Information Processing Theory
Behaviorism Theory
Classical Conditioning
Operant Conditioning
Contiguity Theory
Constructivist Theory
› J. Bruner
› Piaget (Cognitive Development- Genetic Epistemology)
› Vygotsky (Social Development Theory and Social
Situated Learning
Fish is Fish Information
Information Processing –
Human mind’s activity of
taking in, storing, and using
information (Woolfolk, 1998).
 Information-Processing
Model – The procedure by
which either a computer or a
person codes, stores, and
retrieves information (Kalat,
Computers mostly handle
information sequentially, while the
brain handles multiple channels of
information in parallel (Aamodt &
Wang, 2008).
 People have always described the
brain by comparing it to the latest
technologies, whether that meant
steam engines, telephone
switchboards, or even catapults
(Aamodt & Wang, 2008).
As one knows, the brain
contains neurons.
 Brain – The major
neuronal center within
the body; typically
located at the anterior of
the body (Randall,
Burggren, and French,
Nerve cells are found elsewhere in the
human body, from one’s fingertip to the
brain to the spinal cord.
 Nervous System – The collection of all
neurons in an animal’s body (Randall,
Burggren, and French, 1997).
Based on my mental notes from my Educational
Psychology class here at the U of I, much emphasis
was placed on memory.
 My mental notes from this course include a path for
memories, going from short-term memory to longterm memory. Included in my mental notes is also
the apparent mechanical way people handle
 Apparently, the learning about memory in
Educational Psychology, has made the journey into
my long term memory.
Working memory has been called shortterm memory (Woolfolk, 1998).
 “Long term memory is a relatively
permanent store of (mostly) meaningful
information, short-term memory is the
particular subset of information a person is
dealing with at the moment (Kalat, 1990).”
 “Information in working memory can be
kept activated through maintenance
rehearsal or transferred into long-term
memory by being connected with
information in long-term memory
(elaborative rehearsal) (Woolfolk, 1998).”
“Information processing views of many rely on the
computer as a model. Like the computer, the
human mind takes in information, performs
operations on it to change its form and content,
stores the information, retrieves it when needed,
and generates responses to it (Woolfolk, 1998).
“In addition, research in another major area began
to show how learners process information,
remember, and solve problems in nonpriviledged
domains. Known as information processing (Simon,
1972; Newell and Simon, 1972), this branch of
psychology was quickly was quickly adopted to
explain developments in children’s learning
(Bransford et al., 1999).”
“As information processing theories
began to emerge, the metaphor of mind
as computer, information processor, and
problem solver came into wide usage
(Newell et al., 1958) and was quickly
applied to the study of cognitive
development (Brandsford et al., 1999).”
George A. Miller has provided two theoretical ideas that are
fundamental to cognitive psychology and the information
processing framework.
The first concept is “chunking” and the capacity of short term
memory. Miller (1956) presented the idea that short-term
memory could only hold 5-9 chunks of information (seven plus or
minus two) where a chunk is any meaningful unit. A chunk
could refer to digits, words, chess positions, or people’s faces.
The concept of chunking and the limited capacity of short term
memory became a basic element of all subsequent theories of
The second concept is TOTE (Test-Operate-Test-Exit) proposed by
Miller, Galanter, & Pribram (1960). Miller et al. suggested that
TOTE should replace the stimulus-response at the basic unit of
behavior. In a TOTE unit, a goal is tested to see if it has been
achieved and if not an operation is performed to achieve the
goal; this cycle of test-operate is repeated until the goal is
eventually achieved or abandoned. The TOTE concept
provided the basis of many subsequent theories of problem
solving (e.g., GPS) and production systems.
According to the information processing
model of memory, the manner in which we
enter memories is like the manner in which
we enter information into a computer
(Kalat, 1990).
 “Simon (1972) and others (e.g., Chi, 1978;
Siegler, 1978; Klahr and Wallace, 1973)
argued that development means
overcoming information processing
constraints, such as limited short-term
memory capacity (Bransford et al., 1999).”
The following is based much on readings in
Woolfolk (1998).
Students are able to sense a lot of information.
Much of this information is not even perceived, yet
alone remembered. For information to be
remembered, it needs to make the journey to long
term memory.
Learning involves taking information in and storage
in long term memory.
