Geometer's Sketchpad Full Version
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Make sure to have a working copy of Geometer's Sketchpad. The software can be purchased from Key Curriculum Press. You can download a free demonstration version of Geometer's Sketchpad from the Key Press site. The demo version differs from the full version only in that you cannot save, print, or export your work. It otherwise allows full use of Sketchpad capabilities, including its script tools in particular. Download the desired tools into the proper directory. It is recommended that you create three separate directories where you can store the script tools corresponding to the three different models. For reference, we shall call these directories \"poincare,\" \"poinhalf,\" and \"klein.\" Poincaré Disk Tools: As noted in the Background page, Alexander and Finzer have written the scripts for the ten standard constructions in the Poincaré disk model. Their tools are available here, and can be downloaded into the \"poincare\" directory. This author's tool (pd_to_kd.gss) for mapping points in the Poincaré disk isomorphically to their corresponding points in the Klein disk can be found in the zipped file pd_to_kd.zip. Poincaré Half-Plane Tools: Bennett and Peil have developed some of the hyperbolic tools for the half-plane model, and those tools may be downloaded into the \"poinhalf\" directory. This author has developed the remaining construction tools for the half-plane, and these scripts may be downloaded as the package poinhalf.zip. See the What's in the Toolbox section for more information on what is included in the package. Beltrami-Klein Disk Tools: Also available in a package are the construction tools for the Beltrami-Klein model. The package klein.zip can be downloaded into the \"klein\" directory. See the What's in the Toolbox section for more information on what is included in the package. Unzip any zipped files into the appropriate directory. If you downloaded \"klein.zip\" or \"poinhalf.zip,\" unzip the files in the directory in which you will be storing the tools. There are several shareware and commercial vendors of unzipping utilities (see WinZip or Pkware, for example), and extensive documentation is available. Open the appropriate Sketchpad template file. These templates contain the basic geometric structures associated to each model. For example, the Klein model template \"klnstrt.gsp\" contains a template for the Klein disk. It consists simply of a circle defined by a center point (labeled \"K-Disk center\") and a point on the circle (labeled \"K-Disk radius\"). The labelling is important if you wish to use the scripts in an automated setting (see #5 below). The hyperbolic tools assume those labels as givens for the constructions. If the center and \"radius point\" are labeled differently, then the scripts will need to be played manually (see #5 below). The template for the Poincaré disk (a circle with center \"P-Disk center\" and point \"P-Disk radius\") is found in the file \"poinstrt.gsp\". The template for the Poincaré half-plane model (consisting of a horizontal line through two points labeled \"A\" and \"B\") can be found in the file \"poinhalf.gsp.\" Select and run the scripts of choice to perform the desired non-Euclidean constructions. There are two different ways to run a Sketchpad script: manually by \"playing\" an open script, and automatically by using a script tools directory. We will consider each of these in turn, and include a detailed example for less experienced users of Geometer's Sketchpad. In either case, however, Sketchpad has extensive documentation on using scripts. (Note: The examples and instructions described below were documented using version 3.10 of Geometer's Sketchpad on a Windows 98-based computer. On other platforms or different versions of the software, the general steps should still be the same, but the specific keystrokes may be slightly different.) Running a script manually: Every Geometer's Sketchpad script accepts certain geometric objects as inputs (\"Givens\") and returns a requested geometric object as an output. Running a script manually amounts to opening the appropriate script, informing Sketchpad of the \"givens\" for the script, then \"playing\" the script. For example, suppose one wants to draw a non-Euclidean circle having center O and radius OP in the Klein model. First open the appropriate template file (klnstrt.gsp in this case) as detailed in #4 above. Plot (and label) two points O and P, which will be the respective center and point on the circle. The script that performs the circle construction is titled klncntrpt.gss, and this file needs to be opened as well. This is done by selecting \"Open\" from the \"File\" menu option, then selecting \"klncntrpt.gss\" from the appropriately named directory, \"klein\" in this case (see #2 above). When these steps are completed, the Sketchpad desktop should look something like this: (The above figure comes from a Windows 98 version of Geometer's Sketchpad; the desktop