According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

This paper investigates how individuals' performances of a cognitive task in a high-pressure competition are affected by their peers' performances. To do so, I use novel data from the National Spelling Bee, in which students attempt to spell words correctly in a tournament setting. Across OLS and instrumental variables approaches, I…

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…

The authors present an analysis of portfolio entries submitted by candidates seeking certification by the National Board for Professional Teaching Standards in the area of Early Adolescence/Mathematics. Analyses of mathematical features revealed that the tasks used in instruction included a range of mathematics topics but were not consistently…