Problem solvingWeek 13

Central themes• Task analysis• Are careful examinations of problems, in tended to identify the pro-

cesses needed to solve them• Mathematical problems• 5 yr olds puzzle in which a dog, a cat, and a mourse needed to find

their way to a bone, a piece of fish, and a hunk of cheese, respec-tively. • Klahr’s task analysis different problems created varying degrees of

conflict between the child’s immediate goal of getting each animal to its desired food and the child’s higher goal of getting all three ani-mals to the right positions.• Means-ends analysis.

Encoding & misencoding• Involves identifying the critical information in a situation

and using it to build an internal representation of the situation.• Children do not know what the important features are,

because they cannot comprehend them. • 4 to 11 year-olds and college students watched a mov-

ing electric train carrying a ball on a flatcar. • Misencoding can influence problem solving and reason-

ing.•

Mental model• To solve problems, people often construct mental models of

the task and what they need to do to solve it• 3 yr old: why doesn’t my blood come out when I open my

mouth?• Halford (1993): the most important is that the model accu-

rately represents the structure of the problem.• It should parallel the essential relations in the problem• Forming mental models often requires children to reconcile

what they are told by other people with their own experience. • E.g. the earth is round.

Processes of change• Numerous studies have shown that young children are far more

competent problem solvers than they jhad been given credit for be-ing. • Microgenetic studies1. Change does not ordinarily involve a simple substitution of a more

advanced problem-solving strategy for a less advanced one.2. Children generally think about problems in multiple ways at any

given time. 3. Consistent finding is that innovations follow success as well as

failure. P. 397. Figure 10.2

Problem solving processes• Planning• Causal inference, • Analogy,• Tool use, • Scientific and logical reasoning.

Four steps of problem solving strat-egy(Noh et al. 2001)• Understanding, planning, solving, and checking. • Four steps of problem solving processes (Ge and Land 2003) • Representing problems, developing solutions, making justifi-

cations for generating or selecting solutions, and monitoring or evaluating the problem solutions. • They commonly focused on analysis and judgment of the

problem in the initial stage as well as evaluation of the prob-lem in the final stage. • The problem solving phases are often associated with rea-

soned activities of critical thinking.

Planning • Is future-oriented problem solving (Haith, 1994)• Children are weak on this• Then more skilled people should support them

Means-ends analysis• Demands simultaneously keeping several items in mind:

subgoals, procedures for meeting the subgoals, and dis-crepancies between the current state and the overall goal. • Infants use this: foam rubber barrier, : move the barrier,

pull the cloth, and reel in the string to get the toy. • ELT use: look at the picture or story and find three

steps to be there. Or solve the problem.

Three ways of stopping the wolf

Route planning• One use of planning is to choose the most efficient

route for reaching a destination.

Car: 80km/hBicycle: 20km/hBoat: 40km/hWalk: 5km/h

Helicopter: 150km/h

Causal inference• View concepts as implicit theories emphasize knowl-

edge of causal relations as central to conceptual under-standing.

The Humean variables three fea-tures to infer that events are causally related • David Hume (1739-1740/1911)• Contiguity: the events occurred close together in time

and space• Precedence: the event lableled the ‘cause’ preceded the

event labeled the ‘effect• Covariation: the cause and effect consistently occurred

together on past occasions

Children’s causal inference• By age 5• Use the order of events to infer that one event caused

the other• A-B-C• What made B happen? choose A• Age 5 they choose A • Age 3 and 4: choose C.

Children’s causal inference• By age 5• Read the story of ‘the hungry caterpillar’• Why does the caterpillar have a stomachache?By age 8 or olderRead the ‘Salmon’ story and ask children questions.

Beyond the Humean variables• Physical causality and psychological causality. • Show three pictures, depicting an action

Beyond the Humean variables

ANALOGY• Analogical reasoning is a pervasive and powerful process. • It involves solving problems by identifying corresponding

structures of functions in objects or events that are being compared. • Understanding the metaphorical statement ‘ a camera is

like a tape recorder”• It resembles that of causal inference. • E.g. 6yr: analogize the physical feature of camera and tape

recorder• 9 yr: function of the two.

Tool Use• Children do not solve problems in a vacuum. • They use available tools to help them. • First tools are their mothers to obtain the toys.

Symbolic representations as tools• Maps, scale models, and pictures, • Hiding a doll in the Scale model room. • Use of notation in the matching game : grade 1, 3, 5, 7.

younger child couldn’t make it. • Let them have the success from the beginning. • E.g. make a village map of a story using their own sym-

bolic representations.

Scientific and logical reasoning• Scientific thinking• first and second graders prefer the experiment that

would yield conclusive evidence over the one that would not. • \experimental comparisons that vary only one factors at

a time. • separating theory and evidence.

Logical reasoning

Deductive problem reasoning. • All poggops wear blue boots• Tombor is a poggop.• Does Tombor wear blue boots?

Inductive problem reasoning• Tombor is a porggop. • Tombor wears blue boots. • Do all poggop0s wear blue boots?

4 yr olds use guesses

9 yr olds use deductions

Am I the longest?

Little Boa’s Adventure

A little Boa snake was walking hap-pily in the forest. “My mom told me that I am the

longest snake in the whole world.”Said the little boa snake.“La la la”

“Oh! There is a snake.” Said the little boa snake.“Am I longer than him? Hm~ well, I will find itout.” said the little boa snake to himself andslowly crawled to the snake.

“Hi, how are you? I am Boarino.” said the little boa snake.“Prr Prr. Hi! I am Ratto. I am the rattle snake”replied the rattle snake slowly rattling his bells.

