Connecting theory and practice in teaching is sometimes difficult, as it requires expensive or delicate equipment, thus limiting the teacher to giving demonstrations in which students are passive participants. Numerical mathematics, as an applied discipline, should be taught on real world examples. By using inexpensive Arduino hardware, we can…

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. "Hands-on Activities for Teaching the Common Core Math…

This article reports on the use of a unique number system to facilitate teachers' understanding of the concepts of place value. Teachers' mastery of base-ten may hinder their recognition of the difficulties students have with place value, so the authors created a number system that used five symbols to represent values. Using this system, teachers…

In this article, the author argues that coordinate geometry and all its trappings should be banned from key stage 2 in English schools. To explain why he makes such a strong statement, he discusses geometry problems tackled by the Ancient Greeks, showing how meaningful problem solving can occur without the use of coordinates and the corresponding…

Presented are the results of an investigation of stimulus integration capabilities of three- and four-year-old children in judgments of small and large numbers. There is much evidence that suggested young children have a concept of number for small numbers, but not for large ones. A concept of number was hypothesized by Piaget to rest on the…

In a series of exercises students develop designs in which nodes are labelled according to the isolation rules defined. Strategies for creating new designs from known ones, finding the maximum number of isolation designs on a given configuration, and developing larger isolation designs are encouraged. Sample worksheets are included. (SD)

A game similar to Nim is described. Students in grades three through six have played the game in conjunction with the study of modular arithmetic,and have been able to develop winning strategies. (SD)

An elementary school mathematics program can be structured to allow students to practice computational skills and also become familiar with concepts that need to be mastered in algebra. The activities described begin with students' life experiences, continue through concrete and pictorial experiences, and conclude with abstract activities and…

Three worksheets provide exercises involving triangular arrays of numbers. (SD)

Students, playing the game described, develop strategies for guessing the four-digit number chosen by the opponent. The rules of the game are easily understood by low achievers, yet strategy development is challenging to advanced students. The game can be extended to numbers having more digits. (SD)

Multibase arithmetic blocks are used to investigate the minimum number of blocks of each size to make a square of a given size in a given base. Generalizations are made to any size and any base through pattern recognition. The problem is extended to rectangles, cubes, and rectangular solids. (LS)

This yearbook presents many aspects of mathematics learning by children between the ages of three and eight. Addressed to teachers of primary school children, the book begins with chapters discussing learning and cognition, the primary curriculum, and research on mathematics learning at this age level. Eight subsequent chapters deal with the…

The first in a three-volume set, this book focuses on young children between the ages of four and eight as they construct a deeper understanding of numbers and the operations of addition and subtraction. Rather than offer unrelated activities, this book provides a concerted, unified description of development with a focus on big ideas, progressive…