Educational Psychology | Part 3: Thinking, Learning and Memory | Chapter 9: Thinking: Concept Formation, Reasoning,
and Problem Solving
1. Why Understanding Thinking Is Important to Teachers
A. Critical thinking - Conscious and purposeful direction of thought toward finding a solution to a problem.
2. Concept Formation
A. Concepts - Mental abstraction or category of similar objects, people, events, or ideas.
B. Defining Features of Concepts
1. Defining Features - Features that are necessary and sufficient for defining a concept
C. Characteristic Features of Concepts
1. Characteristic Feature - Features typical of a thing represented in a concept, although not always
associated with it.
2. Prototype - Most representative example of a given concept.
3. Exemplars - Highly typical instances of a concept.
4. Concept Map - Picture or diagram illustrating the relationships between different concepts.
5. Figure 9.1 Example of a Concept Map
a.
Implications for Teaching
A. Use a lot of examples
B. Combine examples with definitions to encourage full understanding of a concept
3. Distinguish between defining and characteristic features
4. Help students link new concepts to what they already know.
3. Reasoning
1. Reasoning - Process of drawing conclusions from evidence.
2. Deductive and Inductive Reasoning
1. Deductive Reasoning - Process of drawing specific, logically valid conclusions from one or more
general premises.
2. Inductive Reasoning - Process of drawing reasonable general conclusions from specific facts or
observations.
Educational Psychology | Part 3: Thinking, Learning and Memory | Chapter 9: Thinking: Concept Formation, Reasoning,
and Problem Solving
3. Developing Reasoning Skills
1. Using Syllogisms
a. Syllogism - Deductive argument that permits a conclusion to be drawn from a series of two
statements, or premises.
2. Encouraging Inductive Reasoning
3. Repairing Fallacious Reasoning and Decision Making
a. Heuristics - Informal, intuitive, and often speculative shortcut in thinking that may solve a
problem but is not guaranteed to do so.
b. Availability Heuristic - Shortcut in thinking by which people make judgments on the basis of how
easily they are able to call to mind what they perceive as relevant instances of a phenomenon.
c. Representativeness Heuristic - Shortcut in thinking by which people judge the probability that a
particular event or object belongs to a certain category by how obviously it resembles, or
represents the population form which it comes.
d. Overconfidence - Heuristic described as an overestimate of the likelihood of the correctness of a
judgment
e. Underconfidence - thought pattern in which people believe they are less likely to be correct
than they actually are.
f. Gambler's fallacy: the false belief that when a sequence of coincidental events occur in a
particular pattern, subsequent events are more likely to deviate from the pattern that to
continue in it.
g. Sunk-cost fallacy: which is the decision to continue to invest in something simply because one
has already invested in it and hopes to recover the investment.
4. Problem Solving
1. Problem Solving - Process of moving from a situation in need of resolution to a solution, overcoming any
obstacles along the way.
2. The Problem-Solving Cycle
1. Step 1: Identify the Existence of a problem
2. Step 2: define the problem
3. Step 3: Represent and organize information about a problem
4. Step 4: Create or select a strategy for problem solving
5. Step 5: allocate resources for problem solving
6. Step 6: Monitor Problem solving
7. Step 7: evaluate the solution to a problem
3. Types of Problems
1. Well-Structured and Ill-Structured problems
a. Well-Structured Problems - Problems with clear paths to their solutions.
b. Ill-structured Problems - Problems that have no clear path to a solution
2. Insight Problems
a. Insight Problems - Problems that require the problem solver to think in novel ways that are not
obvious from the way in which the problems are presented.
b. Table 9.1 Insight Problem
Insightful
Thought
Process
Required
Selective Encoding
Selective Combination
Selective Comparison
Problem
A teacher had 23 pupils
in class. All but 7 of
them went on a
museum trip and thus
were away for the day.
There were 100 politicians at a meeting.