Teaching needs to keep students’ attention and
ensure that new information is integrated with old
to facilitate the storage of information in long term
Assessment is involved with basically verifying what
content is found in long term memory in the brain.
Behaviorist theories of learning seek
scientific, demonstrable explanations for
simple behaviors.
 In this theory, humans are considered to
resemble machines, which is why
behaviorist explanations tend to be
somewhat mechanical in nature.
Psychology should be seen as a science. Theories need to be supported
by empirical data obtained through careful and controlled observation
and measurement of behavior.
Behaviorism is primarily concerned with observable behavior, as
opposed to internal events like thinking and emotion. Observable (i.e.
external) behavior can be objectively and scientifically measured.
People have no free will – a person’s environment determines their
When born our mind is 'tabula rasa' (a blank slate).
There is little difference between the learning that takes place in humans
and that in other animals. Therefore research can be carried out on
animals as well as humans.
Behavior is the result of stimulus – response (i.e. all behavior, no matter
how complex, can be reduced to a simple stimulus – response
All behavior is learnt from the environment. We learn new behavior
through classical or operant conditioning.
The following are valuable:
Small, concrete, progressively sequenced tasks
Positive and negative reinforcement
Consistency in the use of reinforcers during the
teaching-learning process
Habits and other undesirable responses can be
broken by removing the positive reinforcers
connected with them.
Immediate, consistent, and positive
reinforcement increases the speed of learning.
Once an item is learned, intermittent
reinforcement will promote retention.
Pavlov (early 1900’s) founded Classical
 Thorndike (early 1900’s) extended the
concept further and founded
 Watson (1930) proposed that the process of
classical conditioning (based on Pavlov’s
observations) was able to explain all
aspects of human psychology.
 Guthrie (1935) extended the concept
further and founded Contiguity Theory
Classical conditioning was discovered
accidentally by Ivan Pavlov during his
dog salivation experiment
 Found that animals learn through
repetition and rewards
 Classical conditioning was later
developed by John Watson
 Classical conditioning involves learning
to associate an unconditioned stimulus
to a new stimulus
Started from the idea that there are some
things that a dog does not need to learn
(aka salivating when food is near). This is an
unconditioned reflex (or a stimulus-response
connection that required no learning).
 Pavlov discovered that any object or event
the dogs learned to associate with food
(like a lab assistant) would trigger the same
response (conditioned reflex).
 The lab assistant was originally a neutral
stimulus (since it produced no response) but
became associated with the
unconditioned stimulus (food)
Pavlov started a new experiment by using a
bell as his neutral stimulus.
Whenever he gave food to his dogs, he also
rang a bell. After a number of repeats of this
procedure he tried the bell on its own. The bell
now caused an increase in salivation.
The dog learned an association between the
bell and the food and a new behavior had
been learned. This is called a conditioned
The neutral stimulus had become a
conditioned stimulus.
Behaviorism as a movement in psychology
appeared in 1913 when John Watson
published the article ‘Psychology as the
behaviourist views it’.
Watson believed that all individual differences
in behavior were due to different experiences
of learning.
Watson denied completely the existence of
the mind or consciousness.
“Give me a dozen healthy infants, well-formed, and my own specified world
to bring them up in and I'll guarantee to take any one at random and train
him to become any type of specialist I might select - doctor, lawyer, artist,
merchant-chief and, yes, even beggar-man and thief, regardless of his
talents, penchants, tendencies, abilities, vocations and the race of his
ancestors”. -Watson
Famously known as Little Albert (1920)
Little Albert was a 9 month old infant.
Watson and Raynor tested Little Albert’s
reaction to various stimuli
 He was shown a white rat, a rabbit, a
monkey, and various masks. These were all
neutral stimuli since Little Albert was “stolid
and unemotional” to these stimuli.
 When a hammer was struck against a steel
bar behind his head, the sudden loud noise
would cause Albert to cry. This was the
unconditioned response.
When Little Albert was 11 months old, the white rat
was presented and seconds later the hammer was
This was repeated 7 times in 7 weeks and each time
Albert would cry. By this time Albert would see the rat
and would show an immediate sign of fear. He
would cry before the hammer hit and he would
attempt to crawl away.
