Cognitive Science

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Cognitive Science

• And its educational application

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Cognitive Science

• the study of intelligence and intelligent
  systems, with particular reference to intelligent
  behaviour as computation" (Simon Kaplan, 1989)
• Simon, H. A. C. A. Kaplan, "Foundations of
  cognitive science", in Posner, M.I. (ed.) 1989,
  Foundations of Cognitive Science, MIT Press,
  Cambridge MA.

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Cognitive Science

• interdisciplinary study of the acquisition and
  use of knowledge.
• It includes as contributing disciplines
  artificial intelligence, psychology, linguistics,
  philosophy, anthropology, neuroscience, and
  education.
• Cognitive science grew out of three developments
  
• the invention of computers and the attempts to
  design programs that could do the kinds of tasks
  that humans do
• the development of information processing
  psychology where the goal was to specify the
  internal processing involved in perception,
  language, memory, and thought
• and the development of the theory of generative
  grammar and related offshoots in linguistics.
• Cognitive science was a synthesis concerned with
  the kinds of knowledge that underlie human
  cognition, the details of human cognitive
  processing, and the computational modeling of
  those processes.

Eysenck, M.W. ed. (1990). The Blackwell
Dictionary of Cognitive Psychology. Cambridge,
Massachusetts Basil Blackwell Ltd.
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Cognitive psychology

• is concerned with information processing, and
  includes a variety of processes such as
  attention, perception, learning, and memory.
• It is also concerned with the structures and
  representations involved in cognition.
• The greatest difference between the approach
  adopted by cognitive psychologists and by the
  Behaviorists is that cognitive psychologists are
  interested in identifying in detail what happens
  between stimulus and response.

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Types of Information Processing

• Sequential Processing
• Parallel Distributed Processing

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Sequential Processing
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What is
Learning?
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What does make sense mean?
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Example of a semantic Network
Furniture
dog
isa
brown
isa
isa
colour
terrier
colour
Table
chair
isa
shape
shape
4 legs
Tom
colour
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Learning conceptual knowledge

• Knowledge stores in the long term memory
• A piece of knowledge is learned if it is linked
  to other pieces, the more it is rehearsed (linked
  to others), the links will be stronger, and thus
  has more chances to be recalled

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Learning Procedural Knowledge

• Initially as declarative knowledge
• After compilation and composition, it becomes a
  piece of procedure knowledge
• Stored in the long term memory with the related
  conceptual knowledge

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Retrieval of Conceptual Knowledge

• Activation of a node or several nodes
• Spread of activation through links among nodes
  until the required piece is activated.
• Nodes connected to the activated node with
  stronger links will have more chances to be
  recalled.
• Forgetting is the effect of interference.

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Retrieval of Procedural Knowledge

• Procedures with condition part match the
  situation will be fired
• Several pieces may have the same condition, those
  with higher strength will have more chances to be
  fired.
• Strength of a procedure depends on ..

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Learning of Procedural Knowledge

• An Example

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Pattern of Maturation A possible route when a
student learns a rule
UNPREDICTABLE
CONSISTENT USE of MAL-RULES (incorrect rules)
CORRECT
Sleeman (1985)
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MODELS AND THEORIES OF PROCEDURAL ERRORS
WHY STUDY ERRORS
Instruction requires diagnosing well
diagnosing well requires to know
What the errors are?
How are errors formulated?
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Types of Procedural Erros

• Slips
• Careless work
• Intend to perform the appropriate action but fail
  to do so
• Systematic Errors
• Due to mistaken or missing knowledge

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Possible Reasons for slips

• Loss of information from working memory
• deployment of attention or cognitive control
• Completion among the activation levels and
  triggering conditional of coexisting demons or
  schemata

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Schema

• a way of capturing the insight that concepts are
  defined by a configuration of features, and each
  of these features involves specifying a value the
  object has on some attribute.
• The schema represents a concept by pairing a
  class of attribute with a particular value, and
  stringing all the attributes together.
• They are a way of encoding regularities in
  categories, whether these regularities are
  propositional or perceptual.
• They are also general, rather than specific, so
  that they can be used in many situations.
• Example
• References Anderson, J.R. (1990). Cognitive
  psychology and its implications. New York, NY
  Freeman.

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Possible Reasons for Systematic Errors

• Incomplete or misguided learning

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Bugs

• Systematic Errors bugs in the correct procedure
• Slight modification or perturbation of a correct
  procedure (VahLehn, 1984)
• Describes which problem the student gets wrong,
  what each wrong answer is, and the steps followed
  by the student in producing it (VahLehn, 1984)

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Borrowing Across Zero Bug
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Procedure used in Subtraction
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Use of Bug Theory

• A computer programme called Debuggy was designed
  to mimic errors made by the students (100
  correct)

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Why errors formulated explained?

