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

A teaching sequence provides a guide to instruction on initial concepts of fractions, equivalent fractions, and addition with fractions. (MN)

Two mental algorithms, one for addition and one for subtraction, are described. It is felt such algorithms should be taught explicitly. The usual process taught for paper and pencil is seen to inhibit mental arithmetic, and a need to include mental algorithms in the regular mathematics curriculum is promoted. (MP)

Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…

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)

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)

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…

Prior studies indicate that, given time to develop their own algorithms, primary students will process multidigit addition or subtraction problems from left to right. Gives evidence to support that idea, describes methods of getting students to invent their own algorithms, and discusses advantages of child-invented procedures. (21 references) (MDH)

Compares the development of two students' understanding of addition and subtraction. One student's understanding is based on memorized rules and the other's on understanding the concept of place value. Discusses the effects of different goals for instruction and the importance of understanding place value. (MDH)

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)

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)