Watson and Raynor had shown that classical
conditioning could be used to create a phobia
Over the next few weeks and months Albert was
observed and 10 days after conditioning his fear of
the rat was much less marked. This dying out of a
learned response is called extinction.
However, even after a full month the fear was
Connectionist Models – Views of
knowledge as being stored in
patterns of connections among
processing units in the brain
(Woolfolk, 1998).
 Connectionist Model – A model
that represents memory as a set
of links among units (Kalat,
“Thorndike developed psychological
connectionism. He believed that through
experience neural bonds were formed between
perceived stimuli and emitted responses; therefore,
intellect facilitated the formation of neural bonds
(Plucker, 2007).
“Thorndike’s theory consists of three primary laws:
(1) law of effect – responses to a situation which
are followed by a rewarding state of affairs will be
strengthened and become habitual responses to
that situation, (2) law of readiness – a series of
responses can be chained together to satisfy some
goal which will result in annoyance if blocked, and
(3) law of exercise – connections become
strengthened with practice and weakened when
practice is discontinued (Kearsley, 1994-2009).
“Some of the most recent explanation of
how memory works are connectionist
models that assume all knowledge is
stored in patterns of connections among
basic processing units in a vast network
of the brain (Woolfolk, 1998).
 The connectionist model of memory
represents each memory as a series of
connections among items (Kalat, 1990).
The following is based much on readings in
Woolfolk (1998).
New brain connections allow for learning
and affect the learning process.
Learning involves continued building,
elaboration, and adjustment of information.
Teaching needs to account for the
connections being made and adjusted.
Assessment is involved with verifying what
brain connections have been made.
B.F. Skinner came up with the Operant conditioning
idea of Behaviorist Theory in the 1950’s.
The theory of B.F. Skinner is based upon the idea that
learning is a function of change in overt behavior.
Changes in behavior are the result of an individual's
response to events (stimuli) that occur in the
A response produces a consequence such as
defining a word, hitting a ball, or solving a math
When a particular Stimulus-Response pattern is
reinforced, the individual is conditioned to respond.
Skinner explains drive, or motivation, in terms of
deprivation and reinforcement schedules.
Behavior that is positively reinforced will
reoccur; intermittent reinforcement is
particularly effective
 Information should be presented in small
amounts so that responses can be
reinforced ("shaping")
 Reinforcements will generalize across
similar stimuli ("stimulus generalization")
producing secondary conditioning
Reinforcement is the key element in Operant
 A reinforcer is anything that strengthens the desired
 A positive reinforcer is any stimulus that results in the
increased frequency of a response when it is added
› Examples: verbal praise, a good grade, or a feeling of
increased accomplishment.
 A negative reinforcer is the removal of an adverse stimulus
that results in the increased frequency of a response.
Negative reinforcement strengthens behavior because it
stops or removes an unpleasant experience.
› Example: If you don’t complete your homework you
pay your teacher $5
Operant Conditioning has been used to
account for verbal learning and language,
although this effort was strongly rejected by
linguists and psycholinguists.
 Operant conditioning has been widely
applied in clinical settings (behavior
 Operant Conditioning has been applied in
teaching (classroom management) and
instruction (programmed instruction)
Here are some examples of Operant
Conditioning applied to instruction:
1. Practice should take the form of question
(stimulus) - answer (response) frames which
expose the student to the subject in gradual
2. Require that the learner make a response for
every frame and receive immediate feedback
3. Try to arrange the difficulty of the questions so
the response is always correct and hence a
positive reinforcement
4. Ensure that good performance in the lesson is
paired with secondary reinforcers such as verbal
praise, prizes and good grades.
Guthrie's contiguity theory specifies that "a
combination of stimuli which has
accompanied a movement will on its
recurrence tend to be followed by that
 According to Guthrie, all learning was a
consequence of association between a
particular stimulus and response.
Furthermore, Guthrie argued that stimuli
and responses affect specific sensory-motor
patterns; what is learned are movements,
not behaviors.
In contiguity theory, rewards or punishment
play no significant role in learning since they
occur after the association between stimulus
and response has been made.
Contiguity theory suggests that forgetting is
due to interference rather than the passage of
time; stimuli become associated with new
Previous conditioning can also be changed by
being associated with inhibiting responses such
as fear or fatigue.
The role of motivation is to create a state of
arousal and activity which produces responses
that can be conditioned.
