You know what “chunking” means in memorization? It’s also something you can do to understand material before you memorize it. It’s high-leverage in learning math.
Take the equation for a t score:
That’s more symbolic relationships than you can fit into your working memory when you’re learning it for the first time. You need to chunk it. Here’s how I’d break it into chunks:
Chunk 1:
Chunk 2:
Chunk 3:
Chunk 4:
[(Chunk 1) - (Chunk 2)]/sqrt(Chunk 3)
The most useful insight here is learning to see a “composite” as a “unitary.” If we inspect Chunk 1 and see it as two variables and a minus sign, it feels like an arbitrary collection of three things. In the back of the mind, we’re asking “why not a plus sign? why not swap out x1 for… something else?” There’s a good mathematical answer, of course, but that doesn’t necessarily stop the brain from firing off those questions during the learning process, when we’re still trying to wrap our heads around these concepts.
But if we can see
as a chunk, a thing with a unitary identity, it lets us think with it in a more powerful way. Imagine if you were running a cafe, and you didn’t perceive your dishes as “unitary.” A pie wasn’t a pie, it was a pan full of sugar, cherries, and cooked dough. The menu would look insane and it would be really hard to understand what you were about to be served.
I think a lot of people who are learning new math go through an analogous phase. They haven’t chunked the concepts yet, so when they are introduced to these big higher-order concepts, it feels like reading the ingredients list and prep instructions in a recipe without having any feeling for what the dish is supposed to look and taste like at the end, or whether it’s an entree or a dessert. Why not replace the sugar in the pie with salt?
Learning how to chunk, especially in math, is undermined because so often, these chunks aren’t given names.
might be described as “the difference of sample means,” a phrase which suffers the same problem (why not the sum of sample means? why not medians instead of means?).
I find the skill of perceiving chunks, of learning how to see
as a unitary thing, like “cherry pie,” is a subtle but important skill for learning how to learn.
You know what “chunking” means in memorization? It’s also something you can do to understand material before you memorize it. It’s high-leverage in learning math.
Take the equation for a t score:
That’s more symbolic relationships than you can fit into your working memory when you’re learning it for the first time. You need to chunk it. Here’s how I’d break it into chunks:
Chunk 1:
Chunk 2:
Chunk 3:
Chunk 4:
[(Chunk 1) - (Chunk 2)]/sqrt(Chunk 3)
The most useful insight here is learning to see a “composite” as a “unitary.” If we inspect Chunk 1 and see it as two variables and a minus sign, it feels like an arbitrary collection of three things. In the back of the mind, we’re asking “why not a plus sign? why not swap out x1 for… something else?” There’s a good mathematical answer, of course, but that doesn’t necessarily stop the brain from firing off those questions during the learning process, when we’re still trying to wrap our heads around these concepts.
But if we can see
as a chunk, a thing with a unitary identity, it lets us think with it in a more powerful way. Imagine if you were running a cafe, and you didn’t perceive your dishes as “unitary.” A pie wasn’t a pie, it was a pan full of sugar, cherries, and cooked dough. The menu would look insane and it would be really hard to understand what you were about to be served.
I think a lot of people who are learning new math go through an analogous phase. They haven’t chunked the concepts yet, so when they are introduced to these big higher-order concepts, it feels like reading the ingredients list and prep instructions in a recipe without having any feeling for what the dish is supposed to look and taste like at the end, or whether it’s an entree or a dessert. Why not replace the sugar in the pie with salt?
Learning how to chunk, especially in math, is undermined because so often, these chunks aren’t given names.
might be described as “the difference of sample means,” a phrase which suffers the same problem (why not the sum of sample means? why not medians instead of means?).
I find the skill of perceiving chunks, of learning how to see
as a unitary thing, like “cherry pie,” is a subtle but important skill for learning how to learn.