Each politician was either honest or
dishonest. We know the following two
facts: first at least one of the politicians
was honest; second, for any two
Create a novel analogy
by altering the normal
state of something in the
world: If villains are
lovable, then hero is to
Educational Psychology | Part 3: Thinking, Learning and Memory | Chapter 9: Thinking: Concept Formation, Reasoning,
and Problem Solving
How many of them
remained in class that
day?
politicians at least one of the two was
dishonest. How many of the politicians
were honest and how many were
dishonest, and what were the respective
numbers of each?
admiration as villain is to:
a. contempt
b. affection
c. cruel
d. kind
Solution
Insightful problem
solvers must realize that
the number of students
in the class, 23, is
actually irrelevant in
this problem. Instead
they should notice the
number of students
who did not go on the
trip, and therefore
stayed in class: 7
Problem solvers know that there is at least
one honest politician. That leaves 99
possibly dishonest politicians. Also, they
know that, if you take any two politicians,
one of them is guaranteed to be dishonest
(and maybe both are). Insightful problem
solvers must combine the two clues. If the
honest politician is paired with any of the
99 other politicians, at least one of the
pair must be dishonest. The insightful
problem solver concludes there is one
honest politician and there are 99
dishonest ones.
(Answer: b. affection)
There are two processes
at work. First, the
problem solver must
avoid being confused by
the normal definition of
a villain. Second, the
problem solver must see
the relationship between
the tow other terms in
the analogy (heroes
receive admiration) and
choose the word that
creates a similar
relationship with the
newly defined term,
villain. THIS IS WRONG!
Other
examples
An airplane crashes on
the US-Canadian
border. In which
country are the
survivors buried
(Answer: Survivors are
not buried at all).
I bought one share of stock in the SureFire Corporation for $70. I sold that share
for $80. I bought back the share for $90,
but later sold it for $100. How much
money did I make? (Answer: Combine the
two purchase prices ($70+$90) and
combine the two selling prices
($80+$100). Subtract the total purchase
Fifteen percent of the
price from total selling price ($180people in a certain town $160)=$20 Profit
have unlisted telephone
numbers. You select
200 names at random
from the local phone
book. How many of
these people can be
expected to have
unlisted telephone
numbers? (Answer:
none. If they are in the
phone book, their
numbers are listed)
If lakes are dry, then trail
is to hike as lake is to:
a. swim
b. dust
c. water
d. walk
(Answer: d. walk)
ALSO WRONG!
If broomsticks are flying
machines, then jet is to
pilot as broomstick is to:
a. house
b. hermit
c. witch
d. garden
(Answer: c. witch)
1. Strategies For Problem Solving
1. Algorithms and Heuristics
a. Algorithm - Clear and fixed set of steps that guarantees a solution to a problem
b. 4 most common heuristics:
i.
Means-ends analysis
Educational Psychology | Part 3: Thinking, Learning and Memory | Chapter 9: Thinking: Concept Formation, Reasoning,
and Problem Solving
ii.
Working forward
iii.
Working backward
iv.
Generate and test (AKA trial & error)
2. Problem Isomorphs
a. Problem Isomorphs - problems that have the same formal structure, but different ways of
expressing this structure.
3. Incubation
a. Incubation - Temporarily ceasing to work actively on a problem so as to generate an insight.
2. Impediments to Problem Solving
1. Mental Set - Predisposition to think about a problem in a particular way.
2. Functional Fixedness - Particular kind of mental set in which a person is unable to invent a specific
new use for something because he or she is so used to seeing a conventional use for that thing.
3. Expertise in Problem Solving
1. Automaticity - Execution of mental procedures with hardly any effort or even conscious awareness of
doing so.
Implications for Teaching
1. Define Problems
2. Teach strategies for insightful problem solving
3. Look for isomorphs
4. Help students overcome impediments to problem solving.
5. Transfer
1. Transfer - Carrying knowledge form one problem or situation over to a new problem or situation. It can
either facilitate or hinder the solving of the new problem.
2. Types of transfer
1. Positive Transfer - Transfer that facilitates the solution of a new problem as a result of experience
with an earlier-encountered problem.
2. Negative Transfer - Transfer that hinders the solution of a new problem as a result of experience with
an earlier-encountered problem.
3. Figure 9.5 Positive and Negative transfer as they Apply to the Learning of Vocabulary and Grammar of
One Language as It s Transferred to the Learning of Vocabulary and Grammar of Another Language
4. Low-Road Transfer - Transfer that occurs when a highly practiced skill is carried over from one
situation to another, with little or no reflective thinking.
5. High-Road Transfer - Transfer that occurs when abstract knowledge learned in one situation is
consciously applied to another situation.
