Teachers must put the brakes on,as it were,when they notice

put something on中的on是宾补
as it were是插入语
looking puzzled也是宾补
宾补是在宾语后起修饰作用的
之所以用look+ing是因为look在这里不能当谓语（主句是they notice students.其中notice是谓语,一句话中不能有双谓语）所以用非谓语动词中的动名词形式looking.