The Pirie-Kieren model for the dynamical growth of mathematical understanding and Brent Davis' mathematical mentalities were used as inquiry guides for this study. The work of Pirie and Kieren offered a way to engage students in their thinking about their experiences with mathematics, while Davis' mentalities helped frame questions to explore students' phenomenological experiences of being with mathematics.

Themes were selected as part of an emergence of student relationships during the course of the semester. Each theme was reflective of a relationship which seemed to have the most prevalence among student experiences. Themes emerged from data sources such as conversations, interviews, field notes, assignments, and classroom observations made by the researcher.

The findings indicate that meaningful experiences are important to students' ways of being in the world with mathematics. These experiences are discussed through emerging relationships such as folding back (Pirie & Kieren, 1994), language, relevance, and open-endedness. Other findings indicate ways to combine both theory and practice so that classroom teachers and mathematics educators may find value in the phenomenon of being in the world with mathematics.

This is a phenomenological study of the types of relationships which emerged with a group of elementary education majors. The phenomenon studied was "being in the world with mathematics" and the atmosphere in which the phenomenon was studied was that of a problem-centered learning environment containing pre-service teachers. Students in the environment were accustomed to conversation, exploration, and collaboration. The instructor of the course promoted a dynamic environment which enabled students to experience mathematics education from a variety of perspectives.

Implications for mathematics education may best be discussed in terms of curriculum. These findings call for a different perspective to be taken concerning the mathematics curriculum of schools and universities. This perspective involves viewing mathematics as a space for Richness, Recursion, Relations, and Rigor (Doll, 1993) to occur. It is hoped that this study will enrich the mathematical conversations of a variety of individuals ranging from seasoned practitioners and theorists to first year teachers.