In order for conditioning to occur, the
organism must actively respond (i.e., do
 Since learning involves the conditioning of
specific movements, instruction must
present very specific tasks.
 Exposure to many variations in stimulus
patterns is desirable in order to produce a
generalized response.
 The last response in a learning situation
should be correct since it is the one that will
be associated.
The classic experiment for Contiguity Theory is
cats learning to escape from a puzzle box.
Guthrie used a glass paneled box that allowed
him to photograph the movements of cats.
These photographs showed that cats learned
to repeat the same sequence of movements
associated with the preceding escape from
the box.
Improvement comes about because irrelevant
movements are unlearned or not included in
successive associations.
Contiguity theory is intended to be a
general theory of learning, although
most of the research supporting the
theory was done with animals.
 Guthrie applied his framework to
personality disorders.
 Highly applicable (therapy)
 Emphasizes objective measurement
 Many experiments support the theories
 Identify comparisons between animals
and humans
Ignores mediational processes
Ignores biology
Too deterministic (no free will)
Experiments have low ecological validity
Humanism- can’t compare humans to
Reductionist (describe human behavior in
terms of simple components)
Constructivism is a philosophical position that views
knowledge as the outcome of experience mediated
by one's own prior knowledge and the experience of
Constructivism holds that the only reality we can
know is that which is represented by human thought.
Each new conception of the world is mediated by
prior-constructed realities that we take for granted.
Human cognitive development is a continually
adaptive process of assimilation, accommodation,
and correction.
Social constructivists suggest that it is through the
social process that reality takes on meaning and that
our lives are formed and reformed through the
dialectical process of socialization.
There is no “blank-slate” on which new knowledge is
etched, learners come to learning situations with
knowledge gained from previous experience, and
that prior knowledge influences what new or
modified knowledge they will construct from new
learning experiences.
Learning is active rather than passive. If what
learners encounter is inconsistent with their current
understanding, their understanding can change to
accommodate new experience.
Learners remain active by:
Applying current understandings
Noting relevant elements in new learning experiences
Judging the consistency of prior and emerging knowledge
Modifying knowledge
1. Instruction must be concerned with the
experiences and contexts that make the
student willing and able to learn
2. Instruction must be structured so that it can
be easily grasped by the student (spiral
3. Instruction should be designed to facilitate
extrapolation and or fill in the gaps (going
beyond the information given).
Constructivist theory is very broad
 J. Bruner’s constructivist theory is a
general framework for instruction based
upon the study of cognition.
 Piaget (cognitive construction)
 Vygotsky (social construction)
A major theme in the theoretical framework of
Bruner is that learning is an active process in
which learners construct new ideas or
concepts based upon their current/past
The learner selects and transforms information,
constructs hypotheses, and makes decisions,
relying on a cognitive structure to do so.
Cognitive structure (i.e., schema, mental
models) provides meaning and organization to
experiences and allows the individual to "go
beyond the information given".
Bruner (1966) states that a theory of instruction
should address four major aspects:
› (1) predisposition towards learning
› (2) the ways in which a body of knowledge can be
structured so that it can be most readily grasped by
the learner
› (3) the most effective sequences in which to present
› (4) the nature and pacing of rewards and
Good methods for structuring knowledge
should result in simplifying, generating new
propositions, and increasing the manipulation
of information.
Much of Bruner’s constructivist theory is linked to child
development research (especially with Piaget).
 Bruner illustrated his theory in the context of mathematics
and social science programs for young children in 1973.
› "The concept of prime numbers appears to be more readily
grasped when the child, through construction, discovers that
certain handfuls of beans cannot be laid out in completed rows
and columns. Such quantities have either to be laid out in a
single file or in an incomplete row-column design in which there
is always one extra or one too few to fill the pattern. These
patterns, the child learns, happen to be called prime. It is easy
for the child to go from this step to the recognition that a multiple
table , so called, is a record sheet of quantities in completed
multiple rows and columns. Here is factoring, multiplication and
primes in a construction that can be visualized.” –Bruner 1973
Bruner focuses on language learning in young children.
According to Piaget, our thinking
processes change drastically from birth
to adulthood.
 Piaget focuses on how one comes to
make sense of the world.
