An extensive investigation of pupil understanding of fractions at the secondary education level showed the majority tended to avoid using fractions, could not generalize about them, and probably did not see them as an extension of the set of whole numbers. (MP)

Problems are presented that can be solved with a microcomputer which explore the binary, decimal, and hexadecimal number systems and related problems. (Author/TG)

This calculator experiment for seventh-grade students on prime factorization contains objectives, difficulties, a discussion, several examples, and a worksheet. (MP)

Instructional problems springing from teachers' incorrect use of mathematical models during the initial development of ideas and processes are analyzed. Examples of models for subtraction and division are given, and their appropriate use discussed. (DT)

Presents a lesson that teaches number patterns through the Vedic matrix found in Vedic mathematics from India. (KHR)

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)

The content of the standards focusing on numbers and numeration for grades K-8 are discussed. Several activities for developing number concepts and skills are described. (YP)

Describes a number line created by fourth-grade students containing paper rectangles to represent the basic multiplication facts. The use of this number line can help students to understand factoring, prime and composite numbers, and beginning fraction concepts. (MKR)

Two samples of preschool children's representation and understanding of written number symbols was examined in two time points in one academic year. About 40% of Chinese four year olds (mean=4:7) were able to use conventional number symbols to represent the quantity of ten, on average. The majority of these children (85%) could represent written…

Although increasingly seen as critically important for pedagogy, young children's perceptions of number and of learning about number have not received much attention from researchers. This study uses a phenomenographic approach in that it seeks to map the range of possible conceptions about number and numerically-related learning amongst a group…

A principle of second-order isomorphism asserts that the functional similarities among internal representations parallel the functional similarities among the external objects to which those representations correspond. Research was conducted in accordance with this principle. (Author/BJG)

Three elementary-school students were exposed to Fractions 1, an instructional program for fraction problem-solving skills based on "direct instruction" principles. Fraction performance increases could reasonably be attributed to the instructional program. Improvements were durable across a short follow-up period and transfer occurred to similiar…