in the middle 3 + 4 gives us 7. So 374 = 34 × 11.

Now experiment with it. Let the relationship become familiar enough that the student begins seeing 11 before being told to look for it.

Do the same with divisibility by 3 and 9. If the digits add to a multiple of 3, there's a 3 available. If they add to a multiple of 9, there's a 9. If the number is even and divisible by 3, there's a 6. If it's even and divisible by 9, there's an 18. Endings of 25, 50, 75 or 00 give us another familiar doorway through 25.

These aren't cute tricks. We're building a library of things the student can see.

Confidence Is Seeing Multiple Doorways

Now give the student 204.

One student might see 204 = 2 × 102 = 2 × 2 × 51. The digits of 51 add to 6, so there's a 3. Maybe the student doesn't immediately remember 51 ÷ 3. Fine. Use the calculator and get 17. Now 204 = 2 × 2 × 3 × 17 = 12 × 17.

Another student may immediately see that 204 is divisible by 4. Twenty divided by four is five, four divided by four is one, so now they have 51. Then they see the 3. Another kid may see 6.

I don't particularly care which doorway they use. That's the point.

Now give them:

x² + 5x − 204

They need a product of −204 and a sum of 5. If 12 and 17 are already visible, the signs become the next relationship because 17 + (−12) = 5. The quadratic factors as:

(x + 17)(x − 12)

The roots are −17 and 12, and now another doorway appears. The axis of symmetry sits halfway between the roots:

(−17 + 12)/2 = −2.5

One visible relationship exposes another.

That's what mathematical confidence feels like to me. It isn't knowing that you have memorized the correct procedure for whatever problem somebody puts in front of you.

Real confidence is seeing multiple doorways.

You may see only the first step. You may see the first three. Occasionally you can see all the way to the pail. What matters is that you can begin, and if the first doorway doesn't work, there is another one.

The Calculator Didn't Replace Number Sense

This also changes the role of the calculator.

If the student sees that 51 is divisible by 3 but doesn't instantly retrieve 51 ÷ 3, I have no philosophical objection to the calculator giving them 17. The calculator didn't replace number sense. Number sense told the student what question to ask the calculator.

That distinction matters enormously.

The same thing applies to standardized tests like the SAT. Some problems that look computationally expensive become very fast when the relationships are visible. That doesn't mean rushing. It means avoiding unnecessary work.

Feel >> see quickly >> solve accurately >> conserve time >> spend time where thinking is actually required

We aren't training students to calculate faster. We're training them to see sooner.

Why Isn't the Kid Seeing It?

Eventually that becomes the most important question in the classroom.

Not simply, “Why doesn't the student know it?”

Why isn't the student seeing it?

Those are not necessarily the same problem.

An experienced baseball hitter doesn't consciously calculate the trajectory of a pitch after it leaves the pitcher's hand. The player has accumulated enough experience that perception becomes anticipatory. The hitter begins seeing where the ball is going before the conscious mind could possibly calculate all of it.

That kind of seeing can also be delicate. Introduce enough anxiety, distraction, negative thought or emotional noise and the athlete can lose access to something they absolutely know how to do.

Golf provides an almost ridiculous example. A player stands behind the ball and visualizes the shot, then steps in and somebody's camera clicks. The golfer backs away.

Why?

The physical skill didn't disappear when the shutter fired. The picture disappeared. So the golfer resets, sees the shot again and steps back in.

Now think about an anxious child staring at a quadratic equation. Maybe the student hasn't developed the feel yet, or maybe the student has developed it and cannot access it because the emotional noise has become louder than the mathematics.

Those are completely different instructional problems.

The scoreboard records the shot. The teacher needs to know why the golfer lost the picture.

Life's About Pivoting, Not Perfect

I learned this lesson myself in 1992 when I took the GRE and scored a 790 Analytical, 780 Quantitative and 490 Verbal. The quantitative section taught me one hell of a lesson about performance because, for some reason, I went into that section wanting to be perfect.

