Impact of GeoGebra in Math
Teacher’s Professional
Development
Ana Escuder
Joseph Furner
Florida Atlantic University
Boca Raton, Florida
Twenty-Third Annual
International Conference on
Technology in Collegiate Mathematics
Denver, Colorado
March 19, 2011
Warm-up/Thinker
A square barn measures 14 meters on each side. A
goat is tethered outside by a rope that is attached
to one corner of the barn:
a) Suppose that the length of the rope is 8
meters. On how many square meters of land is
the goat able to graze? What shape is formed?
b) Suppose that the rope is made twice as long as
in part a. On how many square meters of land is
the goat now able to graze?
c) Lastly, an addition to the barn was built making it
rectangular with dimensions 14 meters by 20
meters and extended the length of the rope to
24 meters, on how many square meters of land is
the goat now able to graze?
CRA
• Concrete – Mathematical (physical)
Model
• Representational – Visual Model
• Abstract – Symbolic Representation
Drawing of the situation
A goat and a Barn
Standards Mapped Graduate
Education and Mentoring
Program for Middle Grades
• Funded in 2004
• Partnership: FAU and Broward County
Public Schools
• Goal: eliminate gaps in content and
pedagogy between the universitylevel approach to a teacher’s math
and science preparation and the daily
requirements of a diverse standardsdriven classroom.
Method
•
•
•
•
8 semester long courses
Standards based
Master’s degree
Incorporating math content,
technology, and pedagogy
Standards
Mapped
Standards-based
Connections
Mental Models
• Integration of prior knowledge and
text information to construct an
understanding of the situation
described in the text (Reed, 2007)
• Mental model – dynamic
• Mathematical model – static
Cognitive complexity of
Mathematics
• Connection of mathematical concepts.
• Solidified by their multiple representations and
the connections among the multiple
representations (Goldin, 2003).
• Mathematical representations are ultimately
cultural artifacts, indicative of the
technological developments of society
(Kaput, Hegedus, & Lesh, 2007).
• As technology changes, it also changes what
we do and what we can do as well as the
way we handle traditional instructional
practices (Milrad, Spector, & Davidsen, 2003).
www.GeoGebra.org
• Free, multi-platform, open-source
dynamic mathematics software.
• Combines dynamic geometry,
algebra, calculus, and spreadsheet
features
• Large international user and developer
community with users from 190
countries.
• Markus Hohenwarter and FAU
Strand A
Number Sense
Continued Fractions
13
1
2
1
5
1
1
1
2
Notation
[2;1,1,2]
Euclidean Algorithm
15 = 1 * 11 + 4
11 = 2 * 4 + 3
4=1*3+1
3=3*1+0
15
1
 1
1
11
2
1
1
3

Where is the gcd in
the rectangle?
Theorem
A number is
rational if
and only if it
can be
expressed as
a finite
continued
fraction
1
1
1
1
1
1
3
Lagrange Theorem
An irrational represents the positive
solution of a quadratic equation if and
only if its continued fraction expansion is
eventually periodic.
x = [1; 1, 1, 1, …]
Algorithmic Similarity
2
x=
x + x- 1= 0
2
x + x= 1
x(x + 1) = 1 x =
1
1+ x
1
1
1+
1+ x
1
x=
1
1+
1+
1
1
1+
1+ x
Strand B
Measurement
Mirrors and Images
Strand C
Geometry
A goat and a Barn
Extended
Strand D
Algebraic
Thinking
Baravelle Spirals
Area & Length
1
4
1
16
1
64
1 1
1
1
 

 ...
4 16 64 256
1
4
1
2
1
8
1
16
1 1 1
1
  
 ...
2 4 8 16
Strand E
Data
Analysis
and
Probability
Buffon’s Needle
Impact
•
Raised enthusiasm and changed teachers’ habits
• Provided effective pedagogical model for teachers.
 Modeling the Standards
 Modeling effective pedagogy
 Growth in their ability to use technology with instruction
• Tendency of teachers to incorporate technology in their
classroom jumped from 27.8 percent to 64.3 percent.
• Large data set suggested a connection between the
mathematical skills and activities the project promoted
and student achievement.
• Changes in the district
More resources
• GeoGebra Wiki
http://www.geogebra.org/en/wiki/index
.php/Main_Page
• Florida GeoGebra Chapter
http://floridageogebra.wikispaces.com/
• Matharoundus.com
http://matharoundus.com/
Thank
you for
coming
aescuder@fau.edu
Jfurner@fau.edu