may appear slightly different on different platforms.) In this picture, the script file appears on the upper right-hand of the desktop. Click on the image for an enlarged view. A closeup of an open script file. To construct the desired non-Euclidean circle, the script requires four pieces of information: the two points which define the circle and the two points that define the Klein disk. As a result, the script kcntrpt.gss for a Klein circle accepts as \"Givens\" four different objects: the point defining the center of the Klein disk (called \"K-Disk center\"), and a point on the boundary of the disk (abusively called \"K-Disk radius\"), together with the center O of the circle and a point P on the circle. To construct the circle, highlight the givens in the appropriate order by holding down the \"Shift\" key while selecting the givens in your sketch in the correct order: click on the point \"K-Disk center,\" then click on the point \"K-Disk radius,\" then click on your center point O, and finally click on the point P which will lie on the desired circle. (Remember to hold down the \"Shift\" key while making these selections.) At this point, all of your givens should be highlighted. If the script becomes hidden on your desktop because of these actions, you can bring it on top again by selecting it under the \"Work\" menu option. Now play the script by clicking on the \"Play\" button on the tool: Sketchpad should construct the desired circle, and you should be able to watch the program performing the steps in the construction. Click on the \"Fast\" button to have the construction finished more rapidly. The figure that should result is given in the picture below (click on the figure to see an enlarged view):
Geometer's SketchPad is an interactive geometry software program. It can be used to explore areas of mathematics that include but not limited to Euclidean geometry, algebra, and calculus. To complete the following course you will need full access to the software. If your school district does not already own a license to the program, pricing information can be found at: Pricing. If you are unsure about buying the software, please download a free trial from Trial.
D. Mann, C. Shakeshaft, J. Becker and R. Kottkamp, \"West Virginia Story: Achievement gain from statewide comprehensive instructional Technology Program,\" 1999. [Online]. Available: http;//www.milkenexchange.org/project/wv/wv_fullreport.pdf. [Accessed 21 May 2000].
European Journal of Education and Pedagogy (EJ-EDU) is a peer-reviewed international journal publishes bimonthly full-length state-of-the-art research papers, reviews, case studies related to all areas of Education and Pedagogy.
Our current state of play is that in addition to frequent use of IT for short demonstrations in maths classes we have been trialling the delivery of sections of the pure syllabus to the lower sixth, totally through a computer-based, interactive, open-learning approach. Students are given a brief introduction to the use of the materials and then work through a combination of software activitiesand written worksheets in their own time. Students may use any of the computers around the site to access the maths activity through the college intranet, however they are mainly to be found in the IT centre working on it. In addition to the college IT centre we have a PC in each maths classroom each with a video splitter that allows two monitors each to display the same screen image, enablingall of a class of 20+ to see a demonstration. The full benefit of Geometer's Sketchpad is probably only seen when used in a workshop environment, with each student at a machine and a class exchange of ideas with teacher guidance. There is a useful video provided with the single licence which shows this use of the tool in schools in San Jose, California.
Although the name suggests that the tool is primarily for geometry, the latest release allows the definition of co-ordinates of points via mathematical functions and this, coupled with the locus facility, provides a means to extend its use into Cartesian geometry and into other aspects of the pure syllabus. The demo seems to have most of the function of the full licence except that itregularly reminds the user that it is only a demo and, although files can be edited and new files created, it will not allow anything to be saved. It also appears that some of the help is not there. This is not a great limitation, however, and it is quite useful just to have the demo and to download files produced in other institutions from the net to run on it. We have contacted the distributorsin this country, Capedia[1], and they are quite happy for teaching establishments to follow this same route to evaluate the package. They will provide the demo on disk, actually slightly more convenient than trying to download on our intranet, we found, with the added bonus of a hard copy of key pages of the manual and suggestedlesson activities thrown in. 153554b96e
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