1 Seeing fish

Consider looking at an illustration of a fish

Most likely you are incapable of looking as such an illustration without thinking fish. But when you consider what fish actually look like, with glistening scales and translucent flesh and so on, a pen sketch is pretty far from it; and you were not born with a biological concept fish—you learned it. How did you learn it so robustly?

1.1 Subconscious processing

You are born and/or rapidly develop some processing. Roughly speaking, you know how to recognize regions of color and borders between them without being taught.

You augment this innate ability with additional subconscious processing: in particular, you develop schemata¹ which operate effectively like event handlers in programming: they notice certain collections of thoughts and provide higher-level thoughts as a consequence. For example, you may have a schema that notices a circle near a curved line and interpret is as an eye.

Schemata are learned over time, but operate entirely subconsciously. Your looks like a fish schema, which depends on many other schemata that recognize various parts of the illustration, operates in your subconscious and tells your conscious mind you are seeing a fish whether your conscious mind wants it to or not.

2 Understanding memory

Your memory can be divided into three classes, which operate in different ways. Each also has a parallel storage concept in computing.

Memory	Computing Parallel	Notes
Long-term	Disk, files	Practically infinite space: cannot overfill before you die.
		Practically infinite duration: does not fade in healthy minds (though ability to recall it might).
		Slow to fill; as rough approximation, some short-term memory becomes long-term memory when you sleep.
		Schemata exist in long-term memory.
Short-term	RAM, cache, data structures	Limited space: you remove old thoughts to make room for new ones.
		Limited duration: lasts seconds to hours, not days.
Working	Registers, local variables	All conscious thought happens here.
		Very limited space: roughly 3 ideas.

While all three kinds of memory are important, for education we’ll primarily discuss working memory.

2.1 Working memory

You think using your working memory. But your working memory is small: it can store about 3 ideas at a time. Idea is not a precise measure, and some sources use smaller or larger definitions but 3 ideas is a reasonable approximation.

With so little space, it is worth considering our cognitive load: that is, what we load into the working memory we use to cognate (or think). From an education perspective, cognitive load can be split into three types:

Intrinsic load

This is the memory required to do the task at hand. For example, to add two numbers you need to think about the two numbers.

Extraneous load

This is memory used for things unrelated to the task at hand. I’m hungry, what an odd smell, I really enjoyed that hike yesterday, and many more are examples of extraneous load.

In general, extraneous load is the enemy of learning and we want to reduce it as much as we can.

Germane load

Germane is defined in this context as relevant to the matter under consideration, pertinent.². This definition is given by educational theorists and means, in this case, the working memory being used to learn. There are two messages to take away from this:

Learning requires spare working memory. If you are at your cognitive limit (100% of memory is full of intrinsic load) or distracted (100% of memory is full of intrinsic and extraneous load) then you won’t learn.
When you have working memory available, your brain learns: that is, it creates new schemata and/or strengthens and refines existing ones.

2.2 Intrinsic load changes

Consider the expression

3 + 7

How much working memory was required for you to evaluate it?

I introduced intrinsic load with addition as an example: to add two numbers you need to think about the two numbers. However, you likely used 0, not 2, ideas of your working memory in this case because you’ve developed a ten schema that recognizes many ways of spelling this idea: ten, 10, 3+7, 7 + 3, 11-1, etc.

This is a general rule: the more you learn, the more and more effective your schemata become. As a consequence, the more you learn the less working memory you need to do things: the intrinsic load of tasks shrinks the more you learning.

Additionally, this does not require a conscious effort at learning: your brain will learn and reduce the working memory needed for the present task if it has spare working memory for germane load.

the singular of schemata is schema↩︎
See OED, germane definition 4 ↩︎