This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

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…