 Four factors that contribute to this
change are biological maturation,
activity, social experiences, and
Biological maturation- genetically
programmed changes, parents and
teachers have little influence on this
 Activity- explore, test, and observe aspects
of the environment and own abilities
 Social Experiences- learning from the
interaction with others
 Equilibration- searching for a balance;
organizing, assimilating, and
Piaget believed people organize their
thinking processes into psychological
structures. He called these schemes.
 These are the basic building blocks of
Organization and adaptation are the
two tendencies inherited by all species.
 Organization is the act of combining and
arranging information into consistent
systems. This is an ongoing process.
 Adaptation is the act of adjusting to the
 Assimilation-
the act of trying to
understand something new by
using existing schemes
 Accommodation- the act of
changing existing schemes to
meet a new situation
Piaget believed all people passed
through these four stages in this order:
Sensorimotor, Preoperational, Concrete
Operational, and Formal Operational.
 Although age spans are given for each
group, Piaget also recognized individual
differences in development rate.
Sensorimotor: age 0-2 years, moves from reflex
action to goal-directed activity, begins to make
use of memory and thought, intelligence takes
form of motor actions
 Preoperational: age 2-7 years, able to think
operations thorough logically in one direction,
intelligence is intuitive in nature
 Concrete Operational: age 7-11 years, understand
reversibility, solve concrete problems, intelligence is
logical but depends on concrete referents
 Formal Operational: age 11 years and up, solve
abstract problems Piaget says adults may only
reach this stage in a few areas, intelligence
reaches abstraction
Inconsistencies between the stages- ex.
Students can conserve number far
before they can conserve mass
 Underestimating children’s abilitiesproblems and skills are too simple for the
level they are meant for
 Culture effects learning greatly and is
overlooked in this model
Piaget has influenced many others
including Seymour Papert.
 Piaget’s experiments were focused on
the development of mathematical and
logical concepts.
 Piaget’s findings have been used to help
improve teaching strategies especially in
elementary schools.
As children pass through the different
stages of development, they perceive the
world differently and will therefore give
different accounts of reality.
 Cognitive development is enhanced by
engaging in situations that require the
learner to adapt.
 Learning activities should be appropriate
for the developmental stage the child is in.
 Children must be presented with challenges
in order to further their development.
Teachers must be aware of the way in
which students develop.
 Teachers must understand that every
student is different and develops at a
different rate.
 Teachers must present challenges to the
students to help them further their
 Teachers should understand that adults
likely only reach the fourth level in a few
One of Vygotsky’s key ideas was that our
mental processes can be traced back to
our interaction with others. These
interactions with others are so important
that they actually create our cognitive
 Vygotsky wrote about three themes that
explain how social processes help form
Social sources of individual thinking is the
first of Vygotsky’s themes.
 Vygotsky believed that every function in
a child’s life appears twice. It first
appears with an interaction with another
person. It later appears when the child
internalizes it and uses it alone.
 Example: Language
Language adapts to meet the needs of the
people speaking the language. For
example, if a word is needed to describe a
new state of an object, a word will be
made for that.
 Vygotsky put a lot of emphasis on language
as he believes thinking depends on speech.
Specifically, he highlighted the purpose of
private speech.
 Ex. Parents first help regulate a child’s
behavior, later the child uses private
speech to do this him/herself
Vygotsky’s second theme is cultural tools,
especially the use of language.
 Cultural tools are passed from adults or
more capable peers to children. This
includes ideas such as number systems.
 Cultural tools have limitations and
therefore directly affect the limitations of
one’s learning processes.
 Ex. Roman Numerals
The Zone of Proximal Development is the
third of Vygotsky’s themes.
 The Zone of Proximal Development is the
area between the child’s current
development level and the level the
child could achieve.
 The main idea is that children must
challenged but not pushed over the
Vygotsky saw learning as an active
process that does not have to wait for
 He believes that learning pulls
development up to higher levels.
 This means that others have a crucial
role in a child’s cognitive development.
Vygotsky may have tried to suggest too
many ideas as far as where knowledge
comes from. Children may be born with
more knowledge than was given credit.
 Vygotsky died before he had the
change to make his general ideas
specific or before he could apply them
to teaching methods specifically.
Cognitive development is limited at
every age. In other words, there is
always a range in which a child could
excel at a given time.
