In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

Experiments conducted to find ways of teaching two and three year olds mathematical concepts were found to have general implications for concept learning. The failure of an initial attempt to teach the concepts "fat" and "skinny" led to a design of instructional procedures that would utilize a concept's name while trying to teach its semantic…

The range of meanings of "big" and "little" that mothers and their three children under age two expressed in relatively natural communication situations was studied. Longitudinal data from transcripts of conversations of middle-class mothers and their children were analyzed along with diary records kept by parents of their children's use of size…