Compass+Straightedge with GeoGebra
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Compass+Straightedge with GeoGebra

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A presentation on how to make strict compass and straightedge constructions with GeoGebra.

A presentation on how to make strict compass and straightedge constructions with GeoGebra.

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Compass+Straightedge with GeoGebra Compass+Straightedge with GeoGebra Presentation Transcript

  • The 7th International Conference for Informatics and Information Technology - CIIT 2010
    Feb 24-27, 2011, Bitola, FYR Macedonia
    Compass & Straightedge with GeoGebra
    Linda Fahlberg-Stojanovska
    VitomirStojanovski
    University St. Clement of Ohrid - Bitola
  • Effective technology
    The most effective educational technologies are the ones that require little or no behavioral change on the part of the teacher or the learner.
    They should not increase cognitive load, nor should they require extensive training or technical support.
    Dr. Andrew Van Schaack, Vanderbilt U.
  • Goal: Mathematics Education
    One of our main goals in mathematics education is teaching logical thinking skills.
    That is, the ability to look at a problem and see what is given, what is required and the steps neededto get from the given to the required. And how to check the result.
  • Why Compass & Straightedge?
    We have very, very small set of tools.
    The problems state specifically what is given and what is required.
    Every construction is based on previous constructions – previous learning.
    The construction is visible and measurable. We can see it; we can check it physically to see whether it is correct.
  • Why Compass & Straightedge?
    Creativity and Thinking
    Construct a 30° angle. How many ways?
    Draw an equilateral triangle and bisect one of the angles?
    Draw a right-triangle with hypotenuse double the length of a side?

  • Why Compass & Straightedge?
    Teaches logical thinking skills
    Fun and creative
    Usually is required learning
  • What tools in C&S?
    A pencil
    A compass and
    A straightedge.
  • What can we do with these tools?
    With a pencil
    draw points and
    GeoGebra New Point Tool
    mark intersectionpoints.
    GeoGebra Intersection Tool
  • What can we do with these tools?
    With a straightedge
    draw line through 2 points GeoGebra Line Tool
    draw segment between 2 points
    GeoGebra Segment Tool
    draw ray from 1 point through 2nd point
    GeoGebra Ray Tool
  • What can we do with these tools?
    With a compass
    measure a length between 2 points for a radius and then draw a circle with centered at a 3rd point with that radius.
    GeoGebra Compass Tool
  • Our toolbar in GeoGebra for C&S
  • Construction worksheet
    The BasicConstruct.ggb
    Ready-to-use worksheet with the GeoGebra toolbar for C&S
    Available online (post it freely) at:
    http://mathcasts.org/gg/construct/BasicConstruct.html
    Download and open it with GeoGebra
    http://mathcasts.org/gg/construct/BasicConstruct.ggb
  • First construction
    # 1 Copy a line segment
    geogebrawiki.pbworks.com/Segment-Copy
    YouTube Screencast - Show and Tell
    Online interActivity with GeoGebra
    Printable and online materials
    Online DIY worksheet for making construction
    Metadata
  • First construction
    # 1 Copy a line segment
    Given a line segment AB and a line with a point P on it.
    Copy the line segment AB onto the line so that P corresponds to A.
    We can start with blank and have kiddies draw the line segment and line or
    We can put AB and line on BasicConstruct.ggb
  • Second construction
    # 2 Copy a triangle
    Given a triangle ABC and a line with a point P on it.
    Copy the triangle so that P corresponds to A and the base of the triangle is on the line.
    We can start with blank and have kiddies draw the triangle and line or
    We can ΔABC and line on BasicConstruct.ggb
  • Getting Started with C&S
    http://geogebrawiki.pbworks.com/Compass-and-Straightedge
    Printable materials
    Online interActivity with GeoGebra and/or Download
    Links to pages on the 7 basic constructions
    http://geogebramk.pbworks.com/Шестар-и-линијар
    На македонски
  • FOSS (Free and open source software)
    Can be used on school LANs
    Can be used offline
    Many, many applications
    Ready to use applets are available
    Is easy to use, powerful and dynamic
    Teachers and students can work anywhere
    Students can build animations, simulators, …
    Why GeoGebra?
  • References
    http://math247.pbworks.com/(mathcasts, pencasts, GeoGebra,…)
    http://www.mathopenref.com/ (compass and straightedge)
    GeoGebra YouTube Channel
    http://www.youtube.com/user/GeoGebraChannel
    http://geogebrawiki.pbworks.com
    http://mathcasts.org/mtwiki
    Linda Fahlberg-Stojanovska: emath@emathforall.com