Archive of Our Own ^beta

Daniel has been riding the post-tournament for the last 2 months when a funny little thing happens.

See, as a solid A-minus student, there are concepts he can grasp in the big scheme of 12th grade mathematics. All the other seniors (like Ali, like Bobby too) are taking Calculus. He's perfectly fine where he is taking Precalculus, even if he has to sit with the rest of the juniors. He's no doctor or engineer - and he can afford to waffle around for a bit in sunny California with that All Valley Tournament win under his belt. In fact, all his 11 AM third period has consisted of is running through the simple algebra and finding different numbers and letters. They did not lie - most of this stuff is a review of last year's level.

That is, until they start hitting the log button on their calculators.

Daniel blinks at the whiteboard. log₂(7x) = 3. There's about a billion things going on, his teacher's going on about some change of base formula, and- huh, Johnny's drawing snakes all over his paper again, the epitome of dumb and blonde but he can't say he's being any better right now that he's being sidetracked - and then they've gotten to their answer, 1.14...

He leans over and taps Susan on the shoulder. "Hey, what are we doing?"

She looks at him, deadpanned. "Pay attention next time, champ," she taunts, and then goes back to copying the 5 homework problems they get at the end of class every day before packing her stuff and heading to her next class. "Maybe Ali can help you?"

Daniel frowns. "Yeah, but Ali's studying for her competitions! Wait, I didn't get the-"

Susan's already out the door. Daniel blinks, before realizing that everyone is humming out of the classroom and he needs to gather his papers together if he wants any hope of being early to the lunch line. But god, there's so many things going on at once and he usually finishes copying the problems on the board so he can saunter his way to the front desk if he has any questions about their processes. But there isn't a process, it's just some stupid rearrangement and the tapping of some buttons-

"LaRusso!"

He freezes like a deer in headlights at the sound of that voice. Out of the corner of his eye, Daniel can see some of the old Cobras - nowadays, just a group of bikers, no more no less - dart their heads towards Johnny's loud and piercing voice. Daniel peeks at the whiteboard and tries to commit some of those problems to memory, as if that'll help prove his understanding of whatever they're learning if Johnny's coming up to taunt him about what little knowledge and grasping he has of logarithms.

But then Johnny hands him a lined sheet of paper, folded in half. "Look at me one more time, and you'll be failing more than this unit," he says in a whisper, dark and foreboding, before sauntering away with a nonchalant hand on his satchel bag. “Logarithmic to exponential form. Next time, pay attention, LaRusso.”

In the hallway, he joins Bobby and Tommy who are walking out of the Calculus class next door, immediately glowering red and shoving each other. They must be theorizing the launch angle of their next push-LaRusso-off-a-cliff escapade.

Still — morbid curiosity betrays him, and he opens up the folded lined paper with the expectation of an ass kicking invitation at Coyote Creek, or another chance to humiliate himself at the country club. Instead, he finds… log_b(x) = y => b^x = y.

He shrugs, pockets the homework problems and steps out. Mr. Miyagi helped him win a karate tournament in under 6 months of peripherally no karate training — he might know a thing or two about logarithmic equations.

“Daniel—san, I know nothing about logarithms.”

A loud groan emits from the Miyagi-Do dojo-house. “But you know everything, Mr. Miyagi!” Daniel yells, like that’ll make Mr. Miyagi understand this more than he doesn’t. “You helped Ali with her business calculus homework, you taught me how to get a straight line with a saw, hell, a karate tournament… and you can’t do this?”

Mr. Miyagi pours Daniel some lemonade. “Not fault of bad student. Only bad teacher,” Mr. Miyagi repeats the infamous proverb of past lessons. “Miyagi had no teacher. Miyagi has… no math!”

He laughs heartily, taking a sip of his lemonade and wincing before adding some more honey. Daniel thunks his head on the wooden table and groans in mental exhaustion. “Well, you can’t know everything,” he mutters to himself. “Damn.”

Sympathetically, Mr. Miyagi sits down next to him with the pitcher of lemonade. “Ahh, maybe I look at textbook? Doubt Miyagi ancestors will help with this one.”

“It’s no use. I’m gonna fail, I’m gonna fail!”

“Daniel, Daniel… you looove catastrophizing.”

A comforting hand rests on his back, rubbing up and down his unconsciously hunched over shoulders with a pitiful touch. “Here. You drink special lemonade.”

