When designing software together with other educational materials, one should keep in mind that building software from scratch for every single educational application is not very realistic (especially in the case of three-dimensional (3D) graphics software). It is important (1) to use resources that are already available; (2) to keep in mind other educational applications for the designed software; and (3) make it flexible and customizable.

In the design projects described, I chose to build on previous work from an earlier project (figure 1), where I had already developed a lightweight 3D library to show and manipulate 3D objects and nets as interactive illustrations on the screen.

This pre-existing software enabled me to design the 3D applets discussed in this article in a reasonable time frame. In fact, the software not only formed the initial programming resources, but also the source of inspiration for the educational design described here.

In these projects prototypical lesson material on Measurement and 3D Geometry was developed and tested. Although the students we aimed at were quite different in age and level, a common obstacle for them was their weak ability to make the connection between 3D objects and 2D representations of these objects. We expected that interactive representations of 3D objects on the 2D screen could work as a bridge from the real 3D world to the static and more abstract 2D representations on paper and back.

Programming these virtual 3D objects that could be manipulated with the mouse was just a first step. Designing tasks that use these resources in a productive way was another part of the process and was far from trivial. It would have been possible to present these tasks on paper and use the software as additional tools or interactive illustrations, but we wanted to exploit the medium more extensively, and tried to define tasks within the software to create game-like features. Beside this, we wanted to design more advanced interactions like 3D construction facilities to support richer (and more open-ended) tasks.

The process of the design

In our educational design for the vocational students, we focussed on the subject “Technical Drawing”, which is an application of the mathematical subject Geometry and Measurement. The educational objectives were to develop (1) the ability to interpret the 2 dimensional projections and construct the 3D object; and (2) the ability to draw the 2D projections of given 3D objects. Figure 2 is an example of such a drawing.

Figure 3 represents a (paper and pencil) task for students that is meant to support this learning goal. The student work that was observed in the project showed that gaining insight into the meaning of the different representations was problematic.

To improve this situation we made use of the features of the applet “Drawing Cube” (Applet 1). In this applet a ‘3D’ cube is shown on the screen. The cube can be rotated with the mouse and lines and planes can be constructed by clicking on the vertices. The idea was that quick constructing facilities in a (virtual) 3D environment, combined with the possibility to rotate the object to get the different views, could establish a firmer connection between the different representations. To make a stronger link to the format of the technical drawings, we adapted the software and designed a feature to toggle between the technical drawing and the 3D object. With this prototype we worked with students.

Note: Most of the applets discussed here can be run live by clicking on the picture. You will need Java installed (free download from www.java.com) if you do not already have it.

Note: Most of the applets discussed here can be run live from the online version of this article at: www.educationaldesigner.org/ed/volume1/issue2/article7

We decided to go back to the objects that were used in the paper materials and made virtual 3D versions of those objects that could be manipulated on the screen, with a toggle to the 2D technical drawing. We left out the construction facilities that appeared to be too difficult for the students.

This led to the second prototype: “Profile Viewer” (Applet 2). This applet was used as an interactive illustration within the paper tasks. We observed the students working with this prototype and investigated the problems they met. This gave us ideas for the design of new useful tasks.

The next step was the applet “Guess the View” (Applet 3) in which both representations were shown on one screen instead of separate ones, to make the connection between the representations easier. Moreover, a task in which the student had to determine a sequence of different views was designed within the applet. We implemented this task as a game in which scores can be achieved and feedback is given.

The virtual 3D representation could help to find the requested view by rotating the object with the mouse.

Among the students we noticed many differences in the abilities to play this ‘game’. For a group of weak students who had difficulties with the task, we designed the applet-game “Rotating 3D-Objects” (Applet 3b) that gave extra support and practice in finding the different views by applying the proper rotation in the 3D model.

For this group, this turned out to be a suitable preparation for “Guess the View”.

In a third game “Colouring Sides” (Applet 4) we extended the activity to a more sophisticated level. Students had to connect corresponding parts in the two representations. This applet also provided more of a challenge for the better students in this group.

