The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

Survey sampling is fundamentally an applied field. The goal in this book is to put an array of tools at the fingertips of practitioners by explaining approaches long used by survey statisticians, illustrating how existing software can be used to solve survey problems, and developing some specialized software where needed. This book serves at least…

This case study examined the performance of a 13-year-old highly skilled mental calculator on mental multiplication tasks. She solved difficult tasks by using various ingenious calculation methods, including distributing, factoring, and recalling the product directly. Implications for instruction are reported. (Author/RH)

Discoveries of Charles Babbage in the 1800s are described. Origins of the difference engine, his calculating machine, the principles of computation applied to tables, and the design and construction of his engine are included. (MNS)

The mathematics associated with division is discussed, working from a theorem for the real division algorithm. Real-world, geometric, and algebraic approaches are discussed, as are related topics. (MNS)

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

Describes the development of computers and calculators, noting intitial resistance to and later acceptance of calculators in the classroom. Advocates teaching children to perform simple calculations and stresses estimation skills over speed and accuracy for doing long, complicated computations. Includes recommendations for classroom calculator use…

Repeatedly taking the square root with a calculator yields numbers with logarithmic-type properties, which can be used to define the logarithm functions. (MP)

Computation errors that may occur by expanded use of calculators are discussed. Potential errors with five exact arithmetic examples are described as they are translated into approximate processes. (MNS)

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

Presents a number of transcript examples of correct and incorrect transferences by children. Considers the objects of transference including spoken words, written symbols, models and diagrams, arithmetic procedures, and structures. Discusses the use of transference in arithmetic education. (YP)

Shortcuts to use when performing operations with the calculator are given. Algorithms discussed include reciprocals, powers, parentheses, infinite series, and synthetic division. (MP)

This unit of study for grades K-2 focuses on counting coins and coin equivalencies up to 50 cents, making use of a literature connection. The unit provides key words; recommends subject areas and approximate length of time; poses an essential question or problem; provides a unit introduction; notes four individual lessons ((1) For Sale!; (2)…

Presents two papers commenting on previous published articles. Discusses formulas related to the determinants of sums and tests the formulas using some examples. Provides three special cases of the determinants of sums. (YP)

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)