We present a case study of teaching and learning fraction addition on number lines in one sixth-grade classroom that used the Connected Mathematics Project Bits and Pieces II materials. Our main research questions were (1) What were the primary cognitive structures through which the teacher and students interpreted the lessons? and (2) Were the…

This article reports on models of teaching that developed as outgrowths of a study of middle-grades mathematics classes. Three specific cases are highlighted that represent deductive (associated with univocal), inductive (associated with dialogic), and mixed (a hybrid of deductive and inductive) models of teaching. Teaching practices associated…

Validates a framework for assessing children's thinking in multidigit number situations and uses the framework to evaluate instructional programs. Key constructs--counting, partitioning, grouping, and number relationships--appear stable within each of 5 levels across 12 case studies, suggesting a possible hierarchy of thinking. (DF)

Describes a program in second-grade Dutch mathematics classes that emphasizes mental addition and subtraction of two-digit numbers up to 100. Deals with a strategy of counting by 10s from any number. (Contains 56 references.) (RLB)