I find that before explaining any new concept to students it
is very important to find out what they know. No point in
going on about something most of the class are familiar
with anyway. Equally counter-productive is to skim over
the material students find puzzling.
Most teachers in higher education assume that students
can remove brackets. Many can’t. Dealing with a mix of
differently signed quantities is often a problem.
Several examples have to be considered to introduce what
in the UK schools is called a Smile Rule.
However, this is not enough. Throughout the
year, whenever the necessity for removing brackets arises,
it is advisable to get through the procedure, asking
students to talk about the necessary steps.
Most academics do not like doing that, thinking and saying
that they are not school teachers. But if the students failed
to acquire the necessary skills at school who would help
them if not us? And experience shows that they can be
helped. The teaching strategy I describe here has been
shown to work many times over.