A square-dance number is defined as an even number which has the property that the set which consisted of the numbers one through the even number can be partitioned into pairs so that the sum of each pair is a square. Theorems for identifying square-dance numbers are discussed. (YP)

Shows numeral systems using base-10 positional systems currently in use in other countries. Describes two of the systems, Arab and Nepalese, and one, Chinese, that operates on a different principle. Provides references for getting more information about diverse numeral systems. (YP)

Information on a California senate bill that would establish a common course-numbering system is presented, along with the recommendations of the California Postsecondary Education Commission. After reviewing common course numbering in other states, information is provided on the intersegmental system currently operating in California: the…

Discusses activities using base-10-block skits to teach number system concepts in first grade classrooms. Describes the students' responses to the activities. (YP)

Illustrates the multiple strategies used by second graders to solve a problem with three addends and how their teacher tries to map their thinking into the system of mathematical notation. Describes the American Federation of Teachers' Thinking Mathematics program that the teacher uses. (MKR)

This article discusses three solutions to the "Tower of Hanoi" problem offered by students in a mathematics content course for prospective elementary school teachers. The course uses standards-based pedagogy and teaching via problem solving. Within this work, we consider the growth supported by collaboration at both the students' level…

Negative numbers extend our number line and greatly simplify our calculations, but sometimes students struggle with the concepts. These fun activities will help kids to make sense of the "other half" of our number system.

Problems in mathematics instruction in Thailand that are related to language include the simultaneous use of both traditional Thai numerals and Hindu-Arabic numerals, misunderstanding of mathematics problems for cultural reasons, and/or difficulty in understanding problem context. Research has shown that elementary and secondary school children…

This catalog presents brief descriptions of all lessons developed by the PLATO project for community colleges and adult education. One hundred six lessons are available for computer-based use. Topics range from elementary arithmetic to function theory and trigonometry. For each of these lessons, this catalog presents the title, code name, author,…

This volume presents a partial description of the lessons in the preliminary version of the PLATO fractions curriculum. Each lesson has three parts: review, new material, and a student-selected option. Students receive immediate feedback from the computer as they progress through each lesson. Five groups of lessons are described: meaning of…

Suggests that good number sense is fundamental for success in estimation, approximation, and problem solving. Further, large-number concepts are appropriate for development in upper elementary school, high school, and beyond. Presents examples to enhance a sense of large numbers in middle and high school students. (PK)

Describes how 2 10-year olds developed drawings and numeral systems to symbolize their mental operations while dividing unit bars into thirds and fourths using TIMA: Bars, a computer microworld, as a medium for enacting mathematical actions. The symbolic nature of their partitioning operations was crucial in establishing more conventional…

Number sense is easy to recognize but difficult to define and hence, to teach. In this article, number sense is defined in terms of the knowledge known to underline it, as identified in cognitive developmental theory and research. A preK-2 mathematics program, called Number Worlds, that was specifically developed to teach this knowledge is…

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)

At the request of students and the Board of Trustees, the Connecticut Community Colleges began a system to develop a common course number system. The reasons for creating a common course number system include: (1) it simplifies comparisons between colleges in the system; (2) it facilitates course comparisons, easing the transcript evaluation…