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Anghileri, Julia – For the Learning of Mathematics, 1995
Limitations in children's understanding of the symbols of arithmetic may inhibit choice of appropriate solution procedures. The teacher's role involves negotiation of new meanings for words and symbols to match extensions to solution procedures. (MKR)
Descriptors: Algorithms, Arithmetic, Concept Formation, Division

Johnston, J. H. – Mathematics in School, 1972
After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…
Descriptors: Algorithms, Arithmetic, Mathematical Concepts, Mathematics

Beishuizen, Meindert; Anghileri, Julia – Mathematics in School, 1998
Compares the approaches to teaching division in Britain and in Holland where different emphasis is placed on the development of mental and written methods. Describes how it is common for pupils in Britain to work from an early stage with pencil and paper rather than mentally whereas early emphasis is placed on mental strategies in Holland. (ASK)
Descriptors: Algorithms, Arithmetic, Computation, Division
National Council of Teachers of Mathematics, Inc., Reston, VA. – 1966
PRODUCED AS PART OF A PROJECT FOR THE IMPROVEMENT OF CLASSROOM TEACHING, THIS BOOK DISCUSSES THE BASIC CONCEPTS AND OPERATIONS OF ARITHMETIC WHICH ARE TAUGHT TO ELEMENTARY SCHOOL STUDENTS. THE CONCEPT OF A SET IS USED THROUGHOUT AS A BASIS FOR EXPLANATION, AND THE DISCUSSION STRESSES WAYS BY WHICH STUDENTS CAN BE BROUGHT TO UNDERSTAND THE…
Descriptors: Algorithms, Arithmetic, Elementary School Mathematics, Mathematical Concepts

Hennessy, Sara – Learning and Instruction, 1993
This article describes an empirical investigation of the extent to which incorrect arithmetic algorithms persist over time. Results with 30 fourth-year and third-year English students over up to 3 months shed light on "bugs," or students' learning of incorrect concepts, and indicate that they are not very stable in children of this age.…
Descriptors: Algorithms, Arithmetic, Concept Formation, Elementary Education

Myerscough, Don; And Others – Mathematics Teacher, 1996
Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)
Descriptors: Algorithms, Arithmetic, Educational Strategies, Mathematical Concepts

Thipkong, Siriporn; Davis, Edward J. – School Science and Mathematics, 1991
A study on the impact of misconceptions on preservice elementary teachers' processes in solving problems involving multiplication and division of decimals is described. Included are the purpose of the study, a description of the subjects, instruments, and interviews, the findings, and discussion. (KR)
Descriptors: Algorithms, Arithmetic, Decimal Fractions, Elementary Education

Blando, John A.; And Others – Journal for Research in Mathematics Education, 1989
Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)
Descriptors: Algorithms, Arithmetic, Computation, Error Patterns

Burke, Paul – Journal of College Admissions, 1990
Argues that the vast majority of adults have no use for the specialized mathematics taught in high schools and required by colleges--algebra, geometry, or calculus. Suggests that colleges should accept applicants who have studied percents, formulas, logic, computer commands, and basic statistics. (TE)
Descriptors: Algebra, Algorithms, Arithmetic, Calculus
Dahlberg, Cecilia, Ed. – 1989
This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…
Descriptors: Algorithms, Arithmetic, Cognitive Structures, Concept Formation