 Social interaction is necessary to full
cognitive development.
Teachers must take into account
students’ cultural differences and what
they could mean with respect to the
children’s learning abilities.
 Teachers must challenge students to
help them grow without pushing them
into a zone that is too complex for their
abilities. This will cause frustration and a
sense of failure.
"Learning would be exceedingly laborious,
not to mention hazardous, if people had to
rely solely on the effects of their own
actions to inform them what to do.
Fortunately, most human behavior is
learned observationally through modeling:
from observing others one forms an idea of
how new behaviors are performed, and on
later occasions this coded information
serves as a guide for action.“ – Bandura
A cognitive behavioral approach to
personality that emphasizes the role of
social learning, cognitive processes, and
Social learning: observing other individuals’
actions changes future actions
Cognitive processes: the processes related
to intelligent thinking
Self-regulation: regulation of one’s social
behavior in accordance with situational
Related to the work of Vgotsky
› “A cognitive structure that represents
knowledge about a concept or type of
stimulus, including its attributes and the
relations among those attributes”
(Fiske & Taylor, 1986, p.98)
› Types of schema
 Person, role, event, self
Learning – the encoding of schemas
through observation
Understanding – expecting that the use of a
schema well have a desired effect
Knowledge – the social appropriateness of
a schema
Knowing – appropriate use of schema in a
given situation
Transfer – using a particular schema in
another situation
Memory – encoded schemas
Implications for teaching
– Motivation and expectancy play an
important part in social cognition
– Behavior is a direct result of the application
of schemas
– Social modeling creates the opportunity for
students to learn appropriate behaviors (“Do
as I do.”)
– “People will behave similarly in situations that
[sic] have important characteristics in
1. Constructivist learning environments provide multiple
representations of reality.
2. Multiple representations avoid oversimplification and represent
the complexity of the real world.
3. Constructivist learning environments emphasize knowledge
construction instead of knowledge reproduction.
4. Constructivist learning environments emphasize authentic tasks in
a meaningful context rather than abstract instruction out of
5. Constructivist learning environments provide learning
environments such as real-world settings or case-based learning
instead of predetermined sequences of instruction.
6. Constructivist learning environments encourage thoughtful
reflection on experience.
7. Constructivist learning environments“ enable context- and
content- dependent knowledge construction."
8. Constructivist learning environments support "collaborative
construction of knowledge through social negotiation, not
competition among learners for recognition."
Learning is building new ideas from old ideas
based on new knowledge or experience, or
learning is making connections between new
and old ideas.
 Teaching is creating a learning environment in
which you can flexibly facilitate learning.
 Assessment is the testing and/or verifying that
correct learning has occurred.
 Transfer is the ability to use previously learned
skills in a new context.
› Near transfer is the automatic application of
previously learned skills.
› Far transfer is the deliberate application of
knowledge from one context to a different context.
Teaching cannot be viewed as the transmission
of knowledge from enlightened to
unenlightened. Teachers act as guides who
provide students with opportunities to test the
adequacy of their current understandings.
If learning is based on prior knowledge, then
teachers must note that knowledge and
provide learning environments that exploit
inconsistencies between learners’ current
understandings and the new experiences
before them.
› This can be a challenge, teachers cannot assume
that all children understand something in the same
way and children may need different experiences to
advance to different levels of understanding.
If students must apply their current understandings in
new situations in order to build new knowledge, then
teachers must engage students in learning. Teachers
can ensure that learning experiences incorporate
problems that are important to students.
Encouraging group interaction helps students
become explicit about their own understanding by
comparing it to that of their peers.
If new knowledge is actively built, then time is
needed to build it. Ample time facilitates student
reflection about new experiences, how those
experiences line up against current understandings,
and how a different understanding might provide
students with an improved view of the world.
Situated Cognition is a recent term for a family of
research efforts that explain cognition, including
problem solving, sense making, understanding,
transfer of learning, creativity, etc., in terms of the
relationship between learners (agents) and the
properties of specific environments (affordances).
The emphasis of research on situated cognition is to
study realistic complex "situated" learning, problem
solving and thinking. A contrast can be made with
schema theories in which knowledge is considered to
be solely contained within the learner (represented in
memory as schemata or mental models), and with
behaviorist theories in which cognition plays a less
central role. – Michael Young
Child street vendors in both Lebanon
and Brazil have learned to solve
arithmetic and ratio problems with large
numbers without any formal education in
mathematics. However, these same
children struggle when given
computational problems instead of word
or logic problems.
