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…

Compares methods of subtraction used by children and teachers. Suggests ways to encourage children to invent their own subtraction algorithms. (CCM)

A subtraction algorithm for numbers having several digits is described. The algorithm requires that, for digits in the same place, the smaller is always subtracted from the larger. (SD)

The major portion of the article establishes the basis for the stated rule - to divide by a fraction, turn it upside down and multiply. With this background, three justifications for the rule are given. Several possible errors in students' use of the rule are noted. (LS)

The arithmetic needed for complex calculation using an electronic calculator is explained and exemplified. Problems involving square roots, number theory, Fibonacci numbers, and electrical resistances are solved. (SD)

Speed and accuracy in adding a colunm of one addend numbers directly down a column was compared to adding by looking for combinations which add to ten. Ninety-two fourth-grade subjects learned one of these two methods for one week and then learned the other method the following week. Using timed tests after each treatment, it was found that the…

The teacher's guide for the second unit of this SMSG series covers the two chapters in Unit 2 of the student text on algorithms and flow charts and on problem formulation. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed,…

Individual fifth grade classrooms in five schools of differing socioeconomic levels were used in a study to analyze the reaction of the school to the experimental format, the adequacy of the test instrument, and the differential effects of the experimental treatments. Students were instructed in one of two experimental addition algorithms,…

One hundred seventy-six seventh grade students underwent a recorded interview where each was given a set of computational exercises and asked to say aloud his thinking as he worked them. The most frequently used strategies in computations with whole numbers and fractions are described in detail, an analysis of the nature of wrong answers is…

When two methods of transforming numbers from one base to another were taught sequentially, the first interfered with learning of the second. (SD)

Computational algorithms appearing in early American arithmetic text are discussed. (SD)

Described is a case in which a young student stumbles upon the "integer" technique for subtraction which differs from the techniques of decomposition and equal addition. (MN)

An algorithm for the calculator is given for determining the day of the week for any date. An instructional sheet, a worksheet, and a BASIC program are included. (MP)