“Um Um…, My mum told me that I am the longest snake in the whole world.” said the little snake in a small voice.

“ What? You are the longest snake? Ha Ha Ha.” The rattle snake laughed loudly.

“ Um ~ So I think I am longer than you” Said the little boa snake in a very small voice.

“Oh! Boy! I don’t think so. I think I am longer than you” said the rattle snake confidently rattling his tails .

“ I don’t think so. I think I am longer than you” Said the little boa snake in a loud voice.

“ No I am longer than you” replied the little rattle snake in a loudervoice.

“ OK, then, let’s measure!” said the little boa snake.“ OK!”

“Tara!” shouted the little boa snake and the little rattle snake.“ You see? I am longer than you. Ha Ha Ha” said the little

boa snake laughing merrily.“ Oh, no!!! .” sighed the little rattle snake sadly and he

went away. “Hooray! I am the longest snake in the whole world!!!”

shouted the little boa snake merrily.

After a while, in the woods, the little boa snakefound another snake, a cobra sleeping under therocks.“Oh! There is another snake” said the little boasnake fixing a big smile on his face.“Hee, Hee, I am longer than him.” the little boasnake confidently whispered to himself andcrawled towards him.“Hi? I am Boarino.” said the little boa snake.“Um? Hi!” replied the cobra snake without payingattention. 

“My mum told me that I am the longest snake in the whole world. So I think I am longer than you” said the little boa snake clearly.“What?” replied the Cobra waking up from his sleep. “My mum told me that I am the longest snake in the

whole world. So I think I am longer than you” said the little boa snake in a loud voice.“----“ The little cobra looked at the boa snake closely

and said confidently

“Oh I don’t think so. I think I am longer than you” .“Oh I don’t think so. I think I am longer than you” said

the little boa snake in a loud voice.“ No I am longer than you” replied the little cobra snake

in a louder voice.“ OK, then Let’s measure!” Said the little boa snake.“ OK!”

“Tara!” shouted the little boa snake and the little cobra snake.

 “ You see? I am longer than you. Ha Ha Ha” said the lit-

tle boa snake laughing merrily.“ Oh No!!!!! ” sighed the little cobra snake sadly and

went away. “Hooray! Hooray! I am the longest snake in the whole

world!!!” shouted the little boa snake very happily.

After a while, by the lake, the little boa snake found another snake, swimming in the lake.

“Oh! There is another snake” said the little boa snake fixing a big smile on his face.

“Hee, Hee, I must be longer than him.” the little boa snake said confidently to himself and crawled towards him.

“Hi? I am Boarino” said the little boa snake.The snake in the lake did not say anything. “My mum told me that I am the longest snake in the whole

world. So I think I am longer than you” shouted the little boa snake clearly.

“What?” asked the snake popping her head out of the water. “My mum told me that I am the longest snake in the whole

world. So I think I am longer than you” shouted the little boa snake in a louder voice.

“----“ The snake looked at the boa snake closely and said confi-dently

“Oh I don’t think so. I think I am longer than you”.“Oh I don’t think so. I think I am longer than you” said the little

boa snake in a loud voice.“ No I am longer than you” the snake replied gently.“ OK, then Let’s measure!” Shouted the little boa snake.“ OK!”   “Tara!” shouted the little boa snake and the other snake. “ You see? I am longer than you. Ho Ho Ho” said the snake smiling

gently.“ Oh No!!!!! ” said the little boa snake sadly and asked.“Who are you?”

“ Ho, Ho. I am an Anaconda” said the snake.

“ Oh Anaconda. I think you are the longest snake in the whole world!”

said the little boa.“ Ho, ho, ho, thanks! But you are a

very long snake too.” said the snake swimming in the lake.

Fantasy

Types of fantasy• Animal fantasy• Toy fantasy• Eccentric and extraordinary characters• Enchanted journeys and imaginary lands• Heroic or quest fantasy• Supernatural and time fantasy• Science fiction and space fantasy

Animal fantasy

• The animals talk and display some human traits• The Wind in the Willows.• Finding Nemo

Toy fantasy

• Similar to the animal fantasy toys become human• Toy story• The Velveteen Rabbit• Alexander and the Wind-up Mouse.

Eccentric and extraordinary charac-ters• Slapstick, exaggeration and eccentricity• The pushcart war• Mary Poppins• Pippi Longstocking• Charlie and the Chocolate Factory, • James and the Giant Peach,• Matilda.

Enchanted journeys and imaginary lands

• The journey motif is one of the oldest in literature, • Odyssey• Alice in Wonderland.• The Wizard of Oz• Gulliver’s Travels

Heroic or quest fantasy

• Heroic, remain clearly grounded in the primary world, the touchstone against which the wonders of the fan-tasy world are measured.• Fight against the veil power, • The fate of an entire civilization often depends on the

coutcome of the struggle. • The dark is rising• The Lion, the Witch and the Wardrobe• The Lord of the Rings

Supernatural and time fantasy

• Include ghost and witch stories, stories of mysterious and unexplained occurrences. • Tom’s midnight garden• The Ghost of Thomas Kempe

Science fiction and space fantasy• Twenty Thousand Leagues under the sea• From Earth to the Moon Direct• Space cat• The Far Side of Evil.

Simplify ‘the Wizard of Oz’• Highlight the most important parts into a few steps.

(Physical points)• Think about psychological aspects to highlight• Think about repeating sentences• Think about points the learners to solve problems.

Homework• Finalize your story with pictures and tasks• Read chapter 15. • Make some activities around a story reflecting some

problem solving concepts in chapter 19.