Effective strategies for mental and written arithmetic calculation from the third to the fifth grade

The strategies used to solve mental and written multidigit arithmetical addition, subtraction, multiplication and division were observed in 200 third, fourth and fifth grade children. A strategy was classified as effective if it resulted in the correct solution at least 75% of the time. For mental addition and subtraction, primitive strategies such as counting on fingers and counting on (mental counting from a specific point), and the more sophisticated strategy 1010 (solution of the calculation problem using tens and units separately) were more effective than the strategies learned at school. In written addition, subtraction and multiplication there was a shift from the CAR+to the CAR- strategy (tabulating with, or without, a carried amount) from the third to the later grades. Results show that typical strategies taught at school progressively substitute every other strategy both in mental and written calculation, but without reaching the criterion of effectiveness. The implications for maths curricula are discussed.     

On Codes of Ethics,The Individual and Performance

In this paper I contend that, although codes of ethics are very good things and could potentially improve performance by acting as a normalising agent for a profession, they are not problem‐free. In particular, they lend themselves to reification (making something abstract into something concrete and thus, reduce the potential for their full impact), they are time dependent (that is, they are relevant only to the time in which they were formulated), subject to different lenses (that is, they are relevant only to the culture in which they were formulated), and emotionally challenged (that is, they are rarely formulated in a way that encompasses the emotions around the particular situation). An individual's role in a situation is hard to delineate via codes of ethics and, thus, these codes of ethics should be seen as a proposition, rather than as a solution for performance problems regarding ethical challenges.