This study was set up to assess the contribution that a computer modelling approach using the language LOGO could make to the quality of mathematics learning in primary school children. Following a constructivist theory of mathematical learning it is argued that many problems children have with their mathematics results from instrumental learning without understanding, rather than relational learning. LOGO was developed, in part, to provide a learning environment for children to investigate mathematical ideas and thus develop their own understanding. Previous research has not provided much evidence that this happens, nor specified what mathematical learning could be expected to take place and what pedagogic approach could bring it about. Other questions relating to the maturity of the children and their aptitude for programming have similarly been neglected. This study was set up to identify the mathematical ideas intrinsic to Turtle Geometry and to explore the conditions under which this learning could best be fostered. The study was carried out in three phases. The first phase considered the constraints of maturity and the need to program on the learning of 9 and 11 year old children. The second phase of the study followed up the programming of the older children, to see what mathematics they were encountering, and what sort of activities encouraged them to think mathematically. Pre and post tests were used to identify the mathematical learning which was taking place. In Phase III a control group was used to identify the particular mathematical learning which could be attributed to LOGO experience, and to assess the transfer of mathematical learning from the LOGO context to novel problem solving. The first two phases revealed considerable mathematical activity intrinsic to Turtle Geometry. The need to learn some simple programming apparently did not present a barrier to mathematical investigation. The test results in the third phase showed that the children had deepened their understanding of angles, variables and general process aspects of mathematics through using LOGO. The performance of the children on the computers was monitored and was found to be revealing of their current mathematical understanding.

<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.

This document deals with introduction focused on pragmatically oriented research at branch of theoretical computer science and with presentation of designed methods for chosen application topics. At this study the theoretical subject is represented by kind of generative system - multisequential grammar and application topics are chosen according to possibilities supported by multisequential grammars. In order to follow results published by Thompson (see [9]), Lindenmayer (see [26]), Mandelbrot (see [8]) and also studies published by Morneau (see [17]), which shows the relation between natural laws and human discipline - mathematics, we study the applications of multi-sequential grammars from two points of view: generative L-systems (which further includes applications of fractal geometry and biomathematics) and natural language processing (which further includes the design of proper abstract language). Some problems related to compiler construction are also mentioned.