Math is about the relationship between numbers. Right answers are not the only thing to look for when examining students' work in mathematics. Looking at how children solve computation problems can give teachers insight into their thinking and help determine what math skills they already know and what they still need to learn. The author contends…

Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting third graders' development of mathematics problem solving. In the fall, 122 third-grade students were…

The issue of lower than expected mathematics achievement is a concern to education leaders and policymakers at all levels of the U.S. PK-12 education system. The purpose of this quantitative, quasi-experimental study was to determine if there was a measurable difference in achievement on the mathematics section of the state test for students (n =…

The authors propose a strategy for studying the effects of time-varying instructional treatments on repeatedly observed student achievement. This approach responds to three challenges: (a) The yearly reallocation of students to classrooms and teachers creates a complex structure of dependence among responses; (b) a child's learning outcome under a…

Through her work as a consultant, Burns has found that a handful of students in all classes lack an adequate foundation in basic math concepts and lag far behind their peers in both understanding and skills. Students who lack a foundation on which to build new learning are generally not well served even by well-planned, differentiated instruction;…

This set of 13 activities, adapted from "Mathmatters: Developing Computational Skills with Developmental Activity Sequences (by Randall Souviney, Tamara Keyser, and Alan Sarver) was designed to help teachers using the Indigenous Mathematics Project materials (in Papua New Guinea) understand the basic processes involved in computation with…

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…

Flexible pavement materials exhibit complex mechanical behavior, in the sense, that they not only show stress and temperature dependency but also are sensitive to moisture conditions. This complex behavior presents a great challenge to the faculty in bringing across the level of complexity and providing the concepts needed to understand them. The…

Thirteen research reports related to mathematics education are abstracted and critiqued in this publication. The topics of the research include counting, addition, subtraction, ratio, proportion, geometry, problem solving, and teaching strategies. Also included is an editorial comment by T. Kieren on mathematics education research. Research…

Ways to use a calculator as an integral part of mathematics instruction in existing curricula are provided. Activities are proposed that will help children think about mathematics rather than merely push buttons. (MN)

This study compares three methods of introducing two-digit numeration. It is concluded that teachers should build on the preschool exposure children have in counting past ten, rather than have children begin by counting out groups of tens and ones and only later in the process use the normal number names. (MN)

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)

The paper details teaching methods that have proved successful in teaching money management skills to secondary special education students (e.g., use of real money, organization of money before counting, transitions when counting different bill denominations, instruction in various bill combinations, sequence of introducing coin combinations, and…

Describes a finger pattern method for teaching subtraction. It is suggested that the method has several advantages over the usual methods children adopt. (PK)

The general combinatorial problem of counting the number of regions into which the interior of a circle is divided by a family of lines is considered. A general formula is developed and its use is illustrated in two situations. (PK)