I had never done that before in mathematics. Ever. Normally, I could look at a problem and see something. I might not immediately see the entire solution, but I could see a step, a relationship, a doorway into the problem. If I couldn't see enough to get moving, I moved on and came back later. That was just how I took math tests.

This time I wanted to be perfect, and I hit one problem that I couldn't see. I couldn't see the problem, couldn't see the first step and, for some reason, couldn't see any of the processes that normally would have been available to me. Then came the really important part: because I wanted to be perfect, the fact that I couldn't see it immediately created an emotional spike.

Now I really couldn't see it.

The first failure to see the problem created emotional noise, and that emotional noise made it even harder to see the problem. Instead of doing what I had always done naturally and pivoting to the next problem, I stayed there trying to force myself to see something that was becoming increasingly difficult to see.

Can't see it >> emotional spike >> more noise >> see even less >> refuse to leave >> more noise

Eventually I looked at the clock and realized I had five minutes left with nine problems to go. I flew through eight of them and ran out of time before I could finish the ninth. I missed two problems and got a 780.

Had I not gone into that test wanting to be perfect, would I have been perfect? Probably not. But I probably would have gotten a 790 instead of a 780, which would have been cool. Instead, I blew it because I had placed an importance on being perfect that I had never placed on a math test before.

My mathematical ability hadn't changed. I hadn't suddenly forgotten mathematics or how to take a test. What changed was the emotional condition under which I was trying to access what I knew. I wanted to be perfect, I couldn't see one problem immediately, that bothered me because I wanted to be perfect, and the resulting emotional noise made the doorways I normally could see disappear.

That is Ben's fourth putt.

It is also why, when a kid is sitting in front of a mathematics problem and apparently can't do it, I keep coming back to the same question: Why isn't the kid seeing it? Sometimes the kid doesn't know the mathematics. Sometimes the kid knows a hell of a lot more mathematics than the performance in front of you suggests. The difference may be whether they can see it through the noise.

When I tell my athletes, “Life's about pivoting, not perfect,” I didn't get that from a motivational poster.

I learned that one the hard way.

How to Be a Champion in the Math Classroom

Sports psychology gives us something far more useful than motivational posters because champions don't merely develop skills. They learn how to create the psychological conditions that allow those skills to appear when they need them.

Jack Nicklaus famously described visualization as seeing a movie of the shot before playing it. The target, trajectory and behavior of the ball existed in his mind before he stepped into the performance. What sometimes looked from the outside like Nicklaus standing around thinking harder was almost the opposite. He was progressively eliminating everything that did not belong there.

That is the performance routine.

The routine is not the golf swing. The routine creates access to the golf swing.

That distinction matters in mathematics. A mathematical procedure is a sequence of operations for solving a class of problems. A performance routine is what helps the student access the mathematics they already possess.

Have confidence in your game. Have confidence in your routine. Have confidence in what you see.

Then perform.

The goal isn't to become obsessed with the outcome. Once the ball leaves the putter face, the golfer has lost control of it. The green, gravity and whatever imperfections exist between the ball and the cup take over. The golfer's job was to prepare, see the picture and make the stroke.

The mathematics student needs a version of that freedom too.

Celebrate the Makes. Acknowledge the Misses.

For me, the phrase on a miss became very simple:

Oh well. It's how you learn.

That isn't pretending the miss didn't happen, and it isn't saying the outcome doesn't matter. The miss may contain enormously useful information. Take the information without taking the emotional baggage.

The make gets different treatment. Celebrate it. Let the kid experience what just happened and let that success acquire some emotional weight. They saw something they couldn't see before. They figured something out. They did something they didn't think they could do.

Those are memories worth strengthening.

The miss needs to be acknowledged without being given enough emotional energy to become indelible. You don't want the student's next problem beginning with a replay of the previous failure.

Celebrate the make >> strengthen the picture of competence

Acknowledge the miss >> extract the lesson >> pivot

That is not positive thinking. It is performance management.

