What%20Change%20Is%20Technology%20Bringing%20to%20%20Conceptual%20Understandings%20of%20Mathematical%20Ideas?

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What Change IsTechnology Bringing to
Conceptual Understandings of Mathematical Ideas?

• Mara Alagic
• Wichita State University
• Wichita USA

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Paradigm Shift

• Teaching/learning of mathematics is influenced
  by
• standards-based teaching (NCTM, 2000)
• current findings about the nature of human
  learning (NRC, 2000)
• development of the IC technologies, e.g.
  Pythagorean Theorem

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Pythagorean Theorem

• What does it say?
• Pythagorean triples?
• How does that make sense to you?
• Proof anyone?
• Demonstration? (Water-Demo, Behold)

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Learners Meaning Making

• Tool - knowledge construction
• Information vehicles - exploring
• Context - doing, representing and simulating
• Social medium - conversation
• An intellectual partner - reflecting

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Mathematics Teaching and Technology

• Technology Principle
• "Technology is essential in teaching and learning
  mathematics it influences the mathematics that
  is taught and enhances students' learning"
  (NCTM, 2000)
• Technology in context

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Teaching for Conceptual Understanding

• Understanding as flexible performance (Perkins,
  1993)
• Computational versus calculational orientation
  (Thompson, Philipp, Thompson, Boyd, 1994)

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Representations

• Representing knowledge
• Problem-based representations
• Representation standard
• both process and product
• Things before words, concrete before abstract.
  (Pestalozzi,1803)

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(No Transcript)
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Conceptual Understanding via Multiple
Representations

• Perception-based representations
• Multiple representations
• External and internal representations
• Problem-based representations
• Translations among representations

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MENTAL MODELS/ INTERNAL REPRESENTATIONS
EXTERNAL REPRESENTATIONS TRANSLATIONS
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Impact of Technology on Student Learning . . .

• . . .
• depends on how the technology is
• used and therefore implies the need
• for different instructional processes
• and better preparation of teachers(Jonassen,
  Peck, Wilson, 1999)

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Technology-based Environment Cognitive tools

• Dynamic geometry
• Spreadsheets
• Concept maps
• Programming
• Web Quests
• Computer algebra systems

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Question 1

• How are technology-based representations of
  mathematical concepts different from standard
  representations? Explain in details an example
  appropriate for the level you are teaching (or
  will be teaching).

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Question 2

• What do you think is the influence of
  technology-based representations on YOUR
  conceptual understanding of specific mathematical
  ideas and on the development of your pedagogical
  content knowledge?

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Question 3

• What criteria are you as a teacher going to
  use to balance between technology-based and
  "other" representations?

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Question 4

• How can technology help in differentiating
  instruction for individualized learning? Be
  specific.

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IF TIME, ...

"... the defining characteristic of knowledge
workers is that they are themselves changed by
the information they process" Kidd (1994, p. 186)
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IF TIME, ...

• http//education.wichita.edu/alagic/summer2002/752
  r/752r_first_page.htm
• Promoting Appropriate Uses of Technology in
  Mathematics Teacher Preparation
  (http//www.citejournal.org/vol1/iss1/currentissue
  s/mathematics/article1.htm)