Impact of GeoGebra in Math Teacher’s Professional

Development

Ana Escuder Joseph Furner

Florida Atlantic UniversityBoca Raton, Florida

Twenty-Third AnnualInternational Conference on

Technology in Collegiate MathematicsDenver, ColoradoMarch 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 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).

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

52

1

11

11

2

Notation

[2;1,1,2]

Euclidean Algorithm

15 = 1 * 11 + 411 = 2 * 4 + 3 4 = 1 * 3 + 1 3 = 3 * 1 + 0

15

111

1

2 1

11

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

11

1 1

11

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

x2 +x- 1=0

x2 +x=1

x(x+1)=1 x=

11+x

x=1

1+1

1+x

x=1

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

4

116

1 64

1

...256

1

64

1

16

1

4

1 ...

16

1

8

1

4

1

2

1

2

14

1

8

1

16

1

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 Wikihttp://www.geogebra.org/en/wiki/index.php/Main_Page

• Florida GeoGebra Chapterhttp://floridageogebra.wikispaces.com/

• Matharoundus.comhttp://matharoundus.com/

Thank you for coming

aescuder@fau.eduJfurner@fau.edu