Talking at students or talking to (with) students

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.