Bob Rotella tells a story about Jack Nicklaus that captures this beautifully. Nicklaus once claimed that he had never three-putted the final green of a tournament, even though people listening knew that he had. Rotella's point was not that Nicklaus literally had never done it. Nicklaus was demonstrating how champions think.

The miss happened. He wasn't interested in carrying it.

Failure doesn't deserve unlimited access to the next performance.

Chris Jones Got Destroyed Too

You can see the same philosophy at a completely different scale.

When the Kansas City Chiefs lost Super Bowl LIX 40–22 to the Philadelphia Eagles, Chris Jones was not dealing with a six-foot putt or a missed mathematics problem. His team had just been thoroughly beaten on the biggest stage in American sports.

Jones talked to his teammates afterward about learning from it. The loss was supposed to hurt, but it was also a lesson they could build from. Philadelphia had been better that day. Accept it, learn from it and use it the next time you're there.

That's how you disarm a miss.

You don't pretend you didn't just get destroyed by the Eagles. You don't minimize it, and you don't manufacture some story in which it secretly wasn't a failure. You acknowledge exactly what happened and ask what it can teach you.

Then you pivot.

The miss is allowed to contain information. It is not entitled to define the next performance.

Memorialize What You Need to Do

There are going to be wobbles. You get distracted, a negative thought gets in, you stop trusting the routine, you become outcome-focused or you lose the picture.

Don't beat yourself up over it. Write it down in a little journal so the useful information has somewhere to live, and then work on those things.

But be very careful about what you memorialize.

Don't memorialize the failure. Memorialize what you need to do and what you should have done.

If I miss a putt because I lost the picture and became obsessed with the outcome, I don't need to write, “I blew the six-footer on 18.” I already know that. Writing it down simply gives the failure another opportunity to become emotionally indelible.

What I need is something like: I lost the picture. Next time, back away, reset, rebuild the picture and don't step back in until I can see and feel the putt again.

Now I have preserved the lesson without preserving the failure.

The mathematics version is the same. Instead of memorializing, I screwed up another quadratic, memorialize what needs to happen next time: I saw the factors but didn't check which signs produced the middle term. Next time, check the product and the sum before committing.

The failure belongs in the past. The lesson belongs in the future.

What Should the Performer Actually Assess?

Golf has a wonderfully cruel scoreboard because every stroke counts. You don't get to negotiate with the scorecard.

But the scorecard is not the only assessment I should give myself.

The ultimate assessment for me is this: Did I make an honest effort to get engaged, stay engaged and have confidence in my routine on every shot I took?

Those are things I can influence. I cannot control every bounce, every imperfection in a green or what happens to the ball after it leaves the clubface. I can control whether I prepare myself to perform. I can notice when my attention wanders, recognize when a negative thought appears, rebuild the picture and return to what I am trying to do.

That gives us a very different internal scoreboard for the mathematics student. Did I make an honest effort to engage? Did I stay engaged? Did I have confidence in what I could see? When one doorway didn't work, did I look for another? When I missed, did I learn from it and pivot?

Those are things a student can actually work on.

The external score still exists. The test is still graded. The golfer still writes down the six.

But the performer doesn't have to become the score.

The Assessment Tsunami Teaches the Opposite Lesson

Now compare that with what happens as many schools approach an end-of-course exam.

Assessment follows benchmark, benchmark follows assessment, data meetings lead to remediation, remediation leads to another assessment, and another set of numbers is generated to determine whether the student is on track to pass the EOC.

The intention is understandable. The school wants the child to succeed.

But the constant tsunami of assessment can create exactly the opposite psychological environment from the one we would deliberately create for an athlete trying to perform at the top of their game.

Every miss gets recorded, scored, analyzed, revisited and tested again. Instead of teaching the child how to disarm a miss, the system can keep handing the miss back to them.

For an anxious student, the next assessment is no longer simply another opportunity to do mathematics. It can carry the previous score, the approaching EOC, the fear of another failure and the growing emotional importance of what the next number is going to say.

