A procedure that has been found by a number of teachers to be exceptionally effective in helping children to learn basic addition and multiplication facts was studied in three settings. It is felt that the results showed how well-established principles can be applied effectively in classrooms. (MP)

Ways to make a discussion of the commutative properties of addition and multiplication more interesting to students are reviewed. An alternative promoted is a transposition-of-digits property, seen as useful in a number of instructional situations. The proposed investigation could be structured around calculator use. (MP)

The author recommends allowing elementary students to use pocket calculators, so that they may concentrate on the sense of a math problem without getting bogged down in computation. He presents calculator activities on place value, estimation, and arithmetic operations, suitable for grades 1-6. (SJL)

The author's plans for Kinesthetic Initial Training (KIT), a system of interrelated subjects designed to teach handicapped and gifted students basic reading, writing, arithmetic, and grammar skills through the use of concrete materials, are described. KIT components are reviewed, and implications are considered for areas of psychomotor,…

Rumpelstiltskin, Robin Hood and other fictional favorites breathe new life into word problems. (Editor)

Outlines Piaget's late ideas on categories and morphisms and the impact of these ideas on the comprehension of the inclusion relationship and the solution of arithmetic problems. Reports a study in which fourth through sixth graders were given arithmetic problems involving two known quantities associated with changes rather than states. Identified…

Lists some ways that sequences were incorporated into mathematics lessons and explains a teacher's observations about the caliber of thinking and questioning that students develop as they learn appropriate ways to use numbers. Provides a number of questions that have been raised by students and the thinking prompted by a discussion of those…

Discusses examples of children's invented equal-sharing strategies that lay a foundation for reasoning about equivalence by connecting ideas from multiplication, division, and fractions. (KHR)

Examined patterns of conceptual and procedural knowledge of addition in 5- to 8-year-olds. Found that children were more successful in noticing that addends had been reordered rather than decomposed and in noticing the decomposition of addends presented with objects rather than with symbols. Also found that profiles of procedural competence were…

Reports on pre-service primary teacher education students' involvement in a number sense program that was a component of a mathematics education unit. Suggests that students develop and utilize multiple relationships among number, attempt to make sense of the mathematics investigated, and provide considered explanations for results achieved.…