A Closer Look at a Relatively Neglected Mean

The self‐weighted mean (WS) – in which each value is weighted by itself – is presented in several contexts and illustrated. It is incorporated in a set of more familiar means. Intuitions concerning WS are explored.     

Enhancing Reflection with Audiovisual Playback and Trained Inquirer

Much of the literature on reflection treats the role of memory as unproblematic, overlooking the potential for forgetting and memory distortion to interfere with learning and personal development. This paper discusses the reliability of human memory under conditions that often apply when people are encouraged to learn by reflecting on experience, then describes a process which uses audiovisual playback and a trained inquirer to help reduce memory distortion. Applications of the process to some often‐cited models of reflection are discussed along with some practical implementation issues. It is argued that the process increases the reliability of memory and allows a fullness of time to explore events and their effects in depth and detail. It appears particularly suited to exploring ambiguous interpersonal interactions and to the development of intrapersonal insight.     

Numbers defy the law of large numbers

As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin‐tossing experiments, should be incorporated early on into learning the law of large numbers.     

Consensus is Unfair

A coefficient of unfairness in the allocation of goods to people can be extended to measuring consensus among judges. The notion of relative variability underlies the formation of these measures.     

Weighted Means Through the Looking Glass

Each weighted mean of two values has a counterpart, equidistant from the arithmetic mean, obtained by exchanging roles between the weights or by inversing each weight. These elementary relations are apt for introductory courses.     

Three Averages – Ordered by Comparing Areas

This short article gives a geometrical interpretation of the relationship between the harmonic mean, the arithmetic mean and the self‐weighted mean.