Transcript Mathematical writing with geogebra

Mathematical writing with
GeoGebra
Anders Sanne
Morten Misfeldt
A discussion on a mountain in
Iceland…
• How to increase the use of GeoGebra for
producing mathematical text.
– What is the role of GeoGebra in the production of
documents?
• Something that you write about
• A good machine to produce illustrations
– What could it be?
• Interactive illustrations
• Answers to mathematical assignments delivered in
GeoGebra
Why consider text
• GeoGebra is strong on different mathematical
representations
• Text is the archetypical ”discursive” – or linear
– representation.
Semiotic representations: Duval
Concept
T re a tm e n t
R e g iste r A
R e g iste r B
co n v e rsio n
Mathematical activity constist of transformations of semiotic representations
Register: ”space of semiotic representation” (2dplot, algebra, natural language)
Treatment: transformations inside a register
Conversion: transformations that change register but maintain conceptual
reference
Examples
• The unit circle in different registers
x2+y2=1
• Treatment
• 3x+9=0 => x=-3
• Conversion
• 2x+1 =y can be shown as
”the unit circle”
Four main types of registers
Multifunctional
Discursive
Non discursive
Ex: Natural
language
Ex: Geometric
figures
monofunctional Ex: algebra
Ex: Cartesian
graphs
Why text (2)
• GeoGebra is strong in its support for non
discursive registers
• Less strong with Discursive
– Problem with discursive expansion
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Proofs
Explanations
Narrations
All sorts of reasoning activities
Two approaches to text in GeoGebra
• Embed GeoGebra in word processing.
– Google gadget and save as webpage
• Include text processing and formulas in
GeoGebra
– The improved text box
– A ”caption” or text view?
– Dynamic use of txt
A text view could be here
Producing mathematical documents
• Integrated text view could make it possible to
produce simple printable mathematical
documents.
• Using only GeoGebra for math assignments
and test situations
• Avoid cut and paste
• Strong integration with the other views in
GeoGebra
Typical assignments in K-12 ed.
• With a text view GeoGebra could produce
solutions to typical K-12 assignments
– A figure
– Some calculations
– Text describing the problem and solution
Documentation of GeoGebra based
reasoning
• Arguing for reasoning strategies and
procedures
• Describing observations
• A complement to the construction protocol
(there is a caption field in the new
construction protocol)
• Enhancing (mathematical) literacy
Conclusion
• Writing should of course be considered when
using GeoGebra for teaching mathematics
• This can be done by embedding GeoGebra
applets in a text domain
• But creating a simple text view could
supplement this approach