Lecture 3: Problem Solving Flashcards
What us an analogy?
Some common analogies
Some not so good analogies
What is an analogy?
A comparison between two things that are alike, in order to explain something.
Similes and metaphors are examples of analogies.
Some common analogies
“She was a fish out of water”
“He has a velvet voice”
“The relationship began to thaw”
However, some analogies aren’t so great…
“Her eyes were like two brown circles with two black dots in the middle”
“John and Mary had never met, just like two hummingbirds that had also never met”
“The little boat drifted gently across the lake exactly the way a bowling ball wouldn’t”
Making a mental leap in analogical thinking
-relate to children’s abilities
Making an analogy involves seeing one thing as if it were another
The problem solver has to make a ‘mental leap’ across two different domains
Young children find it difficult to see things in different ways
Appearance-reality distinction
False belief tasks
Counterfactual reasoning
Reasonable to expect young children to fail on tests of analogical thinking
Classic analogies
-example
- picture of a glove and picture of a hand matched
- then picture of hat
- have to match with either picture of hook, table, shoe, umbrella or person’s head
- match with person head because hat covers head
Thinking with analogies
A : B : : C : D
Car : Petrol : : Sailboat : ?
Travel Wind Sails Rudder
- A is to B as C is to B
- Piaget analogical thinking can’t do till formal operational stage, ability of this stage involving abstract processing of relations between relations.
Piaget’s study: Fragile Analogical Reasoning
(4 pictures)
ship:ship’s wheel bicycle:handlebars
- 7- to 12-yr-olds could give the correct answer
- But readily accepted “pump” as a correct answer
- Piaget argued that understanding of analogies did not develop until early adolescence
- identifying link then estrapulating to other one
- 5-7 failed to get correct
- 7-12 could get right answer but easily persuaded to get wrong answer
- understanding not until early adolescence
Piaget’s Theory
- Formal operational reasoning involves operating mentally on the results of simpler mental operations
- Find relation between A & B (first-order relation)
- Find relational similarity between A-B & C-D (second-order relational understanding)
- Younger than 7 yr notice associations
- 7 – 12 yr do notice some relations, but are easily persuaded to change their answers
Proportional reasoning and analogies
- Goswami 1992
- proportional reasoning involves analogies
Leather : Shoe : : Wool : Cardigan
3 : 4 : : 15 : 20
- Piaget claimed that proportional reasoning is also a formal operational skill. (shouldn’t be present with children under 12)
- Many researchers have argued that the reasoning needed to understand proportions is the same as the reasoning needed to understand analogies
What could be wring with piaget’s theory?
- Piaget claims that young children suffer a mediation deficit
- Lack the necessary mental apparatus
-But it could also be a production deficit
Children may lack knowledge of key relations
Children may not be aware of the key relations
Children may not think of using the analogy
->did not check if children understood what things were yet
(Goswami 1992
Proportion analogy problem
-Goswami 1989
Task 1 proportional analogies
-shapes
circle half filled: rectangle half filled
circle quarter filled: ?
-different shapes with different filling, correct answer is rectangle quarter filled
->in order to solve child has to know about proportions
Proportion Matching task
- half diamond:half square: half circle: ?
- given choices, choose correct match, correct answer half a rectangle
- slightly easier task because just association
- just had to pick out correct answer
- check if children understand task
- 4 vs 6 year olds
- Poorer performance of 4-year-olds was due to a poorer understanding of the higher-order relations and not a failure to use analogies.
- > more an issue with the proportion task.
Picture analogies
-goswami and brown 1989
Condition 1: appearance same
- > ensure children have knowledge of key relations
- pictures
- playdo:playdo cut up :: apple:apple cut up
- (had to match pic of apple whole)
Condition 2: appearance different
->does the fact the inside loos different or the same make a difference?
loaf of bread:bread slice:: lemon:lemon inside/slice
-(had to match whole lemon)
Condition 3: test of causal understanding
- apple and knife, whats the third picture?
