The computer has great potential as a tool for the teaching of Mathematics; Two tools that can be used to guide the use of the computer in a mathematics classroom are the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards and situated cognition theory. This dissertation will summarize recent research on four computer-based tools in the mathematics classroom: computer simulation, programming, spreadsheet and graphing software, and computer networks. The existing research in each of these areas will be related to the NCTM standards and situated cognition theory. In addition, high performance computing tools and computational science projects will be introduced and their potential use in the mathematics classroom will be illustrated;One specific area of mathematics in which computational science projects may be particularly useful is in the teaching of functions. These projects provide a rich environment for the investigation of a function from several different perspectives. This dissertation reports the results of two studies which investigated the use of computational science projects in developing students' understanding of functions. The first study investigated the use of computational science projects in developing students' skill with variables and their understanding of an iterative function. It was found that students improved in their understanding of an iterative function, and were able to transfer that understanding to a similar problem. High math ability students and males were more likely to show this improvement and make the transfer of knowledge than students lower in math ability and females respectively. Students did not improve in their ability to use variables to model a function. The second study observed a group of students as they completed a computational science project in order to develop an understanding of the process that group of students went through as they completed the project. As they worked on the project, students were observed using and applying many mathematical concepts related to functions. They did not, however, appear to develop a complete understanding of many of these concepts. It was determined that the students did not have the necessary supports to assist them in developing that understanding as they worked on the project.