Then we ask why the kid isn't seeing it.

Maybe we're making it harder for them to see.

In sports, we understand that staring at the leaderboard can interfere with performing the shot directly in front of you. In education, we can turn the leaderboard into the curriculum.

The irony is that in our attempt to produce a better EOC score, we may create performance conditions that make the score harder to produce.

It's Ben's fourth putt institutionalized.

We made the putt important.

Project-Based Learning Changes the Scoreboard

This is one of the things about project-based learning that I find so powerful. The student ends up with a portfolio of work, and that portfolio becomes part of the assessment.

A project allows perseverance to become visible. Something doesn't work, so the student changes it. They try another approach, get feedback, revise, build another version and keep going. The mistake becomes part of the learning process rather than a permanent mark against the student.

Life's about pivoting, not perfect.

That doesn't mean the test disappears. I still want to assess the student's knowledge and skills. The difference is that not all of the assessment is sitting on that one test. Not all of the scoreboard is the test.

The student also has this other thing they have built, revised and persevered through.

Psychologically, that matters. If one test is carrying the entire meaning of whether I am succeeding, every problem can acquire the emotional weight of Ben's fourth putt. If I also have a portfolio filled with things I built, solved, revised, improved and completed, I possess another body of evidence about what I can do.

Baseball makes this obvious.

You can lose the game and still go three-for-four with a home run and three RBIs.

Both things are true. The team scoreboard says you lost, while your individual performance says you had one hell of a game. Maybe your fourth at-bat was a strikeout. That strikeout is real too, but nobody who understands baseball would use that strikeout as the defining evidence of your performance while ignoring the three hits, the home run and the three RBIs.

Different scoreboards tell us different things.

The test can tell us what knowledge and skills the student demonstrated at one moment. The portfolio can show us what the student can accomplish when they are allowed to learn, experiment, persevere, revise and pivot.

We need both kinds of information.

A single scoreboard never tells the whole story of the performer.

Real Empathy Is a Professional Skill

All of this requires something from teachers that I think we dramatically undervalue: real empathy.

Relatable empathy is comparatively easy because somebody experiences something I have experienced and my own history gives me a bridge. Real empathy begins when that easy bridge runs out. It is the ability to connect with another human being whose internal experience may be nothing like yours.

That takes humility, curiosity, observation, work and training.

A teacher sees a child staring at a mathematics problem. Maybe the child doesn't understand it, didn't prepare or simply isn't engaged. Maybe the child is ashamed or terrified. Maybe the problem has become Ben's fourth putt, or maybe we're looking at Ben's fifth.

Same scoreboard. Opposite problems.

The dangerous shortcut is projection: If I behaved this way, it would mean I didn't care. Therefore this child doesn't care.

Real empathy interrupts that conclusion with a much better question: I don't understand this behavior yet. What am I missing?

Teachers don't need to become psychologists. They do need enough experience with different kinds of performers to recognize when the obvious explanation does not adequately explain the human being in front of them.

That makes real empathy a professional skill.

My Instinct Didn't Come From a Teacher-Training Manual

I brought a lifetime of performance into the classroom. I had been a Division I athlete, experienced performance anxiety myself and coached athletes. I knew what hesitation looked like when the skill was there. I knew what frustration could do to movement, and I knew that confidence could appear remarkably quickly when somebody experienced authentic success.

Then I watched mathematics students.

A student hesitating does not necessarily lack knowledge. A student repeatedly erasing correct work is telling you something. A student's performance changing dramatically while the mathematics remains roughly constant is telling you something.

My GRE experience is another reason I recognize it. I know what it feels like to possess the mathematical ability and suddenly be unable to see the problem because emotional noise got in the way.

That intuition isn't magic. It is compressed experience.

Which raises an obvious question: Why should we require teachers to accumulate twenty years of accidental experience before they have access to some of it?

Teachers Need Film Study

Sports solved part of this problem a long time ago: film study.

