Describes a lesson on long division using chip trading which follows that algorithm for long division. (MKR)

Indicates that there has been a lot of work done and that a great deal needs to be done in the future to explore the world of children's early number. Discusses the counting, the use of algorithm, practical mathematics, the use of manipulatives, individual differences and pedagogical concerns, and classroom applications. Contains 18 references.…

Discusses the use of manipulative materials to model operations and algorithms. Indicates that they clarify the several interpretations of each operation, establish a basis for correct mathematical language, and show why algorithms work. (JN)

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

Helping teachers to build a strong bridge from concrete experiences to algorithms is the focus. A detailed sequence of activities is described. (MN)

The use of developmental algorithms to develop skills is described. Children make the transition from using concrete materials to using a standard algorithm. (MNS)

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

A method is presented for helping children make a smooth transition from using manipulative materials to using symbols only in solving multidigit addition problems. (MP)

This paper discusses the results of questionnaires sent to principals and teachers on the subject of manipulatives, computer, and calculator availability and use in the classroom. The study was done in order to develop a better understanding of teachers' inservice needs. Results of the study include: (1) most teachers have at least some…

The instruction of finger counting and finger calculation, also known as Chisanbop, is promoted as a natural method of introducing and teaching the basic processes of addition, subtraction, multiplication and division to children, particularly to those who are mentally and physically handicapped. The sequential process for teaching finger…

This paper describes an educational program developed on the basis that the use of blocks and other manipulatives can be useful both for initial teaching of exchange operations in arithmetic and for remediation of the faulty strategies which very commonly arise during acquisition of written calculation algorithms. This computer program is a…

Describes teaching strategies in which children are encouraged to develop computational procedures that are meaningful to them. Authors state that classroom observation reveals most primary students to be capable of developing their own accurate solution procedures for multi-digit addition and subtraction as well as for simple multiplication and…

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

This two-volume teacher's guide is to be used with a second-semester, sixth-grade mathematics program. The manner of presentation and the pedagogical ideas and tools are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings ("papygrams") and models of our numeration system (the…