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: 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?

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 university-level approach to a teacher’s math and science preparation and the daily requirements of a diverse standards-driven 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). 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.

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 Notation [2;1,1,2]

Where is the gcd in the rectangle? Euclidean Algorithm 15 = 1 * 11 + 4 11 = 2 * 4 + 3 4 = 1 * 3 + 1 3 = 3 * 1 + 0 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

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

Strand B Measurement

Mirrors and Images

Strand C Geometry

A goat and a Barn Extended

Strand D Algebraic Thinking

Baravelle Spirals

Area & Length

Data Analysis and Probability 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/

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