The floor function maps a real number to the largest previous integer. More precisely, floor(x)=[x] is the largest integer not greater than x. The square bracket notation [x] for the floor function was introduced by Gauss in his third proof of quadratic reciprocity in 1808. The floor function is also called the greatest integer or entier (French…

Three experiments explored the semantics of the mass-count distinction in young children and adults. In Experiments 1 and 2, the quantity judgments of participants provided evidence that some mass nouns refer to individuals, as such. Participants judged one large portion of stuff to be ''more'' than three tiny portions for substance-mass nouns…

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)