This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

Technology and mathematics. manipulatives have been brought together in a new format. This joining has resulted in virtual manipulatives that are available on the Internet for students. Virtual manipulatives have been defined as computer based renditions of common mathematics manipulatives and tools. Just as a physical object can be flipped,…

Suggests ways to increase students' computational fluency using concrete materials, engaging tasks, and reflection time to increase number automaticity, flexibility in thinking about numbers, and use of efficient problem-solving strategies to find sums and differences. (Author/NB)

This paper draws on a body of research to present representations of numbers which can assist children in learning mathematics. Sections in the paper deal with counting, quantity, rank, and place value. Also included is a model which shows an approach for teaching two-digit and three-digit numbers in kindergarten, first grade, and the first half…

The number sense program in Texas was developed to help motivate students to learn mathematics and to literally develop "number sense." A description of the program, a 70-item exercise (with answers), and teaching tips are provided. (JN)

Math can be basic and motivational at the same time. Help your students discover numbers and enjoy them. (Editor)

"Chisanbop" is a Korean word which means finger calculation method. It is based on the Korean abacus, and its emphasis is on fives. By using Chisanbop techniques, one can add, subtract, multiply, and divide large numbers. Chisanbop can be taught most effectively to large groups in the second grade. (JN)

Describes number strips, arrow diagrams, and grids for number operations. Provides diagrams for the activity materials. (YP)

Describes a pattern which emerged from an examination of the digits of the squares of numbers. Provides eight examples having the pattern at the units or tens digit of the number. (YP)

Discusses a number series made from the multiplication of numbers to digits. Presents a number series for diverse multiplication numbers. (YP)

Provides an overview of research on transfer, highlighting its main tenets. Looks at interviews of two grade 5 students learning about mathematical concepts regarding operations on positive and negative quantities. Focuses on how their learning is influenced by prior knowledge and experience. (Author/MM)

Discusses mental computation and how and when it should be taught. Describes seven properties of mental algorithms. (YP)

The first four chapters of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

The 5-stage model of Ross was used to examine the role of instruction in facilitating children's acquisition of place value knowledge. Compares children from 2 samples on 10 tasks designed to reveal their thinking about place value. Discusses implications for theory and classroom. (YP)

Children in grades three through five and adults performed a number-matching task. Found that changes in the strength of arithmetic connections occurred with development and accounted for individual differences among adults. Individual differences among children were related to changes in the strength of number-line connections. (Author/GLR)