An updated online version of the original paper submitted to the International Conference ICME-9 in Tokyo on July 31st to August 6th 2000. The section on dynamic geometry originally formed the basis of a presentation at the conference "Good Practice in the Use of ICT in Schools" at the RSA, London on March 6th 2000.
Abstract
1. A vision for future online materials
2. Current examplars:
A Techologies: Dynamic Geometry,
Dynamic Algebra, Spreadsheets, VRML,
Logo, others;
B Websites
3. Issues affecting the success of Online education
4. Conclusion
(A) Exemplar Technologies |
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These steps are certainly not accessible to the less able or younger student. Unless a lot of curriculum time is devoted to the technological aspects of the software, and to the ideas of points and lines, parallel and perpendicular, little progress can be made in school; extremely frustrating for all involved. Consequently, at best the software becomes used for trivial and isolated tasks that do not warrant the time or expense involved, and at worst is not used at all. A great step-forward is provided with Online dynamic geometry. We consider two current examples. |
2.1.1 Geometer's
sketchpad |
Figure 1: Geometer's Sketchpad
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2.1.2 JavaSketchpad
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Figure 2: JavaSketchpad - drag the red
points
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| In JavaSketchpad, an interactive geometric construct is
embedded in the browser (Netscape in the above case). Points can be dragged
with the mouse and the geometry in the diagram will respond appropriately. The
icons and menu options from Geometer's Sketchpad are not present. In fact the
student cannot introduce any new constructs but can manipulate only what is
already there. For anyone who wishes to develop their own expertise, they can
purchase the software package and create their own dynamic geometry. A suitable activity to replace "Construct a square" would be "Here is a geometric shape. By dragging the points, identify what shape it is and what properties the shape has." 
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| The student does not need to know any technological
skills relating to the software but is free to concentrate on the mathematics,
and through observation of what changes and what stays the same can gain
insight into the "squareness" of squares. Thus the problem becomes
accessible to a wide range of abilities and ages. JavaSketchpad does meet three of our basic criteria for Online resources: technology, design and development. With reference to the fourth, content, Many educational websites are using JavaSketchpad with outstanding results. For examples, see JavaSketchpad's home site, MathsNet and Nrich . |
| 2.1.3 Cinderella The second example of online dynamic geometry is Cinderella . This relatively new software was developed specifically for Internet use. In many ways it is similar to JavaSketchpad and provides the same level of interactivity within a browser. See Figure 3 for an example - drag the points. In this figure, all the labeled points can be dragged so that the user should be able to identify, by its geometric properties, what kind of quadrilateral each one is. |
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Figure 3: Cinderella
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| Where Cinderella shows the way forward in terms of Online interactivity, is in its facility to create a full dynamic mathematical exercise, along with icons to increase available options and interactive hints and comments. Figure 4 shows such an example. There are three parts to the screen. The main part shows the geometric construct, here a line with two points on it. Lower left is a text window describing the task to be tackled. This window will also display hints and feedback as the task progresses. Lower right is a set of icons that enable constructions to be made. Which icons are available is within the control of the person creating the webpage. |
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Figure 4: a Cinderella exercise
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| As the user progresses through the task, so the construct and text windows react accordingly. The task can also be pre-programmed to display a hint in the text window after an amount of time has passed with no progress being made. The flexibility afforded by this interface will allow the educator/programmer to create pages that assume a whole range of levels of expertise on the part of the student. Our original task "Construct a square", rejected before due to the conceptual demands it places on students, can be re-addressed. Now the task can be presented at various levels, anywhere from an initially blank window, through to a square completed apart from one side or one vertex. In this way, students can tackle exercises like construct a rhombus, reflect a triangle, rotate a square, construct the centre of a rotation (see Figure 5), and so on. |
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Figure 5: a Cinderella exercise
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© MathsNet 2000
