Bridging Understanding in Math Using GeoGebra: Exploring Quadrilaterals and Measurement Dr. Joseph...

Bridging Understanding in Math Using GeoGebra: Exploring

Quadrilaterals and Measurement

Dr. Joseph M. Furner

Florida Atlantic University

Jupiter, Florida

Dr. Carol A. Marinas

Barry University

Miami, Florida

Ms. Lisa HerronCypress Bay High School

Weston, Florida

National Council of Teachers of MathematicsAlbuquerque, NM – Albuquerque Convention Center

November 4, 2011

Copyright 2011 Carol A. Marinas, Joseph M. Furner, Lisa Herron

Grades 3-5

1. Start with the Concrete using hands-on manipulatives

2. Move to Representational models in diagrams

3. Lastly, connect to the Abstract symbolism where student understand and function at an abstract level completely

Concrete Representational AbstractThe CRA Model


GeoboardThe Concrete

A Geoboard is a board covered in a grid of pegs that is used to construct geometric shapes and explore their relationships.


Virtual Web SitesThe Representational

•National Library of Virtual Manipulatives•National Council of Teachers of Mathematics

•Cut the Knot•Other Resources


http://nlvm.usu.edu/en/nav/topic_t_3.html

http://www.nctm.org/standards/content.aspx?id=25007

http://www.nctm.org/standards/content.aspx?id=25007

http://www.cut-the-knot.org/Curriculum/Geometry/Geoboard.shtml

Technology and Mathematics: Get Connected !

Use of technological tools, students can :•work at higher levels of generalization•model and solve complex problems•focus on decision-making and reasoning

Mathematical power can arise from technology that includes :•increased opportunity for learning•increased opportunities for real-life social contexts •orientation to the future


Using Technology to Teach Mathof NCTM’s Principles for Teaching

* digital tools

* computers

* calculators

* other handheld devices

* dynamic software

* podcasts

Copyright 2011 Carol A. Marinas , Joseph M. Furner, Lisa Herron

* interactive presentation devices

* spreadsheets* Internet-based resources* emerging technology and

novel uses of technology

Technology in school mathematics refers to :


The focus is to :•promote technology as an essential tool for learning mathematics in the 21st century •integrate the principles and process standards with teaching the content standards•provide access to all five mathematics content standards for all students. •support learner-centered strategies that address the diverse needs of all learners of mathematics

Effective teachers maximize the potential of technology to :•develop students’ understanding•stimulate their interest•increase their proficiency in mathematics

Copyright 2011 Carol A. Marinas , Joseph M. Furner, Lisa Herron


GeoGebraThe Abstract

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package.

http://www.geogebra.org/cms/en/info


Having Fun with GeoGebra


Bank of the West

Albuquerque Skyline

Perspective of parallel lines

and right angles

Adobe House

Quadrilateral

Definition of a Quadrilateral: A closed four-sided figure made up of segments.

Link to GeoGebra: Quadrilateral


Square –Parallelogram with equal sides and angles

Link to GeoGebra: Square


Rectangle – Parallelogram with right angles

Link to GeoGebra: Rectangle


Parallelogram – Quadrilateral with opposite sides parallel

Link to GeoGebra: ParallelogramArea of a Parallelogram


Role of Technology in Teaching Math: Things to Think About 1. What role does technology play in providing multiple representations and opportunities for communication to help students develop mathematical understanding? 2. How does technology influence your instructional decisions? And, how do your instructional decisions influence your use of technology? 3. How can technology increase access to significant mathematics to all students? How do you promote social justice for access to and facility with technology in learning mathematics? 4. How are you thinking differently about your use of technology as a result of participating in the Learn-Reflect strand? What are some of the steps you plan to take to promote growth in your own use of technology?



Grade 3

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.Reason with shapes and their attributes.

3.G.1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

3.G.2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Standards for QuadrilateralsCommon Core Math Standards

http://www.corestandards.org/


Grade 4

Geometric measurement: understand concepts of angle and measure angles.Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

4.G.2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Standards for QuadrilateralsCommon Core Math Standards

http://www.corestandards.org/


Grade 5 Graph points on the coordinate plane to solve real-world and mathematical problems.Classify two-dimensional figures into categories based on their properties.

5.G.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).5.G.3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.5.G.4. Classify two-dimensional figures in a hierarchy based on properties.

So why should we use GeoGebra?A Summary

• Free download. Go to geogebra.org• Up and coming dynamic teaching tool in schools.• User-friendly for students and teachers.• Great connection from the hands-on Geoboards to virtual

Geoboards to something even more abstract.• Incorporating technology in the teaching of mathematics.• Provides many resources and teaching tools at its wiki for

educators at: http://wiki.geogebra.org/en• Can even be used for primary-aged students.


Thanks for coming to our Presentation!

PowerPoint and Data Files: http://matharoundus.com/geogebra

Contact Information:Dr. Joseph M. Furner (Florida Atlantic University) [email protected]

Dr. Carol A. Marinas (Barry University) [email protected] Ms. Lisa Herron (Cypress Bay High School) [email protected]


Bridging Understanding in Math Using GeoGebra: Exploring Quadrilaterals and Measurement Dr. Joseph...

Documents

Transcript of Bridging Understanding in Math Using GeoGebra: Exploring Quadrilaterals and Measurement Dr. Joseph...