The ability to count has traditionally been considered an important milestone in children's development of number sense. However, using counting (e.g., counting on, counting all) strategies to solve addition problems is not the best way for children to achieve their full mathematical potential and to prepare them to develop more complex and…

This paper presents a study that investigated the process of change in 5-6-year-old children's successful problem-solving approaches when tackling a multiple-step task in elementary arithmetic. Micro-developmental changes in children's successful problem-solving behavior were analyzed using Karmiloff-Smith's model of representational redescription…

Reviews research using diagrams, number sentences, and algorithms to help students learn to add and subtract; poses questions on the relationship of instruction to children's knowledge construction; and proposes a research agenda in this area. (86 references) (MKR)

Coordinates anthropological and cognitive perspectives on one child's learning of the standard addition algorithm in second and third grade. Analysis showed that the student abandoned his self-generated computational algorithms in favor of less understood conventional procedures. (25 references) (Author/MKR)

Illustrates the multiple strategies used by second graders to solve a problem with three addends and how their teacher tries to map their thinking into the system of mathematical notation. Describes the American Federation of Teachers' Thinking Mathematics program that the teacher uses. (MKR)