My basic issue with cognitive load theory

The idea of “working memory” — well established since the 1950s — is that the most objects someone can hold in their working memory is 7 plus or minus 2. There have been some revisions to the idea since (mainly that the size of the chunks matter; for instance, learners in languages that use less syllables for their numbers have an easier time memorizing number sequences).

This was extrapolated in the 1980s to educational theory via “cognitive load theory” by stating that the learner’s working memory capacity should not be exceeded; this tends to be used to justify “direct instruction” where the teacher lays out some example problems and the students repeat problems matching the examples. The theory here is by matching examples students suffer as little cognitive load as possible.

Cognitive load theory has some well-remarked problems with a lack of falsification and a lack of connection with modern brain science. These issues likely deserve their own posts.

My issue with cognitive load theory as applied to education is more basic: the contention that direct instruction requires less working memory than any discovery-based alternative. It certainly is asserted often

All problem-based searching makes heavy demands on working memory. Furthermore, that working memory load does not contribute to the accumulation of knowledge in long-term memory because while working memory is being used to search for problem solutions, it is not available and cannot be used to learn.

but the assertion does not match what I see in reality.

To illustrate, here’s a straightforward example — defining convex and concave polygons — done with three discovery-type lessons and direct instruction.

Discovery Lesson #1

Click on the image below to use an interactive application. Use what you learn to write a working definition of “convex” and “concave”.

Then draw one example each of a convex polygon and a concave polygon. Justify why your pictures are correct.

Discovery #2

The polygons on the left are convex; the polygons on the right are concave. Give a working definition for “convex” and “concave”.

Then draw one example each of a convex polygon and a concave polygon (not copying any of the figures above). Justify why your pictures are correct.

Discovery #3

The polygons on the left are convex; the polygons on the right are concave. Try to decide looking at the picture the difference between the two.

…after discussion…

A convex polygon is a polygon with all interior angles less than 180º.
A concave polygon is a polygon with at least one interior angle greater than 180º. The polygons on the left are convex; the polygons on the right are concave.

Draw one example each of a convex polygon and a concave polygon (not copying any of the figures above). Justify why your pictures are correct.

Direct Instruction

A convex polygon is a polygon with all interior angles less than 180º.
A concave polygon is a polygon with at least one interior angle greater than 180º. The polygons on the left are convex; the polygons on the right are concave.

Draw one example each of a convex polygon and a concave polygon (not copying any of the figures above). Justify why your pictures are correct.

Analysis

Parsing and understanding technical words creates a demand on memory. The hardcore cognitive load theorist would claim such a demand is less than that of having the student create their own definition, but is that really the case? The student using their own words can rely on more comfortable and less technical vocabulary than the one reading the technical definition. The technical definition is easy to misunderstand and the intuitive visualization is only clear to a student if they have the subsequent examples.

Discovery #1 does not appear to have heavy cognitive load. On the contrary, being able to an immediately switch between “convex” and “concave” upon passing the 180º mark is much more tactile and intuitive than either of the other lessons. Parsing technical language creates more mental demands than simply moving a visual shape.

There might be a problem of a student in Discovery #1 or Discovery #2 coming up with an incorrect definition, but that’s why discovery is hard without a teacher present.

Discovery #3 is exactly identical to the direct lesson except the definition and examples are reversed places. Having a non-technical intuition built up before trying to parse the technical definition makes it easier to read; again it appears to have less cognitive demand.

Overestimating and underestimating

One of the basic assumptions of cognitive load theorists seems to be that the mental demands of discovery are given all at once. Usually the demands involve some sort of scaffolding. For instance, in Discovery #3 the intuitive discussion of the pictures and then definition are NOT given at the same time. Only after students have settled on an idea of the difference between the shapes — essentially reducing down to one mental object — is the definition given, which as I already pointed out is easier to read for a student who now has some context.

On the other hand, cognitive load theorists seem to underestimate the demands of direct instruction. While exact entire sentences tend not to be parsed by the student in definitions (this would clearly fail the “only seven units” test) mathematical language routinely has dense and specific enough language that breaking any supposed limit is quite easy. Using the direct instruction example above, taking everything in on one go would require a.) parsing and accepting the new terms “convex” b.) same for “concave” c.) recalling definitions of “polygon” d.) same for “interior angles” e.) keeping in mind the visual of greater and less than 180º f.) keeping track of “at least one” meaning 1, 2, 3, or more and g.) parsing the connection between a-f and the examples given below.

There are obviously counters to some of these — the definitions for instance should be internalized to a degree they are easy to grab from long term memory — but the list doesn’t look that different from a “discovery” lesson, and doesn’t possess the advantage of reducing pressure on vocabulary and language.

The overall concern

In truth, working memory is well-understood for memorizing digit sequences (called digit span) but the research gets fuzzy as processes start to include images and sounds. Any sort of declaration (including my own) that the working memory is busted by a particular task when the task involves mixed media is essentially arbitrary.

On top of that, the brain is associative to such an extent that memory feats are possible which appear to violate these conditions. For instance, there is a memory trick I used to perform for audiences where they would give me a list of 20 objects and I would repeat the list backwards. The trick works by pre-memorizing a list of 20 objects quite thoroughly — 1 for pencil, 2 for swan, say — and then associating the list with those objects. If the first object given was “yo-yo” I would imagine a yo-yo hanging off a pencil. The trick is quite doable by anyone and — given the fluency of the retrieval — suggests that association of images have a secondary status that exceeds that of standard “working memory”. (This is also how the competitors of the World Memory Championship operate, allowing them feats like memorizing 300 random words in 5 minutes.)

Advertisement