Report

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