For the past five years, Vermont has been developing an innovative statewide assessment system in which portfolios of student work in mathematics and writing are a key element. The use of mathematics portfolios, particularly in elementary school, is a novel aspect of the assessment system. This study examines the elementary school mathematics portfolio assessment and its instructional impact by exploring the conceptions of problem solving, the knowledge of problem-solving strategies, the evaluation of problem-solving tasks, and the instructional practices of 20 fourth-grade teachers. Teachers indicated that the portfolio assessment program has enhanced their understanding of mathematical problem solving and broadened their instructional practices, but that they have encountered difficulty in understanding certain components of the reform and making the relevant changes. Teachers did not share a common understanding of mathematical problem solving or agree on skills that students should master. Eight figures and three tables present study findings. (Contains 13 references.) (SLD)