Problem 8
Learning goals:
Problem A
Problem-solving strategies
Algorithm- a method that will always produce a solution to the
problem, although the process can sometimes be inefficient
- exhaustive search- trying out all possible answers using a
specified system
heuristic- general rule that is usually correct
- if to solve a problem, you would ignore some alternatives and
explore only those that seem likely to produce a solution
- e.g. looking for only pronounceable letter combinations in an
anagram
- you have to weigh the benefits of a heuristic’s speed against the
costs of possibly missing the correct solution
Analogy Approach
analogy approach in problem solving- employing a solution to a
similar, earlier problem to help you solve a new problem
widely used in problem solving and when making creative
breakthroughs
- e.g. comparing a plane’s wings to a bird’s wings designed the
wings so that pilots could make subtle adjustments by using
metal rods and gears
problem isomorphs- a set of problems that have the same
underlying structures and solutions, but different specific details
- e.g. military tanks having to cross to the island over several
bridges as they can’t all cross over one (source problem)
- a radiation beam will destroy a tumour if it gets enough radiation
but will destroy surrounding healthy tissue (target problem)
- 10% solved without the source problem, 30% solved with the
source problem
schema induction- problem solvers map the connections between
two different problems
surface features- the specific elements of the problem. If 2
problems share surface similarity, this means that the parts of the
problem look similar
- e.g. the specific objects and terms used in the question
structural features- the underlying relationships among the
surface features of the 2 problems that they must understand in
order to solve the problem correctly
people pay attention to the obvious surface features but usually fail
to emphasise structural features
, people often fail to see the analogy between a problem they have
solved and a new problem isomorph that has similar structural
features
- have trouble solving the same problem in a new setting as they
fail to transfer their knowledge
- trouble solving the problem when it is ‘dressed up’ with a
superficially different cover story
- those with limited problem-solving skills and limited
metacognitive ability are likely to have difficulty using analogies
factors encouraging appropriate use of analogies:
- trying several structurally similar problems before they tackle the
target problem
- people solve statistics problems more accurately if they have
been trained to sort problems into categories on the basis of
structural similarities
steps necessary for analogies to succeed as problem-solving
techniques
1. noticing- notice that a relationship exists between the two
problems
2. mapping- map the key elements of the problems
3. schema development- must arrive at a general schema
underlying the problems that will allow for the solution of the
target problem
- stage 1 is difficult for people
thinking aloud/ talking through a problem may help one solve it
quicker
- Lane and schooler- ppt read 16 short scenarios and later asked to
read 8 more and had to decide which of the original scenarios
seemed most analogous
- Each of the test scenarios were designed to bear a superficial
relationship (surface similarity) with one of the encoded
scenarios and a deeper relationship (structural similarity with
another of the encoded scenarios
- ½ thought out loud and ½ were silent
- Verbalising seemed to have converse effects on the discovery of
different sorts of analogies. It seemed to encourage ppt to see
superficial analogies at the expense of deeper analogies
- the requirement of verbalisation leads one to focus on superficial
similarities because these are easier to talk about
when ppt have to come up with analogies themselves they will
create ones with structural similarities rather than surface
similarities
- suggests that in everyday circumstances ppl may actually be
more sensitive to structural similarity than suggested by previous
research
◊ Markman- most studies on analogies present the source problem
and the subsequent analogical problems in written form
- Believed people will focus more on structural relationships if
presented with spoken problems
Learning goals:
Problem A
Problem-solving strategies
Algorithm- a method that will always produce a solution to the
problem, although the process can sometimes be inefficient
- exhaustive search- trying out all possible answers using a
specified system
heuristic- general rule that is usually correct
- if to solve a problem, you would ignore some alternatives and
explore only those that seem likely to produce a solution
- e.g. looking for only pronounceable letter combinations in an
anagram
- you have to weigh the benefits of a heuristic’s speed against the
costs of possibly missing the correct solution
Analogy Approach
analogy approach in problem solving- employing a solution to a
similar, earlier problem to help you solve a new problem
widely used in problem solving and when making creative
breakthroughs
- e.g. comparing a plane’s wings to a bird’s wings designed the
wings so that pilots could make subtle adjustments by using
metal rods and gears
problem isomorphs- a set of problems that have the same
underlying structures and solutions, but different specific details
- e.g. military tanks having to cross to the island over several
bridges as they can’t all cross over one (source problem)
- a radiation beam will destroy a tumour if it gets enough radiation
but will destroy surrounding healthy tissue (target problem)
- 10% solved without the source problem, 30% solved with the
source problem
schema induction- problem solvers map the connections between
two different problems
surface features- the specific elements of the problem. If 2
problems share surface similarity, this means that the parts of the
problem look similar
- e.g. the specific objects and terms used in the question
structural features- the underlying relationships among the
surface features of the 2 problems that they must understand in
order to solve the problem correctly
people pay attention to the obvious surface features but usually fail
to emphasise structural features
, people often fail to see the analogy between a problem they have
solved and a new problem isomorph that has similar structural
features
- have trouble solving the same problem in a new setting as they
fail to transfer their knowledge
- trouble solving the problem when it is ‘dressed up’ with a
superficially different cover story
- those with limited problem-solving skills and limited
metacognitive ability are likely to have difficulty using analogies
factors encouraging appropriate use of analogies:
- trying several structurally similar problems before they tackle the
target problem
- people solve statistics problems more accurately if they have
been trained to sort problems into categories on the basis of
structural similarities
steps necessary for analogies to succeed as problem-solving
techniques
1. noticing- notice that a relationship exists between the two
problems
2. mapping- map the key elements of the problems
3. schema development- must arrive at a general schema
underlying the problems that will allow for the solution of the
target problem
- stage 1 is difficult for people
thinking aloud/ talking through a problem may help one solve it
quicker
- Lane and schooler- ppt read 16 short scenarios and later asked to
read 8 more and had to decide which of the original scenarios
seemed most analogous
- Each of the test scenarios were designed to bear a superficial
relationship (surface similarity) with one of the encoded
scenarios and a deeper relationship (structural similarity with
another of the encoded scenarios
- ½ thought out loud and ½ were silent
- Verbalising seemed to have converse effects on the discovery of
different sorts of analogies. It seemed to encourage ppt to see
superficial analogies at the expense of deeper analogies
- the requirement of verbalisation leads one to focus on superficial
similarities because these are easier to talk about
when ppt have to come up with analogies themselves they will
create ones with structural similarities rather than surface
similarities
- suggests that in everyday circumstances ppl may actually be
more sensitive to structural similarity than suggested by previous
research
◊ Markman- most studies on analogies present the source problem
and the subsequent analogical problems in written form
- Believed people will focus more on structural relationships if
presented with spoken problems
