Presented are materials related to the work of the Number and Measure and Rational Numbers working group of the Georgia Center for the Study of the Learning and Teaching of Mathematics. Much of the content reports on attempts to bring constructs from developmental psychology and mathematics to bear in understanding children's ideas of number and measure. The reports included are thought to reflect a stage in a sequence of work, and are presented as a bridge between some of the ideas developed at a 1975 conference and on-going work. Seven individual research reports in mathematics education are included: (1) An Explication of Three Theoretical Constructs from Vygotsky; (2) Quantitative Comparisons as a Readiness Variable for Arithmetical Content Involving Rational Counting; (3) Language and Observation of Movement as Problem Solving Transformation Facilitators Among Kindergarten and First-Grade Children; (4) Aspects of Children's Measurement Thinking; (5) The Rational Number Construct, Its Elements and Mechanisms; (6) Seventh-Grade Students' Ability to Associate Proper Fractions with Points on the Number Line; and (7) The Relationship of Area Measurement and Learning Initial Fraction Concepts by Children in Grades Three and Four. (MP)