Focuses on children making sense of multiplication. In an activity called "Silent Multiplication," students use what they know about easier multiplication problems to solve increasingly difficult, related problems mentally. (Author/NB)

Established methods of teaching multiplication (tables, flash cards, repetitive exercises) do not work well with adult underachievers. The properties and concepts of multiplication of whole numbers must be presented as observable, fun, and practical. Finger math methods may succeed where pencil and paper fail. (SK)

Proposes a four-category classification of semantic structures of one-step word problems involving multiplication and division: forming the n-th multiple of measures, combinatorial multiplication, composition of operators, and multiplication by formula. This classification is compatible with semantic structures of addition and subtraction word…

The "count-by" technique of multiplication was taught to a fourth grade student with learning disabilities. The student learned to count by numbers not typically taught (e.g., fours, sevens, and eights). The method resulted in substantial increases in correct multiplications performed per minute, which were maintained and generalized to…

Defines spatial structuring as the mental operation of constructing an organization or form for an object/set of objects. Examines in detail students' structuring and enumeration of two-dimensional rectangular arrays of squares. Concludes that many students do not see row-by-column structure. Describes various levels of sophistication in students'…

Having children create and solve their own story problems is a valuable activity to use for them to think carefully about and apply a concept to create and solve a problem. Describes using two books to help children learn about the concept of multiplication. (ASK)

This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…

If the goal is to promote mathematical thinking and help children become flexible problem solvers, then it is important to show students multiple representations of a problem. Because it is important to help students develop both counting-based and collections-based conceptions of number, teachers should be showing students both number line…

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…

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)…

In an effort to examine the impact of the changes being made at San Jose State University (California) in the calculus curriculum, multiple measures were collected and analyzed. This study focuses on the relationship between performance on a pretest and the class grade. Through written responses on the pretest, a belief and knowledge profile for…

Assesses conditional states of item mastery found among items from different item domains and the effectiveness of various procedures for identifying such conditional relations. Item domains considered were from the curriculum area of multiplication of whole numbers, and were defined by a domain referenced testing system. (Author/RC)