On the Study of Constructible Learning Facets with Technology Approach: Cognitive Constructivism and

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On the Study of Constructible Learning Facets
with Technology ApproachCognitive
Constructivism and the World Wide Web Using
XML Based Equation Technology

• Pao-Ta Yu, Chung-Ming Own
• Department of Computer Science
• and Information Engineering
• National Chung Cheng University
• Taiwan 62107, R.O.C
• emailcsipty_at_cs.ccu.edu.tw

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Internet
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Motivation

• WWW
• Platform independent
• Unified transmission protocol
• Consistent and friendly user interface
• Interaction in time
• More learning resources
• Most of the educational institutions, government
  agencies, commercial companies, and other
  organizations around the world are moving into
  the WWW.

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Education WWW

• For the good of saving cost and easily updating
  materials, learning via Web is seen as an
  effective alternative to traditional face to face
  modes of education.

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Deficiencies in Distance Learning

• If we want to show mathematic notations in a web
  page, we have some ways but not an easy way to
  do.
• Due to the feature of mathematical equation, its
  representation possesses the highly complicated
  two-dimensional symbolic notations. Therefore,
  the general text editor cant edit it easily.

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Learning

• Learning would be exceedingly laborious, not to
  mention risky, if people had to rely solely on
  the effects of their own actions.
• The learning performance says that our knowledge
  is actively constructed by the learner, not
  passively received from the environment.

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• Constructivism

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Constructivism

• Constructivism is building on knowledge known by
  the student. It is a theory, a tool, a
  methodology for examining educational practices.

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Cognitive Constructivism and Social Constructivism

• Social
• Reading/ Writing Workshop
• Whole Language 
• Situated  Learning
• Collaborative  Learning
• Anchored  Instruction
• Games, Simulations, Case-Based
  Instruction,Problem-Solving

• Cognitive
• Anchored  Instruction
• Microworlds
• Information  Banks 
• Symbol  Pads 
• Construction  Kits/Simulations 
• Whole Language

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Piaget's Theory

• Humans cannot be "given" information.
• They must "construct" their own knowledge.
• They build their knowledge through experience.

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• Symbol Pads

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Perkins Theory

• Symbol pads is the basic function in educational
  environments, it provide surfaces for the
  construction and manipulation of symbols and
  language for a long time

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Jonassens Theory

• The main concept of symbol pad can be classified
  into two points
• To provide a symbolic surface to let the learners
  progress their learning sequences.
• To provide a thinking mechanism or memory
  mechanism to let the learners construct their
  deep thinking and knowledge.

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• The platform on WWW

• We use the technology of web page to realize the
  concept of symbol pad for mathematical education.
  

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QMath
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QMath

• QMath is an authoring tool following What You
  See Is What You Get rule, therefore students can
  edit and modify the math expression easily.

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• Concept Map

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Concept Map

• Concept map
• It was proposed by Novak and Gowin in 1984.
• It is a visible graph of an individuals
  knowledge structure on a special subject as
  constructed by the individual.

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Concept Map (Con.)

• Students will set the concepts, which are
  learned, into the structure of the more general
  concepts gradually.
• Teachers can construct a concept map to organize
  course content and teach students the concepts or
  materials through the concept map.

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Our Focus

• We propose the QMath to realize the symbol
  surface. On the other hand, we use concept map
  to realize the thinking mechanism.

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• Concept Map
• Web-based System

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Concept MapWeb-based System

• This system provides some incomplete concept
  maps, which exist some blank for concept.
• Students must fill these blanks according to the
  concept map provided.
• When students finish this test, the system will
  evaluate these answers and grade students.

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Concept Map Web-Based System (Con.)
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• Experiment

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Environment

• The environment is supported in the lecture of
  probability in 2001 spring semester for 49
  students.
• Our system supports concept map about the course
  contents of Bernoulli distribution, Poisson
  distribution and Normal distribution.

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• Case 1
• Compare the performances about the students with
  system support.

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• Two Groups
• Group1 It is an unrestrained group with lower
  performance.
• Group2 The opposite.

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Ration
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Ratio of the students who make progressed with
system support

• The summary test includes the course content
  about Bernoulli distribution, Poisson
  distribution and Normal distribution

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• Case 2
• Compare the performances about the students in
  experiment group and contrast group

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• Two groups
• Experiment group -the former includes 23
  students those who take the lecture with system
  support.
• Contrast group- the latter includes 26 students
  those who take the lecture with traditional
  learning.

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Ratio
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Ratio of the students who make progress in
contrast group and experiment group
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Conclusion

• The Cognitive Constructivism is a brilliant
  solution. Applying the learning environment of
  symbol pads, we can realize the teaching and
  learning concept into the technology domain. In
  essence, the results of experiment shows that
  student can make more progress Cognitive
  Constructivism learning environment on WWW.