kitchen table math, the sequel: "chunk decomposition" - the matchstick problems again

## Saturday, July 30, 2011

### "chunk decomposition" - the matchstick problems again

Belatedly, I'm posting this abstract from the matchstick math study. It relates to the Why is SAT geometry hard? post I began writing the other day; it also relates to the two different meanings of the word "chunking" that cropped up in the matchstick comments.

When we're talking about memory, "chunking" means chunking several bits of information together into one larger chunk, allowing working memory to hold more than the 3 or 4 separate items it is capable of holding at one time. So, for instance, instead of remembering 2 - 0 - 3 as three separate numbers, you come to remember 203 as just one chunk.

When we're talking about perception, "chunking" means something closer to an automatic and entirely unconscious perceptual bias towards seeing -- visually seeing -- 'wholes' or 'chunks' instead of the parts that make up the chunk. "Visual chunking" happens instantly and naturally, whereas memory chunking requires practice over time. Crucially, visual chunking is extremely difficult to resist or to undo.

I've mentioned in a couple of comments threads, I think, that I believe autistic people (and children and animals) much more readily perceive parts instead of wholes -- something Temple Grandin absolutely believes. Temple told me once that the hidden figures in hidden figures puzzles always 'pop' at her, and I believe it. After 9/11 she and I used to talk about using high-functioning autistic people to man the carry-on scanners at the airport.

Here's the abstract:
Constraint relaxation and chunk decomposition in insight problem solving.
By Knoblich, Günther; Ohlsson, Stellan; Haider, Hilde; Rhenius, Detlef
Journal of Experimental Psychology: Learning, Memory, and Cognition, Vol 25(6), Nov 1999, 1534-1555.
Abstract
Insight problem solving is characterized by impasses, states of mind in which the thinker does not know what to do next. The authors hypothesized that impasses are broken by changing the problem representation, and 2 hypothetical mechanisms for representational change are described: the relaxation of constraints on the solution and the decomposition of perceptual chunks. These 2 mechanisms generate specific predictions about the relative difficulty of individual problems and about differential transfer effects. The predictions were tested in 4 experiments using matchstick arithmetic problems. The results were consistent with the predictions. Representational change is a more powerful explanation for insight than alternative hypotheses, if the hypothesized change processes are specified in detail. Overcoming impasses in insight is a special case of the general need to override the imperatives of past experience in the face of novel conditions.
This study of Perceptual contributions to problem solving: Chunk decomposition of Chinese characters looks interesting.