This study documents the efforts of a teacher/researcher to learn to use computer algebra software applications as pedagogical tools through systematic self-study, clinical observations of secondary students and collaboration with groups of preservice teachers. The study also involved the ongoing development of a computer-based learning environment which accompanied the research process and served to embody the main results. Complementing action research methods with grounded theory analysis, the study describes and explains the ways in which individuals (six secondary students and two groups of six preservice teachers) used available software tools for algebra learning. The subsequent grounded theory situates tool use within contexts of mathematical and pedagogical thinking on the part of the user. Effective use of available software tools was also found to be conditional upon characteristics of both the software and the learning environment. Analysis of pedagogical beliefs of both students and preservice teachers revealed a consistent culture of mathematics learning which devalued external support factors and exploration in favour of repetitive individual skill development within teacher- dominated instructional sequences. Detailed analysis of students' algebraic imagery revealed that, while some algebraic forms served a strong and consistent signal function in eliciting meaning and action strategies, others ( including simple expressions and tables of values) were associated with unclear signals, frustrating students' abilities to act appropriately in both traditional and computer-based learning situations. These factors acted as impediments to the effective use of mathematical software tools. At the same time, strategic use of appropriate mathematical software (defined as goal-directed, flexible and insightful) supported the development of algebraic skills and understandings in students. Such use was associated for the students with increased manipulative and representational repertoires and increased confidence in their results. The graphical representation was most favoured by all participants, although it was commonly associated with superficial and automatic use. The table of values, while recognised as effective for detailed comparison of functions, was more difficult to interpret and less favoured. Computer algebra tools were found to be most effective in supporting mathematical investigation and the explicit development of extended algebraic processes, such as equation solving