Learning – “a process of enculturating that is supported in
part through social interaction and the circulation of
Understanding – meaningful participation in a given
Knowledge – a product of activities and situations that
index the world (not wholly contained by learner)
Knowing – performing actions that are relevant to the
Memory – a system of relevancy for pieces of information
Transfer – recognition of invariants between certain
situations (learning in unrelated situations does not
Implications for teaching
– Teaching strategy
• Explore implicit knowledge
• Discover explicit knowledge
• Generalize
– Focus on inventive problem solving that leads to
standard algorithms
– Group learning
Collective Problem Solving
Displaying Multiple Roles
Removing Ineffective Strategies
Teaching Collaborative Working Skills
Collective Problem Solving – Group work
introduces insights and solutions that would
not be realized working individually.
• Displaying Multiple Roles – Group work
forces students to reflect on nature of each
cognitive task when divided among group.
• Removing Ineffective Strategies – Students
will be able to confront and correct each
others misconceptions.
• Collaborative Working Skills – Teaches
students collaborative skills needed in the
We personally liked the Constructivist
 This perspective focuses on building from
prior knowledge which we feel is an
important part of a mathematics lesson.
 Constructivism ties nicely with the ideas
in Fish is Fish by Lionni.
Fish is Fish is a story about learning, that involves
a frog and a fish (Lionni, 1970).
“Fish is Fish is relevant not only for young
children, but for learners of all ages. For
example, college students often have
developed beliefs about physical and
biological phenomena that fit their experiences,
but do not fit scientific accounts of there
phenomena.” (Bransford et al., 1999)
“This tale illustrates both creative opportunities
and dangers inherent in the fact people
construct new knowledge based on their
current knowledge.” Brandsford et al. (1999)
The fish learned only from what the frog described based on
his prior knowledge
› It’s important to pay attention to students’ prior
knowledge, that way you can predict where students’
misconceptions might be and correct them before they
become an issue.
Students build on misconceptions if they aren’t corrected
(frog = fish)
› Since the fish was never corrected on his idea that
everything looked like a fish, by the end of the book he still
had these misconceptions. The frog should have started
his teaching by explaining that frogs and fish are not the
same things, and there are a lot of things out in the world
that are different from fish. Only after this concept is
grasped should the frog introduce new ideas.
Two students began at the same level and grew
differently because of different opportunities
› No two students are the same, especially in
kindergarten the new students coming in are at
all various levels (some having no education
about reading and the alphabet, some being
able to read short story-books). It’s important to
try to give all students opportunities to learn to
try to level the playing field.
When the fish jumps out of the water, the frog pushes him
back in
› It is important to encourage students to “think outside the
box” and push their learning, but once a student goes
overboard (whether that means getting frustrated and not
wanting to learn anymore or getting upset about the
amount of work something takes) a teacher needs to be
able to push a student back into his or her comfort zone so
that they can continue their learning process.
› Teachers need to know the limits of their students
Teachers must pay attention to prior knowledge and possible
› The frog in the story never once thought about the
student’s knowledge, he based all of his teaching off of his
own knowledge. This caused a lot of misconceptions
In the book the frog never assessed the fish’s learning
› This made it so that the teacher was never aware of
the misconceptions that existed, and therefore the
misconceptions were never fixed
 The fish jumps out of the water his learning is “selfassessed” by the world because he realizes he can’t
live in the world which means that a fish is not equal to
a frog
› Students can self-assess, and often self-assessment
makes students more aware of their learning and
can correct misconceptions. It is important to be
around when a student is self-assessing to be able to
correct misconceptions and be able to help a
student if he or she is pushed out of their comfort
The fish found out what he knows and doesn’t know by
› Self-assessment cannot be the only form of
assessment because it doesn’t allow for students to
build on their knowledge
 Assessment helps students know what they know and
don’t know
 Assessment helps students by correcting
misconceptions and it helps teachers to realize what
kind of misconceptions they are creating or what types
of things have been overlooked in a lesson
 It is important to observe student work to analyze what
the student knows or doesn’t know
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Behaviorist Theory