Spurred by Kilpatrick's (1987) "Where do good problems come from?", this study explores problem-posing triggers of experienced problem posers for mathematics competitions. Triggers are conceived as instances of noticing, where an impulse draws a poser's attention and "triggers off" a mathematical re-action, one of the outcomes…

One of the most salient arguments in favor of a semiotic approach, put forward on various occasions among others by Luis Radford, claims that semiotics is most appropriate to treat the interaction between socio-cultural and objective aspects of knowledge problems. But if we want to take such claims seriously, we have to undertake revisions of our…

We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith,…