At the beginning of preschool (M = 46 months of age), 197 (94 boys) children were administered tasks that assessed a suite of nonsymbolic and symbolic quantitative competencies as well as their executive functions, verbal and nonverbal intelligence, preliteracy skills, and their parents' education level. The children's mathematics achievement was…

Four kinds of understanding of mathematics are suggested: instrumental, relational, intuitive, and formal. Each type of understanding is described and illustrated. (MN)

This paper discusses six aspects of current practice in mathematics instruction of elementary school children: (1) use of symbolization, (2) use of models, (3) consideration of child development, (4) "logical" vs. "natural" approaches, (5) individualization, and (6) diagnosis and prescription. The author argues that symbols are frequently…

This paper examines sixth-grade children's thinking related to solving ratio and proportion problems before these children had received any instruction in the domain. It explores unitizing and norming, one of the processes identified by both content analyses (Behr, Harel, Post, & Lesh, 1990); Harel, Behr, Post & Lesh, 1990) and research in…