A systematic search is given for products where reversing the digits does not change the answer. Related questions are suggested that can be solved by the same discovery approach. (MP)

A study of two adolescents with behavior disorders examined the effects of a sequence of three, single-digit multiplication problems on the latency to initiate multiple digit multiplication problems. During the preference assessment, both students most often selected the single-digit problems and intervention decreased the latency between problems…

Discusses the language used in mathematics classrooms and states that appropriate language is based not only on the words we say but also on how those words are being perceived. Indicates that teachers should give students time to develop the meaning of numbers, operations, or problems. (ASK)

Reports the results of an intervention program for students with difficulties learning mathematics. Compared two kinds of math intervention, guided versus structured instruction, to regular math instruction for students from regular and special education aged seven to thirteen and concludes that both forms of intervention were effective for low…

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…

Research addressing the effectiveness of feedback for learning has focused on many dimensions of feedback, including the timing (Kulik & Kulik, 1988), type (Mory, 2004), and amount of available information (Dempsey et. al, 1993). Much of the feedback research in education has tacitly assumed that the available information is perceived, and any…

This study examines a wide range of numerical representations (i.e., quantity, knowledge of multiplication facts, and use of parity information) in adult deaf signers. We introduce a modified version of the number bisection task, with sequential stimulus presentation, which allows for a systematic examination of mathematical skills in deaf…

Drawing upon research, theory, classroom and personal experiences, this paper focuses on the development of primary-aged children's computational fluency. It emphasises the critical links between number sense and a child's ability to perform mental and written computation. The case of multi-digit multiplication is used to illustrate these…