Various algorithms used in addition, subtraction, and division problems were identified. The percentages of people in the National Assessment survey populations using each method are reported, as are the percentages of those using the most popular methods who answered correctly. Implications for instruction are discussed. (SD) Aspect of National…

The author develops a four-stage model for concept-internalization. The stages are: (1) concrete structure; (2) linguistic structure; (3) algorithm; and (4) mastery. The model is related to teaching methods and the teaching of long division is examined in detail. (SD)

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)

Presents a developmental taxonomy which promotes sequencing activities to enhance the potential of matching these activities with learner needs and readiness, suggesting that the order commonly found in the classroom needs to be inverted. The proposed taxonomy (story, skill, and algorithm) involves problem-solving emphasis in the classroom. (JN)

A learning pattern designed to help students cut down the amount of memorization needed in learning the basic multiplication facts is suggested and reviewed. (MP)

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)

A teaching sequence providing a smooth transition from concrete materials to the subtraction algorithm is presented. (MP)

A teaching sequence for the division algorithm is detailed. (MP)

Changes in the elementary and junior high school mathematics curriculum that have occurred in the last 20 years and that may occur in the future are discussed. (MK)

Four procedures used by children for deriving answers to unknown subtraction facts are described. They are counting forward, counting backward, derivation, and bridging. (MP)

One teacher's struggle with conveying a concrete realization of the subtraction algorithm to students leads to a discussion of elementary mathematics instruction in general. (MP)

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real…

Basic computational problems admit several different solution algorithms. A student's choice of method may be related to personal characteristics which also bear on his ability to learn other mathematical techniques and theories. (SD)

This document is intended as a resource for persons using, designing, or evaluating instructional materials in whole number subtraction. Its purpose is to provide conceptual machinery: (1) for describing/specifying subtraction tests and exercises and (2) for formulating related questions and conjectures. It is mainly a logical analysis subject to…

This study investigated the relationship between the level of conservation of displaced volume and the degree to which sixth graders learn the volume algorithm of a cuboid, i.e., volume = length x width x height (v = l x w x h). The problem is a consequence of an apparent discrepancy between the present school programs and the theory of Piaget…