- > answer cut up apple
Results:
- 3-year-olds showed a positive correlation between knowledge of causal relations and use of analogy
- Failed when lacked knowledge, not because unable to use analogies
- An example of a production deficit
- > much less correct answers on all conditions than 4 and 6 years old
Analogical problem solving in children
Holyoak 1984
- Transfer marbles from one bowl to another
- Tools: scissors, string, paper, stick, tape
- Two groups
- > Story about a character who solved a similar problem (magic carpet, magic staff)
- > No story
- Can children use the story analogy to solve a practical problem?
Results:
Is failure at 5 years due to:
Inability to use analogies? (Mediation deficit)
Being unaware of key relations? (Production deficit)
Not knowing what to do with the story? (Production deficit)
-did well with magic staff but not as well with magic carpet
-5 y/o: 30% story and 10% no story
-11 y/o: 100% story, 0% no story
Difficulties thinking with analogies
-obstacles and improved performance?
-Young children have difficulty gaining access to their knowledge
- Two main obstacles:
- > Extracting the analogy or relational structure from the source
- > Applying the source analogy to a new problem
- Improve performance – extract the analogy
- > Provide several examples
- > Reflection – highlight the goal structure
- Improve performance – apply the analogy
- > Training children so they know what to do
Providing more than one analogy
-Chen and Daehler 1989
6-year-olds had to retrieve a ball from inside a tall container
There were two possible methods:
- Make a tool
- Pour water
Two stories were told about characters who used one of these methods
Monkey wanted food outside cage – joined sticks together to reach food
Bird was thirsty but couldn’t reach wwater – put stones in to raise level
- only got one thing
- stick but not enough water or water but not long enough stick
Story analogy condition
-Child is asked to explain how the stories are alike
Schema training condition
-Experimenter explains how the stories are alike
There were two groups in each condition
Positive transfer: story method works on the test problem
Negative transfer: story method will not work, but other method will work (story didn’t match with what able to do)
One control group
Told two unrelated stories
6-year-olds are capable of generalising abstract principles
Extracting the analogy from two examples produced transfer
Children understood what to do
But analogies can have negative as well as positive effects
-schema training transfer + 90%, story analogue transfer + 60%, control 30%, story analogue transfer - 10% and schema training transfer -
->negative condition hindered performance
Highlighting the goal structure
-Brown, Kan and Echols 1986
-two different stories, genie and easter bunny
-All children were told the Genie & Jewels story, and shown how to solve the Genie’s problem with the materials
-Three groups:
Explicit goal structure – asked 4 questions
Who has the problem?
What is the goal?
What is the obstacle?
What is the solution?
Recall story – child recalls the story with no prompting
Control – Genie & Jewels story & demonstration, but no questions or recall
Then given the new Easter Bunny problem (weren’t told similar to genie problem)
- 4 and 5 y/o
- read and illustrated in book
- then acted out (paper to transfer jewels)
- then split into three groups
- explicit goal almost 70%, recall 50%, control 20% for solving problem
- > in recall, those that recalled goal structure 80% solved problem vs partial recall only 20%
- > some better than explicit if recalled goal structure
second recall study established a production deficit
- 5 vs 3 y/o
- complete recall: 5 y/o half able to recall, lots solved the problem, 3y/o very few able to recall but 100% solved problem
- prompts: 5 y/o less 3rd recall but most solved problem of those, 3 y/o most recalled with prompts and most solved problem
- no prompts: 5 y/o no recall and only one solved problem
Young children can think with analogies
They may fail to access their representation of the solution (production deficit)
Young children often need prompting to think about the analogy
-is it they forgot goal structure or is it divided attention?
Training to use an analogy
-brown and Kane 1988
Tool Use Problem Pairs
Pair A: (Stacking) A1 (tyres) — A2 (bales)
Pair B: (Pulling) B1 (spade) — B2 (fishing rod)
Pair C: (Swinging) C1 (tree) — C2 (wire)
-solution: stack 2 of the tires then climb us and stack rest
Groups
Reflection: Discuss solution; prompts, teach Kermit
No Reflection: No discussion, prompts or teaching
Control: Irrelevant A and B stories, only pair C
-3, 4 and 5 y/o
- 3 y/o performed much better on reflection condition (85% vs 40% no reflection and 10% control)
- 4 y/o better on reflection and no reflection vs control but reflection only slightly higher
- 5 y/o reflection and no reflection no difference, and improvement in all conditions performance with age
