This study examined 11 U.S. textbooks written for prospective teachers to investigate how standard decimal multiplication and division algorithms are presented, especially the rationale of both algorithms. Analytical frameworks of various methods used in different textbooks were developed. The findings suggest that half of the textbooks do not…

Many students persistently misinterpret histograms. Literature suggests that having students solve dotplot items may prepare for interpreting histograms, as interpreting dotplots can help students realize that the statistical variable is presented on the horizontal axis. In this study, we explore a special case of this suggestion, namely, how…

This study explores student flexibility in mathematics by examining the relationship between accuracy and strategy use for solving arithmetic and algebra problems. Core to procedural flexibility is the ability to select and accurately execute the most appropriate strategy for a given problem. Yet the relationship between strategy selection and…

The authors have found that having students learn accessible standard algorithms by explaining them using mathematics drawings increases students' sense of place--value numbers and enables students to articulate their understanding of what is actually happening with the numbers and why. In this article, they will discuss three standard algorithms…

Two sequences of activities were developed to provide instruction on the algorithms for addition and subtraction of two-digit numbers. In the integrated sequence (I) the mechanics of "carrying" and "borrowing" were treated as a single process "regrouping." In the sequential treatment (S) the addition algorithm was developed before the subtraction…

Two sequences of activities were developed to provide instruction on the algorithms for addition and subtraction of two-digit numbers. In the integrated sequence (I) the mechanics of "carrying" and "borrowing" were treated as a single process "regrouping." In the sequential treatment (S) the addition algorithm was developed before the subtraction…

Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

Describes a lesson on long division using chip trading which follows that algorithm for long division. (MKR)

Facts are given about the ninth-century Arab mathematician Al-Khwarizmi, from whose name the word algorithm is derived. His influence on algebra and arithmetic are discussed. (MNS)

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

A discussion of the various algorithms used for multiplication. Repeated addition, arrays, the distributive law, Egyptian and Russian Peasant Multiplication, Gelosia, Napier's Rods and Genaille's Rods are all described, and examples of multiplying using each method are explained. (DT)

Describes two experiments that investigate how "buggy algorithms" in multi-digit subtraction are used. The first experiment tested third grade students (N=110) and repeated the test two years later. The second experiment tested students in grades 3-6 (N=301). Contains 21 references. (DDR)