This in-depth examination of a line explores several ways that the infinite nature and finite representation of a line can be perceived. These attempts to understand the nature of the line give insights into the nature of understanding itself. (MDH)

Several common errors reflecting difficulties in probabilistic reasoning are identified, relating to ambiguity, previous outcomes, sampling, unusual events, and estimating. Knowledge of these mistakes and interpretations may help mathematics teachers understand the thought processes of their students. (MNS)

Objectives are defined in a manner that eliminates many of their attributes that have been criticized as being harmful or unappealing. Examples of objectives appropriate for secondary school mathematics are given and the relationship between classroom processes and objectives is discussed. (MK)