ECON 1 Lecture Notes - Lecture 5: Talc, Problem Solving, Knowledge Base
Missing:
Process monitoring
Positive (Near vs far) & negative transfer (analogy)
General info about problem
• Problem solving requires the following:
1) there are two states of affairs;
2) the agent is in one talc and wants to be in the other state;
3) it is not apparent to the agent how the gap between the two states is to be bridged
4) bridging the gap is a con consciously guided multi-step process.
• Well-defined problems – all aspects of the problem are clearly specified (= initial state, goal,
methods available) (e.g. maze or chess)
→ Used in research as there is an optimal strategy and errors/deficiencies can easily be
identified
→ The goal is well specified lied because it is clear when it has been reached
→ planning is much less necessary with well-defined problems
• Ill-defined problems – definition of problem is underspecified, initial state, goal state & methods
unclear (e.g. keys locked in car)
→ Most everyday problems
• Knowledge-rich problems – can only be solved with considerable amounts of prior knowledge
• Knowledge-lean problems – can be solved without prior knowledge as necessary info is provided
by problem statement
→ Most traditional research on problem solving involved knowledge-lean problems because
such problems minimise individual differences in relevant knowledge
UNDERSTANDING THE PROBLEM
Understanding= that you have constructed a mental representation of the problem, based on the
information provided in the problem and your own previous experience (Robertson, 2001).
• In order to understand a problem, you need to construct an accurate mental representation
•
PAYING ATTENTION TO IMPORTANT INFORMATION
To understand a problem, you need to decide which information is most relevant to the problem’s
solution and then attend to that information.
• Attention: important in understanding problems because attention is limited, and competing
thoughts can produce divided attention
• focusing on the appropriate part: decided which information is essential and which can be
disregarded
attention is a necessary initial component of understanding a problem
METHODS OF REPRESENTING THE PROBLEM
• choose an inappropriate method: you might not reach an effective solution to the problem
• find an effective representation: you can organize the information efficiently and reduce the
strain on your limited working memory.
o more likely to select a useful strategy
SYMBOLS
• Sometimes the most effective way to represent an abstract problem is by using symbols
• Challenges: problem solvers often make mistakes when they try to translate words into symbols
o translating sentences into symbols is that the problem solver may oversimplify the sentence,
thereby misrepresenting the information
MATRICES
Matrix: a chart that shows all possible combinations of items.
• excellent way to keep track of items, particularly if the problem is complex and if the relevant
information is categorical
• especially suitable when the information is stable, rather than changing over time
DIAGRAMS
• useful when you want to represent a large amount of information.
• hierarchical tree diagram: figure that uses a tree-like structure to specify various possible
options in a problem.
o especially helpful in showing the relationship between categorized items
• Advantage:
o can represent complicated information in a clear, concrete form, so that you have more
“mental space” in working memory for other problem-solving activities
o diagrams attracted people’s eye movements to relevant areas of the diagram, helping them
solve problems more successfully
VISUAL IMAGES
• advantages:
o can let us escape from the boundaries of traditional, concrete representations.
o provide an advantage when a problem requires you to construct a figure
SITUATED COGNITION: THE IMPORTANCE OF CONTEXT
situated-cognition= argue that our ability to solve a problem is tied into the specific context in which
we learned to solve that problem (Lave, 1997; Robertson, 2001; Seifert, 1999).
• The traditional cognitive approach to thinking emphasizes the processes that take place inside an
individual person’s head.
• The situated-cognition approach argues that the traditional cognitive approach is too simplistic
• situated-cognition perspective has important implications for education:
o suggests that children should have experience in solving authentic math problems that they
are likely to encounter outside a school setting.
o suggests that college students can learn especially effectively during internships and other
practical settings
• ecological validity= conditions in which the research is conducted are similar to the natural
setting in which the results will be applied.
• One important principle of the situated-cognition: people learn skills within the context of a
specific situation, such as a grocery store.
How do we solve problems?
PROBLEM SOLVING CYCLE
• Problem identification: Do we actually have a problem?
• Problem definition and representation: What exactly is our problem?
• Strategy formulation: How can we solve the problem? The strategy may involve
o Analysis= breaking down the whole of a complex problem into manageable
elements. Instead, or perhaps in addition
o Synthesis= putting together various elements to arrange them into something
useful.
o Another pair of complementary strategies involves divergent and convergent
thinking.
▪ divergent thinking= try to generate a diverse assortment of possible
alternative solutions to a problem.
▪ convergent thinking= narrow down the multiple possibilities to converge on
a single best answer.
• Organization of information: How do the various pieces of information in the problem fit
together?
• Resource allocation: How much time, effort, money, etc., should I put into this problem?
• Monitoring: Am I on track as I proceed to solve the problem?
• Evaluation: Did I solve the problem correctly?
THEORIES
GESTALT APPROACH
• Early research on problem solving was dominated by the Gestaltists
• Trial-and-error learning – a solution is reached by producing fairly random responses rather than
by a process of thought
• Reproductive thinking – re-use of previous experiences/ knowledge to solve a current problem
(Thorndike’s cat experiment)
Document Summary
Positive (near vs far) & negative transfer (analogy) Used in research as there is an optimal strategy and errors/deficiencies can easily be identified. The goal is well specified lied because it is clear when it has been reached. Planning is much less necessary with well-defined problems. Ill-defined problems definition of problem is underspecified, initial state, goal state & methods unclear (e. g. keys locked in car) Most everyday problems: knowledge-rich problems can only be solved with considerable amounts of prior knowledge, knowledge-lean problems can be solved without prior knowledge as necessary info is provided by problem statement. Most traditional research on problem solving involved knowledge-lean problems because such problems minimise individual differences in relevant knowledge. Understanding= that you have constructed a mental representation of the problem, based on the information provided in the problem and your own previous experience (robertson, 2001). In order to understand a problem, you need to construct an accurate mental representation.
