COGS 200, UCSD, Sept. 24, 2004

Problem Solving, Complex Cognition,and Child Development:

Are There Joints To Carve? Where?

Gedeon O. DeákDepartment of Cognitive ScienceHuman Development Program

COGS 200, UCSD, Sept. 24, 2004

Overview

• The problem of defining a domain of study– Failures of sub-division

• The problem of development• Scientific progress (or revealing silliness):

– abandoning insight (then resurrecting it, thenabandoning it again)

– questioning deduction– variability of strategy use (Siegler)– problem solving as context for concept learning

• Another way to divide the domain?

COGS 200, UCSD, Sept. 24, 2004

Defining a domain:The problem of problem solving

• “Problem solving” and “thinking”:– Selz (1913, 1922):

• unit of thought = structured complex of relations• thinking = complete structure by testing conditions

– Isn’t this Newell & Simon (- 40 years)??– “[thinking that results in] finding a way out of a

difficulty” (Polya, 1965)– Gestaltists: productive vs. reproductive thought– “manipulation of…operations on knowledge… [that is]

directed and results in behavior that ‘solves’…or isdirected toward solution” Mayer, 1992)

• defined by givens, goals, & obstacles

COGS 200, UCSD, Sept. 24, 2004

Question: Do these strike you as useful? Dothey give you any understanding? Would theyhelp you plan a study or interpret a data set?Tell a teacher how to boost students’ learning?

COGS 200, UCSD, Sept. 24, 2004

Does sub-dividing help?

• Reitman (1965): • Greeno (1978):– Transformation (T of H)– Arrangement (anagram;

Düncker)– Inducing structure

(Raven’s matrices)– Evaluate argument

(syllogisms)transmutelead gold

which kidswill drop

out?well-defined

design SUVthat gets50+MPG

reducedisciplineproblemsin school

ill-defined

well-definedill-definedgiven goal

Q: Do these distinctions reflect any important differencesin brain events and cognitive processes?

COGS 200, UCSD, Sept. 24, 2004

Easier vs. harder problems show thatmost sub-divisions are arbitrary

• Categorical syllogisms:– Easy: All A are B. All B are C. Which is true?

• (1) All A are C; (2) All A are not C; (3) Some A are C; (4)Some A are not C; (5) none of these

– Hard: (from Stratton, 1967)– Is this easier?

• I want to drive my big SUV fast, but the gas costs too much! Hey,some tar sands have gas in ‘em…. Oh, also, some of this kerogenstuff has gas in it, too. I wonder if tar sands and kerogen are thesame thing, or different? What do you think?

• Classification: well-defined/well-defined; evaluate argument• What makes them harder?

– many “mental models” or indeterminate quantifiers– status of information as real/known, real/novel, or clearly arbitrary– lots of distracting information

COGS 200, UCSD, Sept. 24, 2004

…hard syllogism…

As technological advances and natural petroleum resourcesare depleted, the securing of petroleum from unconventionalsources becomes more imperative. One such source is theAthabasca tar sands of Northern Alberta. Since some tarsands are sources of refinable hydrocarbons, these depositsare worthy of commercial investigation. Some kerogendeposits also are sources of refinable hydrocarbons.Therefore…

(1) All kerogen deposits are tar sands(2) No kerogen deposits are tar sands(3) Some kerogen deposits are tar sands(4) Some kerogen deposits are not tar sands(5) None of the above

COGS 200, UCSD, Sept. 24, 2004

…another example…

• Insight problems:– Make a hat rack:

• Easy: from a music stand;• Hard: with wooden rods and clamps (Maier)

– 24% success (math/engineering students)– 48% success after seeing related solution

• Classification: well-defined??/well-defined;arrangement

• Things that make these harder:– Prior similar experience helps; prior different experience hurts– Perceptual support (available example) helps– Some labels help, others hurt– Subject’s introspection of progress is, at best, distracting.

COGS 200, UCSD, Sept. 24, 2004

…and another…

• Classification: well-defined/well-defined;inducing structure

• Made harder by:– More variables– Variability in differences in

variables– insight is usually a good indicator

? ?

COGS 200, UCSD, Sept. 24, 2004

…just one more, I promise…

• Conditional syllogisms (Wason, 1966): hard– “If a card has a vowel on one side, then it has an even

number of the other side.”• Choose exactly and only the cards you must turn over to

see if this set meets the rule:A 74K

• Now the easier one:– “If an envelope is sealed, then it has a 50-cent stamp on it.”

• You work in a post-office. Pick the letters you must turnover to see if they must go in an “insufficient postage” bin:

50 40

COGS 200, UCSD, Sept. 24, 2004

• Classification: well-defined/well-defined;evaluate argument

• Things that make these harder:– Tendency to make specific misinterpretation(s) of

premise (i.e., biconditional: Staudenmayer, 1975)– Negative terms (working memory?)– Concrete materials help only if they cue familiar

scenarios (possibly generalized-- e.g., permissionscheme)

COGS 200, UCSD, Sept. 24, 2004

What do these examples show?

• Even in well-defined problems, or evaluationproblems, there are no impressive patterns.The only generalizations are…– Problems like ones you’ve solved before are easier– Problems that tax working memory are harder– Problems are harder if you misunderstand them

(for this, we came to a talk?)

COGS 200, UCSD, Sept. 24, 2004

So what is problem-solving “like?”

