The author redefines basic numeracy as the ability to use a four-function calculator sensibly. He then defines "sensibly" and considers the place of algorithms in the scheme of mathematical calculations. (MN)

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)

A multiplication algorithm based on a perfect square is described. (SD)

Upper elementary school students created their own algorithms for finding products of whole numbers. The algorithms were similar to familiar ones for finding products involving 9 and 11. (SD)

Three alternative methods of finding averages of two numbers are presented. (MP)

In a two-year study, frequencies and descriptions of systematic errors in four algorithms in arithmetic were studied in regular and special education classrooms. (Author/SD)

Students who were unsuccessful in performing long division were taught to use a successive subtractions algorithm. (SD)

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real…

The observations of a fifth-grade student concerning number patterns are recorded and discussed. (SD)

Alternative algorithms, "tricks," and shortcuts are viewed as ideally suited for inclusion in a systematic program of practice because of their motivational effect and the mental stimulation involved in discovering why they work. (MP)

The use of counting for subtraction was investigated. Counting for subtraction is related to counting-on for addition and to four skills: the ability to use the subtrahend cardinality to gain entry into the count sequence, the ability to use the minuend cardinality to gain entry into the count sequence, the ability to use the count sequence to…

This paper is designed to provide teachers with more guidance on how to help students become proficient in the recall of basic number facts. Activities and practices are placed in a sequence designed to aid all instructors. The learning of number facts is divided into three stages: (1) the development of basic number facts; (2) establishing number…

This paper focuses on mathematics education in Technical and Vocational Education (TVE) in West Germany. The "dual system" of TVE, a part-time college/part-time on-the-job training scheme that normally leads to a certificate of a qualified worker after three years, is reviewed. Entrance tests for the trainee posts focus heavily on aspects of…

This booklet was written to provide elementary-school teachers with an overview of some of the research results related to the development of computational skills, together with ideas for classroom activities which have grown out of research projects. The booklet is organized into twelve sections, the first of which is devoted to delineating the…