I’m talking about the original, 1984 Karate Kid, not the remakes. Go back and watch it, if you’re not familiar. 

In the Karate Kid, Mr. Miyagi teaches Karate to a young Danny LaRusso but it’s not in a way Danny expects. First, he asks Danny to wash and wax all the cars – there are at least four of them – and then wax them. Wax on (right hand). Wax off (left hand). Both in circular patterns. Then, he asks him to sand the floor using sanding disks (one for each hand), again in circular patterns. Next, paint the fence. Up and down, flex the wrist. Stand knees bent. Large boards, right hand. Small boards, left hand. Finally, paint the house. Side to side this time. Flex wrist. 

Watching this for the first time as a teen with some friends, I wasn’t sure Mr. Miyagi wasn’t just trying to get some chores done around his house for free. Until, the structure was made visible. The structures: building strength, stamina, and muscle memory for specific karate moves were Mr. Miyagi’s goal all along. 

When Danny began to complain that he hadn’t learned any Karate at all and that he needed to be ready for the upcoming tournament, Mr. Miyagi helped Danny see those structures: “Show me “Wax on, Wax off.” 

Within minutes, the circular movements for waxing and sanding, along with the vertical and horizontal motions for painting were blocks for punches and kicks. The structures he had helped Danny build were made visible. Danny’s confidence grew and, well… re-watch the movie and see what happens. 

That moment can happen in math classrooms, too. When it happens, it’s because, just like Mr. Miyagi, the teacher helping to make the structure(s) visible. Sometimes students say it out loud, too… “Wait, this is like that other thing we did.”

That moment is the whole game – a Miyagi Moment.

What they’re noticing isn’t a trick or a coincidence. They’re seeing structure — the relationships and properties that hold regardless of the numbers on the surface. And once a student starts seeing these structures and making sense of how they operate, mathematics stops being a collection of disconnected procedures and starts being a coherent system that actually makes sense – and is useful!

Structures like (properties of operations, equality, and place value) are everywhere in K–5 mathematics. A student who solves 6 × 7 by thinking “5 sevens is 35, plus one more seven is 42” is using the distributive property — they just don’t know it, yet. A student who finds a common denominator before adding fractions is using equivalence — same idea, different context. A student who notices that adding zero doesn’t change a number, ever, is bumping up against the additive identity — one of the most fundamental properties in all of mathematics.

The structure was always there. Most students just never got the chance to see it.

What changes when teachers make structure the focus — not as strategies to memorize, but as relationships to notice and use — is hard to overstate. Students stop asking “what am I supposed to do?” and start asking “what can I use to work with what I have?” That shift in question is a shift in mathematical identity. It’s the difference between a student who executes and a student who reasons.

The good news: you don’t need a new curriculum or a different set of standards. The structures are already in the mathematics you’re teaching. The move is to make them visible — to point at the relationship, name it simply, and ask students where they’ve seen it before.

They’ll surprise you with how much they’ve already noticed. 

Time to channel your inner Mr. Miyagi.