6. Forward-Reaching Transfer - Transfer that occurs when a person intends to bring knowledge to a new
situation.
7. Backward-Reaching Transfer - Realization of the applicability of what you learned in the past only
after it becomes relevant.
3. Teaching For Transfer
1. Meaningfulness
2. Encoding Specificity
a. Encoding Specificity - Ability to transfer learning only in conditions similar to those in which the
original learning took place.
3. Organization
4. Discrimination
a. Discrimination - Ability to recognize when information previously learned is not relevant in a
new situation.
6. Decision Making
Educational Psychology | Part 3: Thinking, Learning and Memory | Chapter 9: Thinking: Concept Formation, Reasoning,
and Problem Solving
1. Satisficing
1. Satisficing - Decision-making model in which the decision maker considers options one by one,
immediately selecting the first option that appears to be satisfactory.
7. Teaching for Thinking
1. Stand-Alone Program - Program in which thinking is taught as a separate unit or even a separate course.
2. Infused Instruction - Teaching how to think as an integral part of a curriculum
3. Table 9.2 Essential and Teachable Thinking Skills
Ability
Definition
Example
Focusing on
a question
Identifying or formulating the key
question in a situation and keeping
the question in mind
A student proposes the central question of a term
paper: "Was Hamlet sane?"
Analyzing
arguments
Identifying the parts of an argument,
conclusion, and supporting reasons,
and seeing the structure of an
argument.
The student reads articles from literary scholars
claiming that Hamlet suffered from hallucinations
(when he saw the ghost of this father), and
depression. The student summarizes the arguments in
support of these diagnoses.
Asking and
answering
questions
Being able to ask and answer
The student asks himself or herself, "what do these
questions that clarify or challenge an writers mean by depression?" and "Does Hamlet
argument
really display all the symptoms of depression?"
Judging the Rating the expertise, reputation, and The student notices that none of the literary scholars
credibility of motivations of a person making an
who claim Hamlet suffered from mental illness is a
a source
argument
qualified psychologist or psychiatrist
Observing
and judging
the reports
Making careful notes and reports of The student notes several instances of Hamlet's wellobservations of others' observations adapted behavior throughout the course of the play
without including judgments or
rating the quality of others'
observations.
Deducing
and judging
others'
deductions
Using general logical rules to draw
specific conclusions
The student knows that not everyone who has
hallucinations is mentally ill, and therefore deduces
that whether or not the ghost of his father really
existed, Hamlet could be sane.
Inducing and Drawing general rules based on
judging
specific instances, but always
others'
looking for an exception to the rule
inductions
A key point in the arguments that Hamlet suffered
from depression is the famous "To be or not to be"
speech, which many scholars interpret as Hamlet
considering suicide. However, the student notes that
Hamlet does not consistently express an interest in
dying throughout the play.
Making
Value
Judgments
Weighting and balancing alternative
beliefs or plans
The student compares the writings of those who claim
Hamlet was depressed with articles that claim he was
in full mental control
Defining
terms and
judging
others'
Examining definitions closely to see
how useful or well constructed they
are
The student carefully examines the definitions of
sanity and insanity presented in the articles about
Hamlet
Educational Psychology | Part 3: Thinking, Learning and Memory | Chapter 9: Thinking: Concept Formation, Reasoning,
and Problem Solving
definitions
Identifying
Pointing out unstated reasons or
assumptions assumptions
The student notices that many of the writers who
claim Hamlet was sane because he carried out
complicated travel and other plans seem to assume
that people with mental illnesses cannot do these
things
Deciding on
an action
Based on the steps of the problem
cycle, after identifying and defining
the problem and generating
alternative solutions, choosing one.
The student chooses a position on the question of
Hamlet's mental health and prepares an outline for
the term paper
Interacting
with others
Arguing, debating, or presenting a
position
The student writes the paper summarizing the
evidence on both sides of the question, and the
reasons for his or her own conclusions about Hamlet's
sanity
A. Dialogical Thinking - Ability to see not only one's own point of view, but also the points of view of others.
B. Dialectical Thinking - Thinking characterized by a progression in which first a thesis is proposed, then an
opposing antithesis, and finally an integrative synthesis.
C. Use role Playing
D. Use Groups
E. Model and Explicitly Teach Thinking Skills