This book reports on young students' strategies, the ways they construct knowledge, and how to support such development over time. Focus is placed on how to develop an understanding of multiplication and division in grades 3-5. The book describes and illustrates what it means to do and learn mathematics, provides strategies to help teachers turn…

An analysis is presented of pupil responses to several items on the second National Assessment of Educational Progress (NAEP) mathematics survey which focused on the concepts and models of the fundamental operations. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

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…

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)

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)

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…

THIS BOOKLET, ONE OF A SERIES, HAS BEEN DEVELOPED FOR THE PROJECT, A PROGRAM FOR MATHEMATICALLY UNDERDEVELOPED PUPILS. A PROJECT TEAM, INCLUDING INSERVICE TEACHERS, IS BEING USED TO WRITE AND DEVELOP THE MATERIALS FOR THIS PROGRAM. THE MATERIALS DEVELOPED IN THIS BOOKLET INCLUDE (1) ADDITION AND SUBTRACTION WITH WHOLE NUMBERS, (2) PATTERNS AND…

The purpose of this study was to compare instruction in multiplication and division by means of manipulative materials and pupil discovery to instruction using abstract and semi-concrete materials combined with teacher explanation and exposition. The effect of the two methods on pupils' attitude and achievement also was compared. Ten classrooms…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…

How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)

Over 600 pupils in grades five, seven, and nine in Italian schools were asked to choose the operation needed to solve 26 multiplication and division word problems. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. (MNS)

The Cockcroft Report on English Schools recommends that all schools design their syllabuses and examinations on the assumption that all students will have access to calculators. How to use calculators sensibly to improve what is taught and how curriculum content may change are discussed. (MNS)

Directions for making a device that parents can use to help children practice basic skills are given. (MK)

Curriculum for teaching multiplication and division story problems was delivered via either computer-assisted tutorial or teacher-assisted instruction to two groups of mildly handicapped middle school students (n=19). No significant differences were found, indicating that computer-assisted instruction is effective when sound instructional design…