1. 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

2. 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:
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?
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?
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?

3. CRA Concrete – Mathematical (physical) Model
Representational – Visual Model
Abstract – Symbolic Representation

4. Drawing of the situation

5. A goat and a Barn

6. Standards Mapped Graduate Education and Mentoring Program for Middle Grades

7. Funded in 2004
Partnership: FAU and Broward County Public Schools
Goal: eliminate gaps in content and pedagogy between the university-level approach to a teacher’s math and science preparation and the daily requirements of a diverse standards-driven classroom.

8. Method 8 semester long courses Standards based Master’s degree
Incorporating math content, technology, and pedagogy

9. Standards Mapped

10. Standards-based Connections

11. 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

12. 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).
A mathematical idea takes on its initial meaning and further evolves as learners come into closer contact with a variety of related concepts and relations.

13.
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

14. Strand A
Number Sense

15. Continued Fractions
Notation
[2;1,1,2]

16. Where is the gcd in the rectangle?
Euclidean Algorithm
15 = 1 * = 2 * = 1 * = 3 * 1 + 0
Where is the gcd in the rectangle?

17. Theorem
A number is rational if and only if it can be expressed as a finite continued fraction

18. 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, …]

19. Algorithmic Similarity

20. Strand B
Measurement

21. Mirrors and Images

22. Strand C
Geometry

23. A goat and a Barn Extended

24. Strand D
Algebraic Thinking

25. Baravelle Spirals

26. Area & Length

27. Data Analysis and Probability
Strand E
Data Analysis and Probability

28. Buffon’s Needle

29. 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

30. More resources
GeoGebra Wiki
Florida GeoGebra Chapter
Matharoundus.com

31. aescuder@fau.edu Jfurner@fau.edu
Thank you for coming