How People LearnBy: Ty Houghton

Krystle StehnoJeremy Kurth

And Holly Yousse

Contents

Information Processing Theory Behaviorism Theory

› Classical Conditioning› Connectionism› Operant Conditioning› Contiguity Theory

Constructivist Theory› J. Bruner› Piaget (Cognitive Development- Genetic Epistemology)› Vygotsky (Social Development Theory and Social

Cognition) Situated Learning Fish is Fish Information

Information Processing

What is information processing?

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, 1990).

Computers and The Human Brain Can Be Compared

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).

The Brain is Part of The Nervous System

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, 1997).

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).

Memory

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 long-term memory. Included in my mental notes is also the apparent mechanical way people handle memories.

Apparently, the learning about memory in Educational Psychology, has made the journey into my long term memory.

Working memory has been called short-term 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).”

The Information Processing Model in More Detail

“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).”

The work of Miller as it relates to information processing theory is described by Kearsley (1994-2009).

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 memory.

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).”

Implications For Teaching and Learning

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 memory.

Assessment is involved with basically verifying what content is found in long term memory in the brain.

Behaviorist Theory

Behaviorist Theory 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.

Behaviorist Theory Assumptions 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 behavior

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 association).

All behavior is learnt from the environment. We learn new behavior through classical or operant conditioning.

Principles of Behaviorist Theory

The following are valuable:› Repetition› 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.

Early Behaviorist Theories of Learning

Pavlov (early 1900’s) founded Classical conditioning

Thorndike (early 1900’s) extended the concept further and founded Connectionism

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

Classical Conditioning

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

Pavlov’s Experiment 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’s Experiment

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 response.

The neutral stimulus had become a conditioned stimulus.

Classical Conditioning- John Watson

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

Watson’s Experiment

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.

Watson’s Experiment When Little Albert was 11 months old, the white rat was

presented and seconds later the hammer was struck. 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 evident.

Connectionism

What is Connectionism?

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, 1990).

Connectionism In More Detail

“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).

Implications For Teaching and Learning

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.

Operant Conditioning

Operant Conditioning 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 environment.

A response produces a consequence such as defining a word, hitting a ball, or solving a math problem.

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.

Principles of Operant Conditioning

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

Operant Conditioning- Reinforcement

Reinforcement is the key element in Operant Conditioning.

A reinforcer is anything that strengthens the desired response.

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- Application

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 modification)

Operant Conditioning has been applied in teaching (classroom management) and instruction (programmed 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 steps

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.

Contiguity Theory

Contiguity Theory

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 movement".

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.

Contiguity Theory 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 responses.

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.

Principles of Contiguity Theory

In order for conditioning to occur, the organism must actively respond (i.e., do things).

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.

Contiguity Theory Experiment

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- Application

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.

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Scientific 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

animals Reductionist (describe human behavior in

terms of simple components)

Constructivist Theory

Constructivist Theory

Constructivism is a philosophical position that views knowledge as the outcome of experience mediated by one's own prior knowledge and the experience of others.

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.

Constructivist Theory 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

Principles of Constructivist Theory

1. Instruction must be concerned with the experiences and contexts that make the student willing and able to learn (readiness).

2. Instruction must be structured so that it can be easily grasped by the student (spiral organization).

3. Instruction should be designed to facilitate extrapolation and or fill in the gaps (going beyond the information given).

Constructivist Theory

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)

J. Bruner’s Constructivism

J. Bruner

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 knowledge.

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".

J. Bruner

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 material

› (4) the nature and pacing of rewards and punishments.

Good methods for structuring knowledge should result in simplifying, generating new propositions, and increasing the manipulation of information.

J. Bruner- Applications 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.

Piaget’s Theory of Cognitive Development

Genetic Epistemology

Influences on Development

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 equilibration.

Four Factors

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 accommodating

Schemes

Piaget believed people organize their thinking processes into psychological structures. He called these schemes.

These are the basic building blocks of thinking.

Organization and Adaptation

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 environment.

Adaptation: Assimilation and Accommodation

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

Four Stages of Cognitive Development

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.

Four Stages

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

Limitations of Piaget’s Theory

Inconsistencies between the stages- ex. Students can conserve number far before they can conserve mass

Underestimating children’s abilities- problems and skills are too simple for the level they are meant for

Culture effects learning greatly and is overlooked in this model

Application of Piaget’s Theory

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.

Principles of Genetic Epistemology

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.

Implications for Teachers

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 development.

Teachers should understand that adults likely only reach the fourth level in a few areas.

Vygotsky’s Social Development Theory

Sociocultural Perspective

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 structures.

Vygotsky wrote about three themes that explain how social processes help form learning.

Social Sources of Individual Thinking

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

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

Cultural Tools

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

Zone of Proximal Development

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 edge.

Learning

Vygotsky saw learning as an active process that does not have to wait for readiness.

He believes that learning pulls development up to higher levels.

This means that others have a crucial role in a child’s cognitive development.

Limitations to Vygotsky’s Theory

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.

Principles of Vygotsky’s Theory

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.

Implications for Teachers

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.

Social Cognition

Social Cognition

• "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 (1977)

Social Cognition

• A cognitive behavioral approach to personality that emphasizes the role of social learning, cognitive processes, and self-regulation

• 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 cues.

• Related to the work of Vgotsky

Social Cognition

Schemas› “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

Social Cognition

• 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

Social Cognition

• 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 common.”

Characteristics of a Constructivist Learning Environment

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 context.

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."

Definitions 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.

Constructivist Implications for Teaching

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.

Constructivist Implications for Teaching

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 Learning

Situated Learning

• 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

Situated Learning

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.

Situated Learning

• Learning – “a process of enculturating that is supported in part through social interaction and the circulation of narrative”

• Understanding – meaningful participation in a given community

• Knowledge – a product of activities and situations that index the world (not wholly contained by learner)

• Knowing – performing actions that are relevant to the community

• Memory – a system of relevancy for pieces of information• Transfer – recognition of invariants between certain

situations (learning in unrelated situations does not transfer)

Situated Learning

• 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

Situated Learning – Group Work

• 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 workplace.

Our Perspective

We personally liked the Constructivist perspective.

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

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)

Fish is Fish- Learning

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.

Fish is Fish- Learning

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.

Fish is Fish- Teaching 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 misconceptions› 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

Fish is Fish- Assessment 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 “self-assessed” 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 zone.

Fish is Fish- Assessment The fish found out what he knows and doesn’t know

by self-assessment› 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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Siegler, R.S., ed. (1978) Children’s Thinking: What Develops? Hillsdale, NJ: Erlbaum

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