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…

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…

This article summarizes the basic concepts of multiplication and provides some evidence that the traditional third-grade curriculum and instruction emphasizing memorization of multiplication facts produces much less understanding of the basic concepts of multiplication than a standards-based curriculum and instruction emphasizing construction of…

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

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 essay clarifies what it means to know mathematics by examining ways of knowing multiplication and explores what those ways of knowing imply for the teaching and learning of mathematics in schools. It reviews the perennial argument about whether computational skill or conceptual understanding should guide the school curriculum. A mathematical…

This study compared the error patterns of third- and fourth-grade children on addition, subtraction, and multiplication exercises in horizontal and vertical formats. The research design used parallel eight-item tests for each operation; the only difference between items on parallel forms was the formal (horizontal or vertical) of the computational…

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…

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, subtraction, and multiplication in modulo seven…

The author investigates elementary school students' performance when solving selected open distributive sentences in relation to three factors (Open Sentence Type, Context, Number Size) and identifies and classifies solution methods attempted by students and students' errors in performance. Eighty fifth-grade students participated in the…

A computer program which generates randomly sequenced problems for testing the abilities of students to add, subtract, and multiply one-digit numbers is described. Appendices provide tables of random sequences with directions for using the tables. The 54-statement FORTRAN program which can be used in generating additional sequences is also…

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…

A computer program designed to give a student practice in multiplication is discussed. The program features Editing of Input, Answer Positioning, and Timing Routines. (MN)