Presents activities designed to help children understand the notion of a sample in a homogeneous group, a concept essential to understanding "R times E" problems. Underscores the importance of children's understanding the situation in a problem so that they can solve it. (JN)

Analyzes multiplication word problems to identify the origin of children's difficulty. Emphasis is given to problems involving the concept of combination. (JN)

Discusses how to help children acquire mathematical concepts and teach for precise mathematical concepts. Describes four activities to reinforce the concepts introduced. (YP)

The author suggests that, through using the outlined question model and suggested classroom activities, elementary students will improve their abilities to analyze routine, one-step word problems and make a plan for the solution. It is further argued that the same algorithm can be applied to multistep problems by using specified questions. (PK)

Presents activities that have been used successfully in leading students from concrete experiences through pictorial and symbolic representations of important numeration concepts and patterns, including place value, multiples, and rounding. Each activity includes concept or skill fostered, list of materials needed, recommended grade level, and…

This article describes the instructional efforts and success of two first grade teachers who cooperated in a year-long subtraction study with a university research team. Performance profiles of students in the experimental and control groups are presented, and implications for teaching are discussed. (PK)

Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)

Discusses some important components of instruction on fractions in the early childhood years. Argues that fractions should be included in the early childhood curriculum and suggests various activities and materials. (PK)

Argues that, though considerable difference of view is evident between Montessori and Piaget about the importance of certain concepts and level of cognitive development necessary for genuine understanding, the ideas and methods first presented by Montessori 80 years ago stand up well when evaluated through the lens of current research. (PK)

Argues that number concepts are not single-faceted ideas that children either have or do not have. Suggests that number concepts can be broadened by helping children develop a collection of relations. Examples of classroom activities are included. (PK)

Proposes that teachers should examine the elements of mathematical understandings that precede conservation and one-to-one correspondence and tailor classroom instruction to benefit both conserving and nonconserving students. (PK)

Describes the Agam program, a 36-unit curriculum program to introduce students to basic visual concepts and that applies visual abilities and visual thinking to learning tasks. Describes two units at the third grade level, "Ratio and Proportion" and "Numerical Intuition," and makes observations of the students' learning. (MDH)

Reports an example of one lesson from a sequence of lessons on fractions from a sixth grade class in which the teacher revises her plans after observing students' small-group work and interactions. The lesson illustrated the teacher's knowledge of mathematics, how students think, and how to observe that thinking. (MDH)

Suggests that a solution to the problem of expensive educational software may be found in public domain software. Included are a definition of public domain software, a discussion of the kinds of software that are in the public domain, ways to obtain such software, and a list of some examples. (PK)