The three ‘games’: “Rotating 3D-objects”, “Guess the view” and “Colouring Sides” turned out to be a successful addition to the subject ‘Technical drawing” in vocational education, and were also appreciated in primary as well as secondary mathematics education. They became popular applets on the WisWeb website.

In the children’s play and reasoning we observed that the objects on the screen did not always lead to a proper 3D-experience of the object, but that in most cases this could be ‘called up’ by using the ‘drag to rotate’ feature. This observation had important implications for the interface of the 3D construction tool we wanted to design. We had to offer an environment in which a proper 3D experience of the representations on the screen is not a precondition for the constructing activity, but an ability that can grow and develop during the constructing activity.

A first prototype was “Houses with Height Numbers” (Applet 5) in which block buildings could be constructed. Clicking in the top view representation results in adding new blocks in the 3D-model. This worked in a way, but the two separate representations were a bit confusing, although in special tasks this confusion could be used to create powerful learning experiences.

The applet “Building Houses” (Applet 6) was a break-through. We achieved an interface that met the requirements in quite a satisfactory way. Cubes can be added or removed just by clicking in the 3D model on the grid or on the cubes that are already in place. The result is immediately visible and with this feedback, together with the drag-to-rotate feature, the students could really explore 3D space on the screen, and even young children showed they were able to ‘build’ their own 3D experiences using the computer.

The next step was designing tasks for the students. We did not want to prevent students (and teachers) to freely use the tool for their own ideas and constructions, but some clear tasks presented in a game-like way appeared to be very attractive for students. Moreover, as a learning resource on the Web, the tasks presented are a means to communicate the ideas and possibilities to a bigger audience beyond the projected educational context.

The final product for the TAL project is the applet “Building with Blocks” (Applet 7). This applet is in fact a compilation of tasks using the same tool, customized in different ways. Most of these tasks emerged during the design process described above. Some of the activities, for example “Copy the building” can be checked by the computer and can be played as a game. Other activities, like “Extra Problems” are more open. And of course the construction tool (“Building Freely”) is included for constructing your own buildings.

With the software being implemented as a package of customizable components, it was not too difficult to adapt it, and to implement challenging tasks for students in secondary education. The applet “Building Houses with Side Views” (Applet 8) is a nice example of a challenging game on a higher level.

The last design in this software collection is “Building Programs”. It is the same block building tool as in the previous examples, but extended with an entirely different interface for making constructions. The user interaction is a kind of programming that makes use of the 3D coordinate system, as well as other mathematical concepts like intervals and variables.

Programming activities within mathematics education already have a long tradition, mainly associated with “turtle graphics” using a subset of the Logo programming language, but also with other accessible programming languages like Basic. In the applet “Building Programs,” a very different approach was tried out, based on a paradigm known in computer science as “functional programming". In functional programming, concepts such as functions and variables have a much closer correspondence to their mathematical namesakes than they do in more common “imperative” or “procedural” approach used in, say BASIC. In “Building Programs”, I tried to present the essence of functional programming is an accessible way, without the need to learn a lot of technical information.

Another promising way of supporting flexibility in the design of technology rich materials is the design of authoring environments. Recently I have been working more and more in this direction.

It is a way of making a new division of labour between programmers and education designers in the development of educational software. Programmers can focus more on the design of high quality interactive components and take the time that is needed for this, while designers without programming skills can combine and customize these components and design interactive tasks more easily. Especially in a context where digital learning environments are becoming mature as a new medium for learning and working, these authoring tools are becoming important.

Figure 4 shows a screen of a prototype of an authoring tool I designed. It works like a text editor. Besides text, many types of interactive components can be used. These interactive components are based on (existing) applets and, in this environment, can be easily customized to fit the designed tasks. The ‘document’ that is made in this way can be exported as either a new applet or as a so called SCORM-package that can be used in a digital learning environment. (SCORM is a standard format for digital learning materials.) By embedding these digital activities in a learning environment, it becomes possible to store students’ results and even make them visible for teachers.

Applet 10 shows a task built using the authoring tool.