• Maybe nothing we can easily summarize• Archilochus: hedgehog & fox metaphor

– In academia (and beyond), people tend to like/reward hedgehogtheories, for various reasons:

• e.g., history:– “…cannot remember…past…condemned…repeat” (who?)– “History is the science of what never happens twice” (?)

(fyi: Valéry)• In psychology: Freud, Hebb, Skinner…• Problem: Problem-solving is a fox

– How do you study it?

COGS 200, UCSD, Sept. 24, 2004

Added problem: Development

• Many aspects of perception, cognition, and behaviorchange during infancy and childhood

• Many of these are used in any given episode ofproblem solving

• Example: Class-inclusion problems (Trabasso et al1978):

“Are there more bunnies or more animals?

COGS 200, UCSD, Sept. 24, 2004

What affects children’s class inclusionanswers? Trabasso et al’s task analysis

1) Represent the array (perceptual analysis)2) Interpret question as request to compare cardinal

quantities3) Find referent for Term14) Quantify Term15) Find referent for Term26) Quantify Term27) Compare quantities8) Respond based on relative-quantity decision rule

**

******

COGS 200, UCSD, Sept. 24, 2004

Possible models

• Presupposition: Problem solving is hard because wemust combine or string multiple functions that are notindividually trivial

• Model 1: Products– Let difficulty of sub-taski = pi (probability of success)– For problem with subtasks 1…i,

total problem difficulty = p1 * p2 *…pi(of course, the function might not be multiplication, or might

include a constant…)• Model 2: “Weakest link”:

– p of total problem success = lowest sub-task p

COGS 200, UCSD, Sept. 24, 2004

“Weakest link” is probably closer tothe truth, at least in some cases…

• Trabasso et al: p of success in standardclass-inclusion task does not approach 0

• Our lab: modification of DCCS task…

ISSBD, Ghent, Belgium, July 2004

Standard DCCS for children1. “First we play the shape game…”

2. “We’re not playing the shapegame any more. No way. Nowwe’re playing the color game…”

Typical results:

3-year-olds: 20-40% flexible

4-year-olds: 60-80% flexible

Designed to testflexibility in rule-following…

ISSBD, Ghent, Belgium, July 2004

What about flexible deduction?3DCCS: rule-using test w/ complexity of FIM-An

ISSBD, Ghent, Belgium, July 2004

3DCCS Results (Means, N = 61 3- & 4-year-olds)

0

1

2

3

4

5

6

3-Year-Olds: 1stBlock

3-Year-Olds: LaterBlocks

4-Year-Olds: 1stBlock

4-Year-Olds: LaterBlocks

Mea

n R

ule

-Appro

priat

e Sort

ing R

esponse

s

Results:

3-year-olds:33% flexible,33% semi-flex.

4-year-olds:77% flexible,

23% semi-flex.

COGS 200, UCSD, Sept. 24, 2004

What else changes?

• Metacognition:– example: predicting

your own memoryspan:

• Relation to problem solving?– “Realization deficits”

(vs. “utilization deficits”)– Beyond Models 1-2:

• Prospective thinking: creating & modifying possiblemodels, based on assessment of future difficultiesand likely usefulless of certain strategies

COGS 200, UCSD, Sept. 24, 2004

What else changes?

• Strategies:– Knowledge (of strategy, its applicability to a problem, etc.)– Use

• Analogy– Knowledge:

RUNAWAY STROLLER: EISENSTEIN::SINKING PIANO: ???– Surface similarity– Can children learn to analogize? Effects of hints; reflection:

• Brown & Kate: 3- to 5-year-olds: Solving causal problems• Effects of hints, “say how alike,” “teach Kermit” vs. no hints• Esp. 3-yr-olds were aided by hints or discussion; older

preschoolers saw analogies faster, w/out extra scaffolding

COGS 200, UCSD, Sept. 24, 2004

Brown & Kane (1988) results…

0102030405060708090

100

% c

orre

ct a

nalo

g tr

ansf

er

3-year-olds 4-year-olds 5-year-olds

hints/disc.no hintcontrol

COGS 200, UCSD, Sept. 24, 2004

What else changes?

• Perceptual analysis & grouping• Processing speed• Working memory• Cognitive inhibition• Pragmatic/task knowledge• Content knowledge

COGS 200, UCSD, Sept. 24, 2004

Where do things stand?

• Problem solving, as often defined, is nearly arbitraryas a category of human activity/thought

• Sub-dividing the concept doesn’t help (at least, not sofar)– Problem: too many different sorts of things are called

“problems”• Content, goals, givens, etc., vary widely• In development, virtually all contributing cognitive

skills change, often simultaneously• Resulting “problem space” is too high-dimensional to

be able to draw interesting general conclusions

COGS 200, UCSD, Sept. 24, 2004

Points of progress…

• Abandoning, twice, introspection…– Rise & fall of “talk-aloud” methods (Nisbett & Wilson is a

must-read!)– Better option: Microgenetic studies (Siegler)

• Abandoning the induction/deduction distinction– e.g., Cheng & Holyoak; Sloman– developmental work: learning “kinds of necessity” (Kalish,

Miller, Harel)• Studies of strategy-use that stress conditions of use,

selection, variability, & metacognition connection– Siegler: variability in children’s strategy use

• “Time for telling”: Problems as contexts forconceptual learning (Schwartz & Bransford)