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If you want to do spaced repetition in a hierarchical domain and not get bogged down doing unnecessary reviews, you gotta keep track of encompassings so that you can know what reviews are being knocked out implicitly.

This is the power of evidenced-based practices like explicit instruction. What an inspiring story.

🎯 "If you have to look it up, it's worthless for creative thinking."

#1 unlock for creativity is having information subconsciously accessible in your brain. Your brain wants to find patterns and connect the dots, but it can only do that if all the data is available for background processing.

Don't let scaffolding become a crutch. Use it at the beginning, but gradually strip it away.

Euler's formula is a gateway drug to mathematical addiction. One of the earliest dopamine hits: multiply two complex exponentials and out pop the sum formulas for sine & cosine.

One of the most common traps that otherwise smart people fall into, cutting short their potential: "my brainpower should be spent on the theory, not the implementation"

Everybody wants to get to stage 3 in the talent development process, but nobody wants to grind through stage 2. Stage 3 can feel like a return to the playful nature of stage 1. But there is no stage 3 without stage 2. Without stage 2, stage 3 is just stage 1.

Lots of pure math skills (pinning down definitions & theorems, looking for counterexamples, etc.) have proven extremely useful in my applied work. For instance, many knowledge graph validations come down to pinning down the formal definition of some desirable mathematical

Plan your broad-strokes journey top-down, but carry out the granular steps bottom-up.

The #1 killer of motivation in math learning is not disinterest but overwhelm. Learning math opens the door to things you've dreamt about, but that door is atop a mountainous skill hierarchy so steep and winding it's inaccessible to most students. Of those who attempt to

Parents might think that an "A" indicates mastery of grade-level standards, but that’s no longer the case. Grade inflation has been a concern for a while now, but the pandemic really exacerbated the problem. Goldhaber & Young (2023) found that, despite severe learning loss

"You cannot comprehend a 'big picture' if your mind's energies are hijacked by low-level processing. Continuity is broken. The goal shifts from understanding the total context to understanding the immediate ... before you." -Hattie & Yates, 2013, on the importance of automaticity

Keep your foot on the gas.

If a student doesn’t achieve automaticity on lower-level skills, it doesn’t even matter how well the teacher scaffolds a new skill – they won’t be able to do it.