A PS-based psychological model - seriation

This model was developed by Richard Young to explain the cognitive development of children in a seriation task. This involves taking blocks from a pile and lining them up by size. Piaget investigated this in The Child's Conception of Number (PSY ED:P 057). He found that the child progressed through three stages:

1. Child lines the blocks up in an arbitrary order; is using ``pre-relative'' concepts ``big'' and ``small'' rather than ``bigger'' and ``smaller''.

2. Child eventually succeeds, but only after repeated trial-and-error rearrangements. Has acquired notions of ``bigger'' and ``smaller'', plus the co-ordination ``X bigger than Y but smaller than Z''. But is still experimenting directly on perceptual data rather than manipulating abstract ideas.

3. Child performs task smoothly, taking the right block each time. All the time, is now considering relationships between all the items, e.g. ``look for smallest overall block''.

Here's a set of rules which model the start of stage 2.

f1: push(Goal = add first block) and
    set(State = continuing task) if
        Goal = seriate and
        State = task just started.

f2: put block at far left and pop goal stack if
        Goal = add first block and
        holding block in hand.

a1: push(Goal = add another block) if
        Goal = seriate.

a2: pop goal stack and push(Goal = place this block) if
        Goal = add another block and
        holding block in hand.

a3: pickup nearest block if
        Goal = add _ block.

p1: put block at right if
        Goal = place this block.

f3: pickup biggest block if
        Goal = add first block.

e1: examine blocks and set BlockOrder = OK or bad if
        Goal = place this block and
        new arrangement of blocks exists.

e2: pop goal stack if
        Goal = place this block and
        BlockOrder = OK.

e3: exchange last two blocks if
        Goal = place this block and
        BlockOrder = bad.

a4: pickup block similar to last if
        Goal = add another block.

These rules come from page 117 of Learning and Problem Solving 3, Open University Course D303, Block 4, Units 26-28. You can find it in PSY Oversize AA:O 2-O M and in the RSL on the Open University bookcase - 2nd bookcase on left as you go in the back entrance to the Lankester Room.

Some points about the rules:

• I've written them in roughly the same format as the skiing example. They involve more complexity of STM. Symbol clusters of the form Goal = ? are stored on a stack in last-on first-off fashion. You can have any number of goals, but only the topmost one is visible to the rule-matcher.

• The rules use a lot of perceptual tests and motor actions.

• In rule a3, add _ block will match either of add first block and add another block. _ is a kind of wild-card.

• The model assumes resolution by specificity.

To simulate, start with a heap of blocks and an STM whose contents is

State = task just started

• What's the model for?