**Proposal Summary**

We propose the funding of two symposia over the course of one year, one at University of Massachusetts Dartmouth, and the other at an institution in Europe (e.g. University of Warwick, UK), to bring together a select group of seminal thinkers in symbolic cognition in undergraduate mathematics, for the purpose of establishing a research agenda in this new line of inquiry. Symbolic cognition in mathematics is concerned with the evolution and use of mathematical symbols, especially their practical side - the specific cognitive and communicative roles that symbols play in helping people to do mathematics and learners to learn undergraduate mathematics. The major impact of these meetings will affect university teachers of mathematics and researchers in mathematics education.

Building on 3 years of work (2001-2003) at the annual meetings of the International Group for the Psychology of Mathematics Education (PME), we will assemble an international group of scholars from the fields of mathematics and mathematics education, for the purpose of critically examining the major research themes emerging from the PME working group meetings, and to develop and produce a seminal work on the use of symbols in undergraduate mathematics instruction that will have theoretical and practical implications.

Our intention is that this international working group will be able, though its focus on research and writing, to bring the issues of symbolic cognition in undergraduate mathematical thinking to a point where it is highly visible and on the agenda of all teachers of undergraduate mathematics through collaboration with national organizations such as the American Mathematical Society.

**Intellectual Merit**

By organizing a core group of international experts in the field, we will produce deeper insights that reflect contemporary issues, such as the new symbols systems that have arisen in dynamic technologies. The field is cross-disciplinary and has the potential to reach multiple educational communities. The symposia and subsequent work throughout the year will lead to many results of intellectual merit including a definitive account of what has been achieved in recent years in this field, a handbook for researchers in mathematics education, resources and important insights for new teaching faculty in undergraduate mathematics, as well as pre-service instruction. On-line resources and research activities, as well as on-going discussion resulting from the symposia will supplement such work.

**Broader Impact**

Evolution and Use of Symbols in Undergraduate Mathematics: Theory and Practice