Answers and examples are given to sixteen questions related to traditional ways of performing the operations of arithmetic. (MP)

A current method of teaching long division using repeated subtraction is analyzed as being an example of a sound mathematical method that falls into disrepute when it results in unnecessary, length calculations. (MP)

The use of the calculator is suggested in teaching algorithms for the four basic operations, in place of any difficult standard algorithm. (MP)

Allowing students to examine different ways of performing an operation is suggested as a means of increasing their understanding. (MP)

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…

The use of developmental algorithms to develop skills is described. Children make the transition from using concrete materials to using a standard algorithm. (MNS)

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

Three types of arithmetic algorithms are discussed and compared. These are algorithms designed to get the right answer, computer algorithms, and algorithms designed to get the right answer and understand why. (MP)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

One teacher's struggle with conveying a concrete realization of the subtraction algorithm to students leads to a discussion of elementary mathematics instruction in general. (MP)

The author suggests that, through using the outlined question model and suggested classroom activities, elementary students will improve their abilities to analyze routine, one-step word problems and make a plan for the solution. It is further argued that the same algorithm can be applied to multistep problems by using specified questions. (PK)

This paper presents an examination of the construction of logic in multidigit subtraction. Interviews were conducted with 90 grade 2 and grade 3 students to determine whether they understood the logic of borrowing and whether the construction of the logic was related to procedural expertise or corresponding conceptual knowledge. Of 34 students…

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…