The principle of inversion--that a + b - b must equal a--requires a sensitivity to the relation between addition and subtraction that is critical for understanding arithmetic. Use of inversion, albeit inconsistent, has been observed in school-age children, but when use of a computational shortcut based on inversion emerges and how awareness of the…

This study involved an investigation of the effects of strategy instruction integrated with the concrete-representational-abstract teaching sequence on students with learning disabilities. A multiple probe design across subjects with one replication was used in this study. Two sets of data were analyzed to determine effectiveness of the…

The study of errors made in subtraction is a research subject approached from different theoretical premises that affect different components of the algorithmic process as triggers of their generation. In the following research an attempt has been made to investigate the typology and nature of errors which occur in subtractions and their evolution…

In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields…

This book is about playing with mathematics, teaching: (1) How to multiply and divide large numbers mentally; (2) Making addition and subtraction easy; (3) Tricks for understanding fractions and decimals; and (4) How to quickly check answers for each calculation. Described as a foolproof way to do multiplication, division, factoring estimating,…

This study examined the effects on math performance of the use of the rekenrek, a manipulative developed by Adrian Treffers. The rekenrek looks like an abacus, but differs in that it is based on a five-structure and not a ten-structure system. It is comprised of two rows of 10 beads, each broken into two sets of 5 by color (i.e., in each row the…

One of the hardest math skills for students to learn is fractions. This study used a multiple probe across participants to evaluate the effectiveness of a mnemonic strategy called LAP Fractions on six middle school students' ability to add and subtract fractions. Five of six participants were able to achieve mastery, and all six students…

Young Filipino children are expected to solve mathematical word problems in English, a task which they typically encounter only in schools. In this exploratory study, task-based interviews were conducted with seven Filipino children from a public school. The children were asked to read and solve addition and subtraction word problems in English or…

This paper reports a study aimed at revealing special-educational-needs pupils' learning potential by means of an ICT-based assessment including a dynamic visual tool that might help pupils when solving mathematics problems. The study focused on subtraction problems up to 100, which require "borrowing". These problems, in which the value…

A math teacher describes an approach to help special education students solve addition and subtraction problems through a system involving finger counting. The systems for subtraction and addition solve the problem faced by students unable to memorize facts and unable to use their fingers when numbers exceeded five. (Illustrations of the approach…

Different methods of subtracting are described; the equal additions and the decomposition methods are discussed in detail. (DT)

Among findings of a study involving 94 elementary learning disabled (LD) students were that Ss with math goals on their individualized education programs did significantly more poorly on a subtraction test than did Ss without math goals, and that Ss' subtraction skills generally improved with age except for age 11. (CL)

Attempts to reconstruct the productive ideas that evolved from already existing sources for the teaching and understanding of negative numbers. Discusses examples from developmental research. (Author/MKR)