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)

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)

A process of teaching fractions is detailed that respects pupil ideas and concept images and builds on these in a way that helps children to develop personal algorithms. This approach is an attempt to get away from perceived one-sided views found in most textbooks. (MP)

An education major enrolled in a mathematics education course ponders confusing definitions of "multiplication" functions in dictionaries and in a handout on Euclid. This student teacher wants to teach elementary students what multiplication really is, not just impart an algorithmic skill. (MLH)

Refinements of work with calculator algorithms previously conducted by the author are reported. Work with "chaining" and the doing/undoing property in addition and subtraction was tested with 24 third-grade students. Results indicated the need for further instruction with both ideas. Students were able to manipulate the calculator keyboard, but…

Instruction on properties of whole numbers, the meanings of operations on whole numbers, symbolic representation and algorithms for completing these operations is discussed. Many activities appropriate to each of these topics, and suitable for primary school children, are presented. (SD)

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.…

A teaching sequence for the division algorithm is detailed. (MP)

The author promotes an earlier introduction of decimals than is currently standard practice in most elementary mathematics programs. Suggested activities and related skills are reviewed. (MP)

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)

Use of the hand-dialed, transparent, nonelectronic SEE-Calculator is proposed. Pupils can dial numbers into appropriate columns, watching the gears work; place-value concepts are enhanced. Both activities and flowcharting are suggested. (MNS)

Compares the development of two students' understanding of addition and subtraction. One student's understanding is based on memorized rules and the other's on understanding the concept of place value. Discusses the effects of different goals for instruction and the importance of understanding place value. (MDH)

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…

Describes teaching strategies in which children are encouraged to develop computational procedures that are meaningful to them. Authors state that classroom observation reveals most primary students to be capable of developing their own accurate solution procedures for multi-digit addition and subtraction as well as for simple multiplication and…

Among 1,453 male and 1,133 female academically talented 7- to 11-year-old students, boys performed better overall than girls on mathematical reasoning. Gender differences appeared as early as second grade, varying according to mathematics subskills. Male performance was better on tasks requiring application of algebraic rules and understanding of…