BCS 111 Lecture 9

Is language essential for problem solving?

-

Not really needed

Satisfying basic biological needs

Needs language

tasks that require verbal skills (e.g., verbal analogy, sudoku, etc.)

Language not necessarily needed but could help the thinking process

tasks that don’t require verbal skills (rotate a magic cube, card sorting, etc.)

What do we need for problem solving?

• Goal setting

• Attention

• Memory

• Experience

• Knowledge about the problem itself: problem-specific

Well-defined vs. ill-defined problems

-

Well-defined problems

• Clear goal/narrower scope

• Narrower set of actions

• Easier to plan ahead than the ill-defined ones

Ill-defined problems

• Open-ended

• Unclear actions needed to achieve the goal

  • May generate some well-defined problems while solving the ill-defined ones.

Common strategies in problem-solving

-

Generate-and-test (trial-and-error approach)

Add two matches to correct the equation

Working backward

• know what the solution should look like

• Perform last step first

  • Planning of moves

  • Tower-of-Hanoi

  • Rules:

    • One disk at a time

    • Smaller disk on top of bigger disks

Backtracking

• step back to track the root of the problem

• Commonly used in coding and debugging

Are these strategies used independently? Can we use some combinations of them? Of course!

Can you use the Tower-of-Hanoi task (or any other examples) to illustrate the following strategies are being used to solve one single problem?

• Generate-and-test

• Working backward

• Backtracking

Tower-of-Hanoi task (cont)

Ideally, only working backward needed if no mistakes are made.
But practically:

1. Generate-and-test: move a peg and see if it works

2. Backtracking: moved a few pegs and found it didn’t work; reversed a few steps back to see where it began to get wrong.

Analogy

Analogy helps with the tumor problem!

How mental set limits our creativity?

• Mental set: one’s strategy/preference to approach a problem e.g., positive vs. negative thinking

• Nine-dot problem

How functional fixedness blocks our creativity?

Functional fixedness: a fixed mental set for the function of an object

• The two-string problem

Functional fixedness

The candle problem (Duncker 1945)

• How would you attach the candle to the wall so that the wax doesn’t fall when the candle is lit?

Functional fixedness – Think outside the box!

• The candle problem

• Context or available cues also matter!

  • Where the tacks are placed

Divergent thinking

• Think outside the box: think in more than one direction

  • The plier in the two-string problem

  • The box in the candle problem

  • The parking lot problem

  • Most brain teasers

Convergent thinking

The ability to associate irrelevant concepts

• Try to find a word that can be combined with each of the three words in the set to create another new set of three words or phrases (The Remote Associates Test)
  1. Snow, down, out
  2. Cross, rain, tie
  3. Opera, hand, dish
  4. Sense, courtesy, place

Problem-solving and intelligence

-

Fluid intelligence

Ability to solve new problems

Crystallized intelligence

Ability to solve similar problems that you encountered before

How do we measure Intelligence?

Wechsler Intelligence Scale for Children (WISC): sample question to test verbal IQ

• Question: How are morning and afternoon alike?”

• Question (to test vocab size): Select the picture that matches the word you heard

Wechsler Intelligence Scale for Children (WISC): sample question to test spatial skills/visual imagery

Which shapes on the bottom panel do you need in order to form the large shape on the top?