To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with…

Measurement is an integral component of the PK-12 mathematics curriculum. At various grade levels, much attention is given to the areas of geometric shapes. However, there is research evidence that measurement is problematic for US students. In this paper, the merits and demerits of two possible sequences (conventional and alternative) in teaching…

The application range of Cohen's Kappa is extended to the field of sequential observation data, where omission mistakes of an observer may often occur. It is shown how the omission mistakes can be incorporated into the calculation of the Kappa coefficient without violating the statistic it is based on. The enhanced coefficient is termed Kappa…