Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

Reviews the historical development of subtraction algorithms used in the United States. Indicates that the algorithms used to teach subtraction have not changed much in the last 40 years, but in the late 1800s and early 1900s, different algorithms were developed that had a great impact. Contains 22 references. (DDR)

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)

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…

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

This paper discusses an approach to the study of algorithms which values students' construction of nonstandard algorithms but also emphasizes the essential roles of the teacher and instructional activities in supporting the development of students' numerical reasoning. Episodes are presented from a 3rd grade classroom in which a 9-week teaching…

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)

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)

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.…

This paper describes how a target group of seven students in a combined fourth and fifth grade mathematics class used structured representations to solve fraction problems situated within various realistic contexts. Emphasis is given to the ways in which students' thinking about rational number concepts influences and is influenced by the…

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…