Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

First, fourth, seventh, and tenth graders were timed when solving simple and complex addition problems, then were presented similar problems in untimed interviews. Manipulation of confusion between addition and multiplication, where multiplication answers were given to addition problems (3 + 4 = 12) indicated an interrelatedness of these…