Lemonade. Like it’ll be any help in this instance, but hey, it’s sweltering hot outside and he would like a sip. Daniel takes the sweaty glass cup and takes a sip, bothers to ask — “What’s in this?”

“Hmm. Lemonade powder, honey. Ice.”

Mr. Miyagi gives him that witty look like he’s done something special again, and Daniel half wonders if he’s drinking some magical juice that’ll make him smart before Mr. Miyagi opens his textbook and skims to the chapter they’re on. He watches his Sensei skim through with furrowed brows, occasionally reaching over to sip from his cup and breathe in deeply. It’s the same position he takes when he’s doing kata, except his fingers trail over the various equations…

And then he closes the book and says, “Ah. Logarithm like karate.”

“...What?”

Mr. Miyagi smiles, like he’s cracked the code. “Logs like karate. Daniel-san, you remember… wax on, wax off?”

Daniel grumbles. “Mr. Miyagi, we just got off training. And these problems are due tomorrow, or else Ms. Barnes is gonna pull me into lunch tutoring to make sure I understand this stuff—”

“Daniel-san.”

Mr. Miyagi grabs his wrists. “Daniel-san, focus. You remember wax on, wax off?”

Daniel swallows. He has the determined look he had before, like he’s on the cusp of getting him to understand or grasp the concept he’s been building for ages. “Yeah,” he nods, and he can recall the movements in his muscles. The blocks. “You made me wax cars for days before I even threw a punch.”

“Good,” Mr. Miyagi says. “Now, what if I ask: what move make car shine?”

“Uh…”

Daniel looks at the textbook, like that’ll give him an answer. “Waxing?”

“Hai!” Mr. Miyagi nods. “But waxing not answer. Waxing process. Question is, how many waxes make car shine?”

The folded up lined sheet is picked up, and Mr. Miyagi unfolds it to open the five problems Johnny had jotted down for him off the board. “Logarithm same way. Exponent is process. Logarithm ask, how many times exponent happen?”

He jots down on the bottom of the paper, away from the problems on the bottom of the page — 10^X = 1000. “I tell you, power of ten make 1000. But logarithm ask—” He circles the x, Daniel understands that this is what they have to solve for — “How many tens make 1000?”

“Three,” Daniel says matter of factly. “Because 10³ equals 1000.”

Mr. Miyagi smiles, nods. “Hai. So… log₁₀1000 is 3.”

“Oh.”

No one had taken the time to explain that to him conceptually. They’d only gone over the formulas, converting from one form to another. Now that Daniel could visualize it, he had a much stronger concept of what he was learning at hand. The problems were much more complicated than working in powers of 10, but the numbers looked recognizable at this point — most of them were perfect cubes or quartics of the numbers the equations they were set equal to.

“That… makes a lot more sense,” Daniel nods, before breaking into a grin and laughing. “Hey, Mr. Miyagi! You do know about logarithms!”

“Ahh, Miyagi know nothing!” he swats, closing the textbook and smacking the paper before standing up. “Textbook know everything. Textbook is teacher’s wisdom.”

“Yeah, well she’s gonna have to look out for me on next week’s test!” Daniel proclaims, approaching his homework with a new sense of vigour. “With you, Mr. Miyagi? We’re gonna solve every damn problem!”

“You solve problem, I solve dinner,” Mr. Miyagi hums, but he smiles and adjusts Daniel’s hachimaki. “Ms. LaRusso is coming over to eat with us. Cannot disappoint the mother!”

Daniel ends up getting a hundred on the test, and when he runs out of the classroom with pride that his name ended up on the board, he doesn’t notice that Johnny’s watching him.

“So! No karate, focus on your precalculus?!”

Sam crosses her arms, slamming the sheet on the kitchen table. “I got a 75 on this week’s quiz, Dad. And the most I can get with test corrections is an 88% — if I get every question right!”

Anthony’s little genius butt, who is already taking Geometry in 8th grade, pipes up with — “I’m telling you, Sam! AP Precalculus is a useless class.” She throws her pen at him, and he screeches unruly before running upstairs with the tag — “Colleges won’t even accept it as an AP!” She holds back every urge to cuss at her little brother in this screwed up household, and then she feels her eyes well up. Anthony isn’t wrong and really, she's only taking this class to prove herself. What if she doesn’t wanna take AP Calculus? What if she doesn’t even want LaRusso Auto? What if all she wants to do is karate? That can’t make her stupid, because she’s the last person anyone would consider stupid—

“Sam, Sam— look at me,” Daniel steadies her, hands on both her arms as she feels the tears fall. “I promise you, a math test is the last thing you need to cry about. It’s okay if you fail one.”

