Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)

Presents teaching methods to rectify the tendency of students and even teachers to divide the smaller number into the larger in problem situations requiring division, while recognizing the impossibility of the answer in the situation. (MDH)

Citing examples from the author's third grade mathematics classroom, describes problems stemming from the use of concrete objects (e.g., fraction bars, base-10 blocks, and popsicle sticks). The vignettes show the fallacy of assuming that students will automatically draw the conclusions that their teachers want simply by interacting with particular…

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)