Examines 250 sixth-grade students' understanding of arithmetic average by assessing their understanding of the computational algorithm. Results indicate that the majority of the students knew the "add-them-all-up-and-divide" averaging algorithm, but only half of the students were able to correctly apply the algorithm to solve a…

Analyzes a didactical sequence for the teaching of addition and subtraction procedures and algorithms. Uses didactical procedures by children in problem solving activities in order to gain a better understanding of the interaction between numbers, numeration, and operations knowledge which are involved in the construction of addition and…

Examines the philosophy behind the issue of computational fluency in "Principles and Standards." (Author)

In order to determine the extent to which the LOGO programming language can be used as a reinforcer for general problem solving ability, this field study used a production theory approach to problem solving as a conceptual model, and then translated the model into a LOGO oriented framework. The methodology tested the use of an algorithm in a…

Forty-eight first and second graders were taught an algorithm for solving concept-attainment problems. Using a 2 x 2 factorial design, a comparison was made of the effects of (a) reverse versus forward sequencing of instruction and (b) elicited verbalization of the algorithm versus nonverbal practice. Reverse groups outperformed forward groups on…

The focus is upon the introduction of multiplication within the framework of an algorithm program. Analysis of some observations of student solutions to multiplication problems is included. (MN)

A case is given against teaching division of fractional numbers. Types of problems usually solved by division are solved by methods involving only multiplication. (JP)

Sixteen Brazilian third graders aged 8-13 were given problems involving multidigit computation. School-taught algorithms were likely to be used in school-taught problems, with little carry-over to real problem situations, but resulted in more incorrect answers. (MNS)

An approach to teaching pupils the long division algorithm that relies heavily on a consistent and logical approach to estimation is reviewed. Once learned, the division estimator can be used to support the standard repeated subtraction algorithm. (MP)

Explains that Year 5 students in ten British schools took a mathematics division test twice in the school year. The test involved context and bare problems to identify changes in approach as the standard algorithm was introduced. Reports that 52 percent of students gained a higher score on the second test. (CMK)

Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

Three differences between the mathematics training of students from Spanish-speaking countries and that typical for pupils in the United States are discussed. (MP)

Presents a developmental taxonomy which promotes sequencing activities to enhance the potential of matching these activities with learner needs and readiness, suggesting that the order commonly found in the classroom needs to be inverted. The proposed taxonomy (story, skill, and algorithm) involves problem-solving emphasis in the classroom. (JN)

A learning pattern designed to help students cut down the amount of memorization needed in learning the basic multiplication facts is suggested and reviewed. (MP)