The aim of the present study was to investigate the potential for children to use the turtle methaphor to develop understandings of intrinsic, euclidean and cartesian geometrical ideas. Four aspects of the problem were investigated. a) the nature of the schema children form when they identify with the turtle in order to change its state on the screen; b) whether it is possible for them to use the schema to gain insights into certain basic geometrical principles of the cartesian geometrical system; c) how they might use the schema to form understandings of euclidean geometry developed inductively from specific experiences; d) the criteria they develop for choosing between intrinsic and euclidean ideas. Ten 11 to 12 year - old children participated in the research, previously having had 40 to 50 hours of experience with Turtle geometry. The research involved three case - studies of pairs of children engaging in cooperative activities, each case - study within a geometrical Logo microworld. The data included hard copies of everything that was said, typed and written. Issues a) and b) were investigated by means of the first case - study which involved three pairs of children and a microworld embedding intrinsic and coordinate ideas. A model of the children's intrinsic schema and a model of the coordinate schema which they formed during the study were devised. The analysis shows that the two schemas remained separate in the children's minds with the exception of a limited number of occasions of context specific links between the two. Issue c) was investigated in the second case - study involving one pair of children and a microworld where the turtle was equipped with distance and turn measuring instruments and a facility to mark positions. The analysis illustrates how a turtle geometric environment of a dynamic mathematical nature was generated by the children, who used their intrinsic schema and predominantly engaged in inductive thinking. The geometrical content available to the children within this environment was extended from intrinsic to both intrinsic and euclidean geometry. Issue d) was investigated by means of the third case - study involving a pair of children and a microworld where the children could choose among circle procedures embedding intrinsic and/or euclidean notions in order to construct figures of circle compositions. The analysis shows that the children employed their turtle schema in using both kinds of notions and did not seem to perceive qualitative differences between them. Their decisions on which type of notion to use were influenced by certain broader aspects of the mathematical situations generated in the study.

<p>With the rise of the Web, there is more interest among end-users to create different kinds of software that use elements from the Web or allow for networked interaction between users. Currently however, many available tools for this purpose are hard to use or lack a sufficient level of expressiveness. To provide new insights on the construction of tools that allow end-users to create their own Web-enabled software, this thesis explores design issues and consequences of applying the Turtle metaphor from the Logo-programming language to an end-user programming environment for Web-enabled applications. </p><p>In order to explore this, CrawLogo was created - a programmable end-user tool that supports the creation of Web-enabled applications using a Turtle-like control metaphor and language adapted from Logo. As a proof-of-concept, several Web-enabled applications were created using this new tool, including CrawLogo Pong, a somewhat alternative version of Atari’s classic Pong game, and a collaborative browsing environment, in which users can browse the Web together. The resulting CrawLogo environment allows for creating Web-enabled applications that - using more traditional programming languages - would be quite complex and require deep technical programming skills. Further, while utilizing a Turtle-like control metaphor in CrawLogo allows for the creation of some new types of applications and some new ways of interacting with the Web, it also raises new problems such as how to successfully design within the CrawLogo metaphor and how to create a meaningful representation of Turtle- geometry-based navigation on the Web.</p>

With the rise of the Web, there is more interest among end-users to create different kinds of software that use elements from the Web or allow for networked interaction between users. Currently however, many available tools for this purpose are hard to use or lack a sufficient level of expressiveness. To provide new insights on the construction of tools that allow end-users to create their own Web-enabled software, this thesis explores design issues and consequences of applying the Turtle metaphor from the Logo-programming language to an end-user programming environment for Web-enabled applications. In order to explore this, CrawLogo was created - a programmable end-user tool that supports the creation of Web-enabled applications using a Turtle-like control metaphor and language adapted from Logo. As a proof-of-concept, several Web-enabled applications were created using this new tool, including CrawLogo Pong, a somewhat alternative version of Atari’s classic Pong game, and a collaborative browsing environment, in which users can browse the Web together. The resulting CrawLogo environment allows for creating Web-enabled applications that - using more traditional programming languages - would be quite complex and require deep technical programming skills. Further, while utilizing a Turtle-like control metaphor in CrawLogo allows for the creation of some new types of applications and some new ways of interacting with the Web, it also raises new problems such as how to successfully design within the CrawLogo metaphor and how to create a meaningful representation of Turtle- geometry-based navigation on the Web.