“But you don’t understand, Dad! If I get distracted one more time, I’ll be failing more than this unit!” Sam argues, and then she pushes herself away from the table so as not to scrunch up the already wet paper with her tears. “I can’t focus, I can’t— I can’t do anything! Miguel gave me some notes that Johnny wrote for him but I don’t even know if they work and— god, he’s missed so much school— and Demetri’s already too bummed out to talk to me because all I remind him of is his broken arm, and— and—”

“Sam…”

He looks down at the paper. In all his years of running LaRusso Auto, he’s taken a few online business classes. It’s usually the basic arithmetic — Amanda does the sales tax, trade-in values, potential profit margins, and thus handles teaching the kids with their homework. (Despite having feuded with her high school math teacher, Amanda proves herself to be just as great with rational functions as she is stunning.) Unfortunately, Amanda isn’t home to hold the fort tonight — and thus, there he is, sitting with his daughter’s math worksheet.

And it’s worse than what he went through. Whatever simple equational setups he had back in his day look like 1+1=2 compared to this, and nowhere does he see Mr. Miyagi here to help him or Sam. He recalls the letter Mr. Miyagi wrote to Yukie — Samantha, makes me feel like I am her tanmee. She really could use a grandparent to help her out here.

But all she has is him. He’s let so many people down — Robby, Miguel, hell, the rest of Miyagi-Do in his faulty instruction, getting caught up in so many old grudges. He can’t let his daughter down at all. If that means sitting down with logarithms and reteaching it to her from square one, that is more than okay with him.

“Alright Sam, here’s what we’re gonna do,” he says, reaching over the table to grab the pitcher of water and a KitKat from the Japanese candy bowl he’s hoarded so he can pour some in a cup to calm her down. “You see that test? We’re gonna go over every problem you messed up on, and then we’ll try some from your textbook. But before that…”

Sam looks up, her eyes wet, but she’s listening. He huffs. “I failed you.”

“...what?” she asks, voice wet. “Dad, what are you talking about?”

“I haven’t been going over the basics with you,” he says guiltily, popping a wafer in his mouth. “And because of that, you’ve lost your balance. You’re trying to throw yourself in all this hard stuff without realizing it conceptually. That’s on me, Sam.”

Sniffling, Sam frowns before wiping her eyes with the back of her sleeve. “Dad, you haven’t failed me at all. At least, not with logs,” she professes. “That’s on Common Core’s standards.”

Daniel laughs. “That, we can both agree on,” he says. “But blame gets us nowhere. Not blaming the system, not blaming the teachers…”

A look of recognition flashes across Sam’s face. “I have a feeling you’re not talking about Precalc.”

“You’d be right.”

He looks back at the worksheet of problems. “A bad student can come from a bad teacher. But never forget that a bad teacher can be a victim of a bad system. And when we forget the fundamentals of that system…” Daniel looks up and away at the page, recalling how lost he felt without Mr. Miyagi’s guidance. “We lose our problem solving skills.”

“Mr. Miyagi isn’t here anymore,” Sam frowns. “And a karate allegory isn’t gonna help. Not when Mom doesn’t want me one inch away from a punching bag.”

Daniel hums, writing a basic equation on the sheet. “Ah, you’re right about one thing there,” he agrees, recalling the first equation his own Sensei had presented him with. “But. Mr. Miyagi once told me, Daniel-san… logs like karate.”

“He did not say that!” Sam giggles, but she humors his method. “Let me guess — they look like the arm movements we made when we’re on the water wheel?”

“You’re… actually not wrong,” Daniel hums, and then he realizes that conceptually, his daughter is miles past 10^x = 1000 turning to log₁₀1000. There’s another problem on her test that has essentially no work written for it, probably where Sam gave up or ran out of time — if 4^9x+1= 16, find 𝑙𝑜𝑔₃𝑥. Daniel thinks they can try going for that one instead. She’s always done her best when they tackled the hard stuff first. “Step-by-step, okay?”

