Virtual Manipulatives

Virtual Manipulatives In the Elementary Math Classroom Cindy Wright Instructional Technology Specialist Columbus Public Schools National Education Computing Conference July 2006

National Council of Teachers of Mathematics
The Technology Principle
Technology is an essential tool for teaching and learning mathematics effectively; it extends the mathematics that can be taught and enhances students' learning
Technologies are essential tools within a balanced mathematics program. Teachers must be prepared to serve as knowledgeable decision makers in determining when and how their students can use these tools most effectively.
http://standards.nctm.org/document/chapter2/techn.htm

NCTM Recommendations
Every school mathematics program should provide students and teachers with access to tools of instructional technology, including appropriate calculators, computers with mathematical software, Internet connectivity, handheld data-collection devices, and sensing probes.
Preservice and in-service teachers of mathematics at all levels should be provided with appropriate professional development in the use of instructional technology, the development of mathematics lessons that take advantage of technology-rich environments, and the integration of technology into day-to-day instruction.
Curricula and courses of study at all levels should incorporate appropriate instructional technology in objectives, lessons, and assessment of learning outcomes.
Programs of preservice teacher preparation and in-service professional development should strive to instill dispositions of openness to experimentation with ever-evolving technological tools and their pervasive impact on mathematics education.
Teachers should make informed decisions about the appropriate implementation of technologies in a coherent instructional program.
http://www.nctm.org/about/position_statements/position_statement_13.htm

Overview: Principles for School Mathematics
The six principles for school mathematics address overarching themes :
Equity- Excellence in mathematics education requires equity—high expectations and strong support for all students.
Curriculum- A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.
Teaching- Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.
Learning- Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.
Assessment- Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.
Technology- Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.
http://standards.nctm.org/document/chapter2/

Let's Compare.... Concrete and Virtual Manipulatives

Concrete Manipulatives

Virtual Manipulatives
"an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge"
http://my.nctm.org/eresources/view_media.asp?article_id=1902
http://www.ct4me.net/math_manipulatives.htm#Definition

Two Types of Virtual Manipulatives according to Judy Spicer
Static
Essentially pictures
Resemble concrete manipulatives, but cannot be manipulated
http://www.visualfractions.com/
Images change on the screen, but the user cannot move or manipulate the image.
Dynamic
Essentially objects
Can be manipulated just like concrete manipulatives
Student can slide, flip, rotate, etc.
Provides opportunity make meaning and see relationships as a result of one’s own actions
http://www.frontiernet.net/~imaging/java-3d-engine.html

Benefits of using Virtual Manipulatives
Math and technology integration are powerful partners in meeting standards
Free access for schools that are online
Available anywhere, anytime, to anyone
Easier to store, and clean up
Older children may view using virtual manipulatives as more sophisticated
Unlimited numbers available, can print out work
Offers options for students with special needs; thus providing for differentiated instruction.
Students like the immediate feedback they receive from the applets, the virtual manipulatives are easier and faster to use than paper-and-pencil, and they provide enjoyment for learning mathematics.

Challenges of using Virtual Manipulatives
Teachers need ongoing professional development
Teachers need up to date tools and time to understand how they fit into the curriculum
Locating and aligning Resources to meet curriculum standards
Finding enough working computers for all students
Following up usage with reflection to enhance the understanding of concepts
Assessing learning using the tools

Using Virtual Manipulatives in the Classroom In this video, a third grade class studies probability. To help enhance students' understanding of probability, the teacher introduces a software program designed to simulate the rolling of dice on a large scale. Students predict the outcome and then examine the results to see how accurate their predictions were. This lesson uses the Silver Burdette Interactive Mathematics software, but many similar programs are available online or with other mathematics curricula. To play the video, click "Watch this clip" under the photograph. http:// nces.ed.gov/nceskids/probability /

How to Find Virtual Manipulatives

Marco Polo http://www.marcopolo-education.org/home.aspx

National Library of Virtual Manipulatives http:// matti.usu.edu/nlvm/nav / Utah State University NSF supported project Began in 1999

eNLVM http://enlvm.usu.edu/ma/nav/doc/intro.jsp
Extending and Enhancing the National Library of Virtual Manipulatives
Tracking Tools Math Modules Collaboration Adaptation Tools

HarcourtSchool & Other Publisher Sites

http:// www.harcourtschool.com/elab/index.html
Extensive collection of interactive applets for grades 3-8. Activities to accompany each one are provided. You can download an E-Lab activity and use it without being connected to the internet.

http://www.glencoe.com/sites/ohio/teacher/mathematics/index.html
Links to activities that are in the Teacher’s Guide

Arcytech
Problem Solving Java Applets –
The objectives of the applets are:
There should be a problem to be solved -- students need to acquire knowledge, through a discovery process, to be able to solve the stated problems
The problems should motivate the students -- Students should feel rewarded by solving the problems
The topic of the applet should be of interest to the students. Something they can relate to and something that can be part of the curriculum
http://www.arcytech.org/arcytech/awards.html#patterns_fbk
http://www.arcytech.org

NCTM Illuminations
Electronic Examples
http://standards.nctm.org/document/eexamples/index.htm
Web Resources
http:// illuminations.nctm.org/swr/list.asp?Ref =2&Std=9

Shodor
http://www.shodor.org/interactivate/activities/index.html
http://www.shodor.org/interactivate/activities/fracfinder1/index.html .

Mathcats
http://www.mathcats.com/contents.html

Math Forum http://www.mathforum.org/mathtools/
http://mathforum.org/mathtools/cell/ALL,ALL,ALL,hh/
Can Browse the Catalog by course and Type of Technology used

http:// www.ies.co.jp /math/products/
The material presented is for middle school students, high school students, college students, and all who are interested in mathematics. You will find interactive programs that you can manipulate and a lot of animation that helps you to grasp the meaning of mathematical ideas.

Ron Eglash's culturally situated design tools
http://www.rpi.edu/~eglash/csdt.html

Closing
As virtual manipulatives are enhanced and become more available, the possibilities for use are limited only by the creativity of the teachers and students who work with them.
~ Patricia S. Moyer

Contact Information
Cindy Wright
Instructional Technology Specialist
Columbus Public Schools
737 E. Hudson St.
Columbus, OH 43211
(614)365.5102
[email_address]

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Virtual Manipulatives

by Cindy Wright on Sep 07, 2008

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Virtual Manipulatives — Presentation Transcript