Teacher preparation could deliberately expose future teachers to performances they may not otherwise encounter until years into their careers. Show them an ADHD student trying to initiate a genuinely low-interest task, an anxious student getting the right answer and then talking themselves out of it, repeated erasing, apparent defiance after embarrassment, or what happens when body-doubling suddenly changes initiation.

Then stop the tape and ask what they see, what the plausible explanations are, what else could explain the behavior, what they would change and what they predict will happen next. Then roll the tape.

That is how you begin building a library of human performance.

We already accept specialized preparation for many learner populations, yet ADHD support is still too often reduced to accommodations such as extra time, preferential seating, breaks and fewer distractions.

That is not an instructional model.

Where is the systematic preparation in engagement, initiation, emotional regulation, shame, confidence, rejection-sensitive responses, short feedback loops, interest, novelty, challenge, urgency and the difference between possessing an ability and accessing it at the moment of performance?

Teachers need that library because real empathy beyond the relatable requires something to work with.

Stop Training Teachers to Read Only the Scoreboard

Our institutional machinery is exceptionally good at generating numbers.

Numbers matter, but numbers are not children.

Finland offers an interesting contrast. Its basic education system does not revolve around nationally standardized testing of every child, while classroom assessment remains substantially teacher-led. At the same time, teacher preparation, particularly for subject teachers, is extensive and generally master's-level.

Finland didn't eliminate assessment. It invested heavily in the people doing the observing.

That matters in mathematics because deep subject knowledge gives a teacher more keys. Method A doesn't connect, so try B. Still nothing? Try C, then D, then approach the same relationship visually, numerically, spatially, verbally or through a problem the student already understands.

But mathematical mastery is only half of the library.

A deep mathematical library provides alternative pathways into the mathematics. A deep human library provides alternative explanations for the performer.

We should be trying to build teachers with both.

The Institutional Blind Spot

I don't think the fundamental problem is that teachers don't care. Most of the teachers I have worked with cared enormously.

The problem is that we ask them to make extraordinarily complex judgments about human performance without necessarily giving them enough preparation in human performance, and then we surround them with scoreboards.

A more precise scoreboard cannot compensate for an inadequate explanation of what produced the score.

A 62 is real. Another benchmark can confirm the 62, a district assessment can validate the 62, and an EOC can produce an even more consequential version of the 62. None of those numbers necessarily tells us why the child produced it.

Worse, measurement itself can alter the next performance when the measurement becomes emotionally important. Enough fourth putts can eventually create a fifth-putt kid who doesn't care, doesn't try and leaves it short.

Then we record that result too and call it another deficit.

That's a big swing and a miss.

Reclaiming the Math Classroom

Sports psychology starts from a simple premise: watch the performer. Watch what changes, watch what happens under pressure, build confidence through authentic success, treat mistakes as information rather than verdicts, create progressions, shorten feedback loops, and know when the scoreboard is useful and when it needs to get out of the performer's head.

Mathematics deserves the same sophistication.

Let students manipulate things, draw, write, retrace, experiment and build visual and kinetic maps. Develop feel instead of merely collecting procedures. Give them enough relationships that numbers and symbols begin talking to them, and teach them to see multiple doorways.

Then prepare teachers to recognize what can interfere with that seeing. Anxiety matters. Shame matters. ADHD matters. Trauma matters. Confidence matters. Performance pressure matters. The history the student carries into the room matters.

Perhaps many of the things we call neurodivergent accommodations have been trying to teach us something larger all along. Interest helps everybody. Short feedback loops help everybody. Authentic challenge helps everybody. Reduced shame helps everybody. Confidence built from genuine success helps everybody.

Assessment still matters. Ronan Flood needed the scoreboard because Harrington's position in the tournament affected strategy.

Harrington needed to hit the golf shot.

Those are different jobs.

Epistemic Status & Testable Predictions

The central argument here is a synthesis of sports psychology, sensorimotor theories of learning, ADHD-informed instruction, athletic coaching and my own frontline observations in classrooms, tutoring and sports. Golf, soccer, baseball and mathematics are obviously not identical activities. The comparison is at the level of performance: learned capabilities being accessed under changing motivational, emotional, cognitive, physical and environmental conditions.

