The transformation to reform mathematics teaching is a daunting task. It is often unclear to teachers what such a classroom would really look like, let alone how to get there. This article addresses this question: How does a teacher, along with her students, go about establishing the sort of classroom community that can enact reform mathematics…

Presents and describes a pedagogical framework that supports children's development of conceptual understanding of mathematics. Advancing Children's Thinking (ACT) is synthesized from an in-depth analysis of observed and reported data from one skillful first-grade teacher's use of the "Everyday Mathematics" curriculum. Indicates that teachers…

Reports on year-long classroom teaching experiments in two predominantly Latino low-socioeconomic-status (SES) urban classrooms which sought to support first graders' thinking of 2-digit quantities as tens and ones. Presents a model of a developmental sequence of conceptual structures for 2-digit numbers to describe children's thinking.…

Researchers from four projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe a common framework of conceptual structures children construct for multidigit numbers, and categories of methods children devise for multidigit addition and subtraction. Conceptions include unitary, decade and…

For six weeks, pupils in grades two, three, and four used either flash cards or a microcomputer program to practice basic subtraction and division facts. Equivalent learning resulted. (MNS)

Ten teachers successfully taught first- and second-grade children to count up while keeping track with finger patterns. Learning to subtract by counting up greatly improved children's performance on take-away, compare, and equalize word problems, and enabled them to accelerate by as much as three years their learning of subtraction topics. (MNS)

The grade placement of topics in addition and subtraction was compared across the five countries through analysis of textbooks. "Remarkable" uniformity in grade placement was noted for Japan, China, the Soviet Union, and Taiwan, but the United States differed substantially. (MNS)

First graders were taught to solve symbolic subtraction combinations by counting up from the smaller number to the larger while keeping track of the number counted up by using one-handed finger patterns. They improved quite considerably on a timed test of the more difficult subtraction combinations. (MNS)

A learning and teaching approach using base-10 blocks to embody the English named-value system of number words and digit cards to embody the positional base-10 system of numeration is described. Examines the students' understanding and arithmetic skills on the multidigit arithmetic. (Author/YP)

Report provides new data concerning children's accuracy as measured by previous studies and clarifies progress of first graders during entire year on difficult single-digit addition and subtraction problems. Discussion focuses on advantages of an adding on interpretation of subtraction and the importance of emphasizing conceptual understanding…

Thirty-six Korean first graders were interviewed to study their ability solving addition problems with sums of 10, single-digit sums between 10 and 18, and subtraction problems with minuends between 10 and 18. Finger methods to show sums over 10 and the regular named-10 Korean number words supported their learning of 3 efficient recomposition…

Reviewed is research regarding multidigit addition and subtraction which may be used to question the organization and placement of topics in curriculum materials. Discussed are issues surrounding multidigit addition and subtraction, and the linguistic and cultural disadvantages in constructing units of 10 experienced by children in the United…