Technology-Based Representations of Some Mathematical Ideas

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Technology-BasedRepresentations of Some
Mathematical Ideas

• Mara Alagic
• Wichita State University
• Wichita, Kansas, USA

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Teaching and Learning Mathematics

• Standards-based teaching (NCTM, 2000)
• Current findings about the nature of human
  learning (NRC, 2000)
• Development of the IC technologies
• Technology Principle (NCTM, 2000)

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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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Representations

• Representing knowledge (Langer, 1989)
• Problem-based representations
• Representation standard (NCTM, 2000)
• Things before words, concrete before abstract.
  (Pestalozzi,1803)

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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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"... 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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Questions Tasks (Jaelyn Barbie)

• 1. DEFINE TESSELLATION(S).
• 2. ARE THERE DIFFERENT TYPES OF TESSELLATIONS?
  EXPLAIN YOUR ANSWER.

• http//www.mathacademy.com/pr/minitext/escher/inde
  x.asp
• http//www.coolmath.com/tesspag1.htm

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Have Fun Creating Tessellations (Jaelyn
Barbie)

• Escher Web Sketch Link
• http//www-sphys.unil.ch/escher/

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Cultural Influences (Jaelyn Barbie)

• IN THE WEB SITES PROVIDED FIND 3 EXAMPLES OF
  TESSELLATIONS USED IN OTHER CULTURES.

  

• Cultural references
• http//mathforum.org/sum95/suzanne/historytess.htm
  l
•  Cultural tilling examples
• http//www2.spsu.edu/math/tile/grammar/index.htm

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Graphs and SlopeRobin Racette

• y -4x

• b 0 m -4
• -4/1 down 4, right 1
• 4/-1 up 4, left 1
• y -1/4x
• b 0 m -1/4
• -1/4 down 1, right 4
• 1/-4 up 1, left 4

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More Slope Robin Racette
Graphing y mx b on the web

• Try these on your own.
• y 1/4x - 4

• b -4, m 1/4
• y -3x
• b 0, m 3

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Adam the early bird
Millionaire Meredith, LuAnne Dan

• Starts at age 22
• Invests 3000 for 6 years
• At 11 interest

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Brenda the procrastinator
Millionaire Meredith, LuAnne Dan

• Starts investing at age 28
• Invests 3000 every year thereafter
• Until age 63
• At 11 interest

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Who retires with the most? Meredith, LuAnne Dan
Adam?
Brenda?
And how much difference between the final
results? Plan A and B.xls
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Meredith, LuAnne, Dan
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Invests 18,000Retires at age 63 with 1,128,249
Invests 108,000 Retires at age 63 with
1,265,947
Meredith, LuAnne, Dan
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Graph of Sin ? and Csc ?Sarah

• Things to Consider
• Period?
• Amplitude?
• Asymptotes?
• Differences?
• Between function and its inverse
• Green Globs

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Sarah
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Cos and Sin Wave
Sarah
Geometer Sketchpad
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Tangent on a Circle
Sarah
Geometer Sketchpad
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What if I still need help?
Sarah

• Ask for help
• Websites
• http//www.drmath.com/
• http//www.gomath.com/
• Play Green Globs
• AND..

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Practice
Practice
PRACTICE PRACTICE PRACTICE
Practice
Practice
TO BECOME AN EXPERT OF TRIG FUNCTIONS
Practice
PRACTICE
Practice
Practice
Sarah