Abstracts of research papers presented at the Research Reporting Sections of the 48th Annual Meeting of the National Council of Teachers of Mathematics were compiled and edited by the ERIC Information Analysis Center for Science and Mathematics Education and are included in this publication. These abstracts describe research involving a wide variety of topics related to mathematics education at the elementary, secondary, and college levels. Topics investigated in these papers include: the relationship of rationalization of conservation and mathematical achievement; the effect of socio-economic differences on the teaching of readiness for mathematical concepts; children's concept of limits; perception of plane sections of solid figures; student evaluation of teachers; the relationship between personality and differential achievement; diagnosis of teacher behavior characteristics; characteristics of students who are successful in problem solving; the effect of different presentations of word problems; the effect of teaching Euclidean geometry via transformations; the use of a developmental model to build a probability unit; performance on certain discovery tasks; understanding certain concepts of logic; comparison of different methods of teaching proof using logic; the feasibility of proof in elementary school; and the role of counterexamples in the development of mathematical concepts. (FL)