Sam nods, putting her trust in his instruction. “Okay. You lead the way, Sensei.”

The remark fills his heart with warmth — he hasn’t felt like a Sensei in weeks, not after losing Robby. Still, he looks down at the page and circles two parts of the equation — 4 and 16. “The first step in karate is recognizing your opponent. Here? You’re going to rewrite your bases. 4 and 16 can both be rewritten in terms of the base…”

“Two,” Sam recognizes, following on her own page and scribbling out 4 = 2² and 16 = 2⁴ on her side. “Like retranslating it into a common style, instead of fighting two different ways.”

“Something I wish Johnny could understand,” Daniel sighs, instinctively reaching up to squeeze the bridge of his forehead. His head wanders back to senior year, Johnny handing him a copy of the homework questions when he couldn’t scribble them out on his own. He cards that memory in a dark place in the back of his head and continues — “You remember the power rule?”

“Yeah. Simplify,” she affirms, rewriting the equation once again until she can set the exponents equal to each other — she ends up with 18x + 2 = 4. From there, she can solve for x as if it were any equation — and she ends up with 1/9. “Wow, Dad. I can’t believe you act like you don’t know this stuff.”

Daniel laughs, recognizing his own gift. “I don’t,” he blinks in surprise, but he looks down at his page and all the steps seem so clear when he recalls how Mr. Miyagi would’ve taught it to him. “Then you find log₃1/9, which we can rewrite as -2log₃3 to get -2…”

“And log₃3 is negative 2!”

Sam laughs, before cheering and circling the answer with so many realizations blooming on her face. “Dad — it was this simple the whole time! Why haven’t you been teaching Precalc this whole time?!” she asks, before blinking at her own red face. “I’m— I’m being stupid!”

“No you’re not,” he reassures her. All Daniel can do is grab a tissue paper and wet it, reaching over to wipe her face down with it so she can cool down. No matter how old she is, she’s always going to be the girl who ends up crying way too easily. “Nothing about this is stupid, Sam. You’ll never be stupid to me.”

Then, he pulls her into a hug. “No matter how many times you lose your way, how many problems you can’t solve…” he tightens his arms around her, trying to will whatever love and patience Mr. Miyagi had for him into her so maybe she can feel the exact feeling of frustration he had undergone. “I will always help you through. Even if I have to relearn a few things myself, okay?”

Sam sniffles, before leaning closer into her father’s hug. “Thanks, Dad,” she says, closing her eyes and squeezing him back. “Gosh, you really know what to say all the time?”

Daniel points up. “I get it from him.”

Anthony grumbles from his place above the stairs, where he’s weaseled himself into watching their exchange. “Okay Mr. Miyagi, now can I get some help with my Geometry homework?!”

They both laugh, and Sam gathers up her papers before smiling at her Dad and saying — “Don’t worry, I got this. You get your rest, Dad.” Sam shoves her homework into the binder. “Besides…”

She leans over and kisses him on the cheek. “Waxing on and off is basically the arc of a circle, right?”

Sam strides away, hurrying up the stairs to quell Anthony’s own math problems with a newfound excitement and understanding of her math homework. It really only seems to be the math homework, which Daniel sighs in exhaustive relief for — she’d mentioned that Demetri was already exhausted emotionally with his new broken arm, but his back was already creaking with how he was carrying his daughter through Physics.

There’s one page left on the desk, however. Daniel picks it up, ready to call Sam back downstairs so she doesn’t forget what might be homework. But he unfolds the folded lined sheet and finds a familiar phrase on it, a phrase he’d never quite forgotten scrawled in messy red pen—

Look at me one more time, and you'll be failing more than this unit. Pay attention in class!

—Johnny

log_b(x) = y => b^x = y

Daniel scoffs, but not in the taunted way he usually is. The note he’s left Miguel is… amusing, kinda like the signs they put on the clocks at school that tell you not to watch the time when you get bored. The kid is, in a way, lucky to have such a helpful mentor. It had never occurred to him that Johnny could teach outside of karate.

He realizes Johnny remembers this unit just as much as he did. Remembers the point in time between the limbo of the tournament and graduation. Where toleration met destiny, where they’d only crossed paths in class willingly that one time to receive and give homework questions…

Once again, Daniel pockets the notes. Who knows when he might need an extra hand when it comes to math tutoring.