My frontline observation is that progressive challenge, immediate feedback, authentic success and gradual removal of scaffolding can reveal abilities that were not apparent in the learner's initial performance. Ben's putting ladder is a small example because the physical skill remained essentially stable while the psychological meaning of successive putts changed dramatically.

Testable Prediction: Emotional Noise Can Make the Doorways Disappear

My hypothesis is that some apparent mathematical deficits are partly performance deficits: knowledge or pattern recognition that becomes less accessible under anxiety, shame, low engagement, excessive importance, negative self-talk or accumulated emotional history.

My own GRE experience provides a personal example of the proposed mechanism. The underlying quantitative ability did not disappear, but once I failed to see a problem immediately and attached emotional importance to that failure, the resulting emotional noise appeared to interfere with my ability to see the mathematical pathways I would normally have accessed.

That produces a straightforward testable prediction. On mathematically equivalent tasks, some students should identify fewer viable first moves, or fewer “doorways,” when performance pressure or emotional load increases. If the pressure is reduced while mathematical difficulty remains constant, some of those pathways should become visible again.

Testable Prediction: How We Practice Changes What Transfers

Students taught through progressive challenge, rapid feedback, recovery after errors, meaningful engagement and multiple demonstrations of competence should show different patterns of persistence and transfer than students whose experience is dominated by procedural rehearsal and outcome-focused assessment.

This should be measurable not merely through final scores, but through what students do when they encounter something unfamiliar. Do they initiate? Do they experiment? Do they recognize multiple possible entry points? Do they pivot when the first one doesn't work?

Testable Prediction: Too Little and Too Much Can Look the Same

For ADHD students in particular, I hypothesize that both insufficient motivational salience and excessive emotional salience can impair performance. The observable outcome can look similar even when the underlying states are nearly opposite.

Ben's fourth and fifth putts are the simplest illustration. One became too important. The other wasn't important enough. Both missed.

If that mechanism carries into academic performance, similar incorrect responses, incomplete work or apparent disengagement should sometimes emerge from very different internal performance states. Changing the motivational or emotional conditions should therefore affect those students differently even when the academic task remains essentially unchanged.

Testable Prediction: The Way We Construct Mathematics May Affect Retrieval

I also hypothesize that handwritten mathematical manipulation can provide spatial, visual, motor and proprioceptive retrieval information that is altered or reduced when mathematical work is moved primarily to generic keyboard input. Existing handwriting research makes that question worth testing; it does not by itself establish the mathematics-specific claim.

If the hypothesis is correct, students constructing mathematical relationships by hand should show measurable differences in later retrieval or transfer compared with students performing equivalent mathematical work primarily through generic keyboard input.

Testable Prediction: The Discrepancy Is Evidence

Most importantly, discrepancies in a student's performance across contexts should not automatically be treated as noise to be averaged away.

A student who can suddenly do something under one set of conditions that they could not do under another has told us something important about the system. If performance changes substantially while the underlying mathematical demand remains stable, we should be investigating what changed around the mathematics rather than simply averaging the performances together.

The discrepancy may be evidence.

The score matters because it tells us something about where the learner is. What it cannot capture is the journey that got them there, the conditions under which they performed, or the journey that might carry them somewhere else.

A champion learns to celebrate the makes and acknowledge the misses. A champion takes the information from failure without giving the failure enough emotional weight to become the picture carried into the next performance. A champion memorializes what needs to happen next, not what went wrong before, and understands that when something does go wrong, the only useful direction left is forward.

Life's about pivoting, not perfect.

The scoreboard is not the game.

The journey is.

And the child is never the score.