• Attempts to explain why errors formed

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1. Repair Theory
Causes
uninteresting to assert merely that an
error can be "explained" by a mal-rule
Questions such as how the bugs are
caused why some bugs are found but
the other possible ones are not
answered.
To develop a theory which can be used
to predict what bugs will exist for
procedural skills they have not yet
analyzed.
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Repairing Theory
Not quit, find ways to repair
Repaired, remembered
Impasse
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Repair Theory (Brown and VahLehn, 1980)

• Get stuck (Impasse) when executing a possibly
  incomplete procedure
• Not quit, but do a small amount of problem
  solving, just enough to get unstuck and complete
  the problem
• The local problem solving strategy (Repair),
  rarely succeed in rectifying the broken procedure
  causes errors

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2. Deletion Theory
(Young O'shea, 1981)
BUGGY produces models that behave
functionally as the students, these models
are not very convicting as psychological
models.
Many of the bugs appear to be very similar
(many are connected with borrowing from
zero).
some of the BUGGY data can be analyzed
more simply in terms of certain competences
being omitted from the ideal model.
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3. Misgeneralization

(Overgeneralization)
overgeneralising from instances,
using an "old" operator instead of a more
recently introduced one,
and regressing under cognitive load. (Davis,
Jockusch, McKnight, 1978)
e.g.
"" instead of "", "" instead of
exponential.
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4. Competition of Rules Payne Squibb

• cooccurrence of a slip and mistake, simultaneous
  representation of alternative rules (correct or
  incorrect) that apply in the same situations
• using some notion of rule strength to resolve
  conflicts
• Errors are represented by faulty rules
• error arises only when weaker, faulty rules are
  preferred to correct, stronger rules

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Origins of Errors Explained?
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where the incorrect versions of rules come
from?
the mistake-generating mechanisms of
misgeneralization and repair have difficulty
predicting the development of novel, incorrect
rules in problem solvers who already know the
correct versions.
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5. Perception of problems and errors(Impasse or
not)

• Correctly perceived and solved
• Correctly perceived but not solved
• Incorrectly perceived and solved
• Incorrectly perceived but not solved.

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Misperceive During Learning and Misperceiving
During Solving(without impasse)

• Misperceived during learning -- mislearned
  mal-rule -- wrong answer
• misperceived during problem solving -- use
  correct or mal-rule -- usually wrong answer.

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Primary Mal-rules Rules that explains mal-rules

• log A treated as log times A
• incorrect use of distributive law in addition to
  treating log A as log times A
• log A X B as log A X log B
• Errors due to confusion caused by the logarithm
  axioms
• log A log B as log A X log B
• log A - log B as log A / log B

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Causes of Confusion

• Incomplete Learning

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Two Examples
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ConclusionOrigins of Errors

• Impasse-Repair
• Misgeneralization
• Misperceiving

Incomplete Learning
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Causes of errors explained?
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Sequential Processing versus Parallel Processing

• Evidence of parallel processing
• human processing posses fast in some cases
• Pattern recognition
• perception

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A Perception Example
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Some More Examples
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Some More Examples
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Why does this happen?
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What Neural Network can do?
Lin. http//home.ipoline.com/timlin/neural/
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What is a Neural Network?
Artificial Neural Network
Biological Neural Network
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A Neural Network
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Pattern Recognition
1. Classification Given a pattern, find its
class 2. Determine a Pattern Given a
classification and part of a pattern, complete
the pattern.
00100 01100 00100 00100 00100 00100 01110
00100 01100 00100 00000 00100 00100 01110
1
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How an ANN Learn from Examples

• Initially as a blank artificial neural network.
• Two basic phases
• Training
• Computation (or Recognition).

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Training

• data is imposed upon a neural network to force
  the network to remember the pattern of training
  data.
• remember the training data pattern by adjusting
  its internal synaptic connections..

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Recognition

• part of the input data is not known.
• The neural network, based on its internal
  synaptic connections, will determine the unknown
  part

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Training Phase

• two data files are used
• Training data file and
• Retraining-data-file.
• starts with feeding the neural network with the
  data from the training-data-file.
• If initial training is not satisfactory, the
  network can be trained interactively over and
  over again by the data in retraining-data-files.

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Recognition phase

• two data files are used
• Recognition data file and
• Output data file.
• The recognition data file contains the data for
  neural network computations.
• The output data file contains the results of
  neural network computations.

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A '5 by 7' Character Recognition Problem
V (C, P).
P is a '5 by 7' character. P has 35 bits. For
example, one of the many images of "1"
is 00100 01100 00100 00100 00100 00100 01
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Group C contains eleven neurons. Ten of them
represent the ten digits 0, 1, 2, ..., 9 and the
eleventh one represents the "other than digits"
class. Only one of them is clamped on and the
other ten are clamped off. In particular, ?class
"0" is 10000 00000 0 ?class "1" is 01000 00000
0 ?... ?class "9" is 00000 00001 0 ?class
"other than digits" is 00000 00000 1.
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Example of training-vectors
Class 0
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A Neural Network Example

• Neural Network
• download Attrasoft Boltzmann Machine for Windows
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• Test how characters (57) can be recognized.

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Running ABM

• Initializing ABM-- click 'Example/5x7 Character
• You can find 3 files opened Example1.trn
  example1.rtn,example1.rec
• Train the neural network -- Click Run/Train or
  the "T" button.
• Click Run/1-neuron-1-class(One) or the "1"
  button.
• open the output data file, by clicking the "O"
  button or "Data/Output File, to check the
  results.
• Check the results, if not satisfactory, then
  retrain, until all vectors are recognized.

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Errors as explained by Neural Network
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Challenging Task

• Think of an example in learning or recognizing
  that can be explained by Parallel Distributed
  Processing