Misconceptions and mathematical misunderstanding
Learners frequently make mistakes, and teachers do too. If teachers make mistakes, do they use them as opportunities for learning, and invite learners to discuss them, or try to play them down, because they feel that making mistakes reduces their credibility as a teacher?
Mistakes need to be explored with learners. Sometimes they are the result of a lapse in concentration or a failure to remember a procedure. At other times, the mistake is a misconception, a reasoned way of thinking which may only work in a limited set of circumstances. A simple example of this is the ‘rule’ of adding a zero to multiply a number by 10, which works for whole numbers but no other types of number.
Deciding to engage with learner misconceptions, rather than merely telling the learner a more appropriate strategy can feel quite challenging for some teachers, as you have no idea what direction the discussion will take, and it may well be outside your comfort zone. Grasp the nettle and have a go, for the rewards in terms of ‘eureka moments', when the penny drops for learners, are great.
Fortunately, there are many good resources to support teachers wishing to teach in this way:
Suggestions for further reading