This study examined 11 U.S. textbooks written for prospective teachers to investigate how standard decimal multiplication and division algorithms are presented, especially the rationale of both algorithms. Analytical frameworks of various methods used in different textbooks were developed. The findings suggest that half of the textbooks do not…

This report describes a randomized controlled study that compared the personalization of educational content based on neural networks to personalization by human experts. The study was conducted in a graphically rich online learning environment for elementary school mathematics, in which N = 135 fourth- and sixth-grade students learn via…

As technology quickly evolves, there are breakthroughs in science, space exploration, medical and engineering fields almost every day. In the future, there will be more complicated science and technology problems that need specialized researchers and scientists to find an optimized solution. This paper presents the role of robotics in supporting…

A technique for doing long division without the usual estimation difficulty is presented. It uses multiples of 2 combined with a recording technique. (MNS)

Two difficulties that students have in computing with fractions are idenfitied. Then a procedure is described, stressing the identity element, that resolves these difficulties and increases students' understanding and retention. (MNS)

Reviews the historical development of subtraction algorithms used in the United States. Discusses different algorithms used and developed throughout history that had a major impact on the way subtraction is taught today. (Contains 22 references.) (ASK)

Computational algorithms from American textbooks copyrighted prior to 1900 are presented--some that convey the concept, some just for special cases, and some just for fun. Algorithms for each operation with whole numbers are presented and analyzed. (MNS)

Discusses the use of manipulative materials to model operations and algorithms. Indicates that they clarify the several interpretations of each operation, establish a basis for correct mathematical language, and show why algorithms work. (JN)

Defines psychic intelligence as an inclination all children possess to use whatever cognitive intelligence they have for learning, adaptive behavior, and pleasure; strongly suggests that algorithmic drill usually damages the mentality of children by stifling psychic intelligence; and discusses the use of pocket calculators to prevent this effect.…

Two alternatives are given to the decomposition and equal addition subtraction algorithms. (MK)

A procedure is described that enables students to perform operations on fractions with a calculator, expressing the answer as a fraction. Patterns using paper-and-pencil procedures for each operation with fractions are presented. A microcomputer software program illustrates how the answer can be found using integer values of the numerators and…

Four methods of filling a square using programing with Logo are presented, with comments on children's solutions. Analysis of the mathematical or programing concepts underlying a few simple algorithms is the focus. (MNS)

Fifty Brazilian children aged seven-13 were individually given addition and subtraction exercises. Counting was the preferred procedure, with use of school-taught algorithms limited. Some children decomposed numbers into tens and units and then worked at both levels. They rarely referred to previous results when doing related exercises. (MNS)

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

This report illustrates a simple, short, yet relatively little known partial check on addition that elementary school pupils can be lead to discover, and later taught to understand. The process can also be used for subtraction and is viewed as more useful than the traditional check of casting out nines. (MP)