References

Clay, V., Leadholm, N., & Hawkins, J. (2024). The Thousand Brains Project: A New Paradigm for Sensorimotor Intelligence. arXiv:2412.18354. This develops the sensorimotor framework discussed in the article, including learning through movement and spatial reference frames. (arXiv)

Finnish National Agency for Education. Basic Information About Primary and Lower Secondary Education. Finland's national education agency states that there are no national tests in primary and lower-secondary schools; assessment is conducted by teachers using continuous and summative assessment and multiple forms of evidence. (Opetushallitus)

Finnish National Agency for Education. Working as a Teacher in Finland With a Foreign Qualification. The agency's qualification guidance states that Finnish subject-teacher qualification requires a master's degree, studies in the teaching subject, and teachers' pedagogical studies. (Opetushallitus)

Harrington, P. (2007). 2007 Open Champion. Harrington's own account of the final round at Carnoustie describes his pre-round strategy discussion with caddie Ronan Flood, his decision not to watch leaderboards, Flood's recommendation of five-wood at the 14th, and Harrington realizing from that recommendation that he was in contention. (Padraig Harrington)

Hawkins, J. (2021). A Thousand Brains: A New Theory of Intelligence. Basic Books. Hawkins develops the broader Thousand Brains theory underlying the article's discussion of sensorimotor learning, movement, location and reference frames. The Thousand Brains Project's technical documentation also identifies this work as a foundational source for the theory. (Thousand Brains Project)

Hawkins, J., Lewis, M., Klukas, M., Purdy, S., & Ahmad, S. (2019). “A Framework for Intelligence and Cortical Function Based on Grid Cells in the Neocortex.” Frontiers in Neural Circuits, 12, 121. This is one of the technical foundations for Hawkins' theory of location-based reference frames and sensorimotor inference. (Thousand Brains Project)

Pinet, S., & Longcamp, M. (2024). “Commentary: Handwriting but not Typewriting Leads to Widespread Brain Connectivity: A High-Density EEG Study With Implications for the Classroom.” Frontiers in Psychology, 15. The commentary identifies important methodological and interpretive limitations in claims that the EEG findings establish a learning advantage, which is why the article treats the handwriting evidence as suggestive rather than conclusive. (Frontiers)

Rotella, B. (2015). How Champions Think: In Sports and in Life. Simon & Schuster. Rotella recounts the Jack Nicklaus story in which Nicklaus insisted that he had never three-putted the 72nd green of a tournament despite a listener knowing counterexamples. Rotella uses the exchange to illustrate Nicklaus's refusal to preserve failures as part of his performance memory. (studylib.net)

Rotella, B. (2004). The Golfer's Mind: Play to Play Great. Free Press.

Rotella, B. (2001). Putting Out of Your Mind. Free Press. Rotella also uses Nicklaus's selective memory for missed putts to illustrate the performance value of remembering successful putts rather than repeatedly rehearsing failures. (Independent)

RTÉ Sport. (2007). “Harrington Wins Open Championship.” Contemporary reporting from Carnoustie records Garcia needing par on the 18th to win, hitting from the greenside bunker to eight feet and missing the putt before Harrington defeated him in the playoff. (RTÉ)

Shook, N. (2025). “Chiefs-Eagles in Super Bowl LIX: What We Learned From Philadelphia's 40–22 Win.” NFL.com.Contemporary game reporting confirms Philadelphia's 40–22 victory over Kansas City in Super Bowl LIX. (NFL)

Sports Illustrated. (2025). “How Chris Jones' Locker-Room Speech After Super Bowl Loss Resonated.” Jones's postgame remarks describe the loss as a lesson and something the Chiefs could build from, while acknowledging that Philadelphia had been the better team that day—the basis for the article's discussion of “disarming a miss.” (SI)

Van der Weel, F. R. R., & Van der Meer, A. L. H. (2024). “Handwriting but Not Typewriting Leads to Widespread Brain Connectivity: A High-Density EEG Study With Implications for the Classroom.” Frontiers in Psychology, 14, 1219945. The study used 256-channel EEG recordings from 36 university students and reported more elaborate connectivity patterns during handwriting than keyboard typing. (Frontiers)