Starting with completing the square

Within any particular content area, is it better for students to have one general method, that always works, even if sometimes it is a bit inefficient, or to have several different methods at their disposal, and choose each time the most appropriate one for every particular scenario? This is not an easy question to answer. The issue is not just which of these two options might be more likely to lead to the student being able to get to the right answer quickly and efficiently – it may be that the action of choosing from among a range of methods is an important feature of working mathematically, and something we need to help students to do.