Fourth-grade students (n=45) either with or without learning disabilities and achieving or not achieving at grade level in math were asked to explain strategies used to solve computational problems. Strategies were classified as reproductive or reconstructive (which varied in applicability and efficiency). Significant group differences were found.…

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

Explores the extent to which presentations about multiplication and division involving decimals within three series of mathematics textbooks for grades three through eight help students to counter common learner misconceptions about multiplication and division. Results indicate that theory on conceptual change with its concomitant research have…

Shares a coded version of the number line to provide concrete experiences for learning abstract concepts. Using the fundamental theorem of arithmetic, appropriate coded symbols are determined for the prime factorization of each natural number and used to study the concepts of greatest common divisor, least common multiple, square roots, and…

Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)

Six male elementary school students with learning disabilities were taught multiplication facts using a computer software program with a five-second constant time delay procedure. Results indicated that the computer-assisted instructional program was effective. Learning generalized with varying degrees of success. (Author/JDD)

Investigated the use of the pronoun "it" by a nine-year-old girl as a concept variable conveying the message that she had something in mind that she believed the listener understood. (MDH)

Investigates the effect of mental schemes corresponding to additive and multiplicative situations in the process of interpreting and solving problems. Classifies relative difficulties of problems according to their situations which are considered through a written test administered to pupils in grades 2, 3, and 4. Supports the assumption that…

Describes an informal research activity in which third grade students invent their own algorithms for multidigit multiplication and division. Discusses teaching implications and action research ideas. (ASK)

Examined two possible explanations for the arithmetic tie effect: faster encoding of tie problems versus faster access to arithmetic facts. Found that the tie effect vanished with heterogeneous addition problems, and for seven out of eight participants, the effect vanished with heterogeneous multiplication problems. Concludes that the tie effect…

Many students have traditionally found the processes of algebraic manipulation, especially factorisation, difficult to learn. This study investigated the value of introducing students to a Vedic method of multiplication of arithmetic numbers to algebra that is very visual in its application. This research considered a possible role of the…

In this study, we investigated the development of basic effects that have been found in single-digit multiplication arithmetic: the problem size, five, and tie effects. Participants (9-,10-, and 11-year-olds and adults) performed a production task on simple multiplication. The procedure replicated Campbell and Graham's (1985) study ["Canadian…

Research suggests component skill performance has a strong positive relationship with composite skill performance. This study examined the association between accuracy and fluency for the component-composite relationship within multiplication. One hundred and fifty-seven fifth-graders did one-minute assessments for single-digit, and multi-digit…

Previous research suggested that Incremental Rehearsal (IR; Tucker, 1989) led to better retention than other drill practices models. However, little research exists in the literature regarding drill models for mathematics and no studies were found that used IR to practice multiplication facts. Therefore, the current study used IR as an…

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared)…