Our role as maths subject teachers is to facilitate both an increase in maths knowledge and maths confidence; as for me the two are intrinsically linked. There can be a vicious, hard-to-break down cycle for many pupils that can go something like this:
In order to improve the confidence of our students in maths I think we need to consider why confidence may be low and what we can do to improve it and maintain confidence. Below is simply a list of my personal observations, beliefs and strategies in this regard:
Right or Wrong
Maths is an unbelievably creative subject often with numerous answers to solutions, some elegant and beautiful even. Maths in school classrooms can be (perceived to be) a rather narrow subject with a right or wrong answer. If focus on being correct all the time is rewarded and praised, students will work hard to get the correct answer and be happy when this is achieved. For students who struggle, they will see an incorrect answer by comparison as essentially a failure and this puts us back in the vicious cycle.
Now in my classroom, I celebrate incorrect answers and mistakes. I tell pupils that they only learn when they make mistakes, embrace those mistakes and learn from them. I use mini whiteboards in every lesson I teach in school and will hold up incorrect answers and show them off more than correct ones. Often when I get a class to hold up their mini-whiteboards and I get 30 correct answers I will mockingly moan that there is no learning going on here so I am going to put up another question because I’m not doing my job if they are not making mistakes (and, as such, learning). I give prizes for the “best” incorrect answer and put their mistake and their name on a wall of fame. Students enjoy trying to guess the incorrect answers and the “clever incorrect answers” (one where you can see it was a mistake born through thought rather than careless error/oversight).
I am harsh on students for poor effort or not checking answers with the procedures I have given for sense-checking and self-checking answers and will duly criticise. But I won’t criticise when effort levels are high and mistakes are what I call fair mistakes. For example, if I see a student trying to answer a question I have set on their mini-whiteboard and when they have finished writing they immediately hold up the answer I will criticise them for being too hasty and not self-checking before they submit this response to me (whether it’s right or wrong). I say you wouldn’t make your parents dinner without tasting it first would you?! This small twist in highlighting, pointing out, celebrating errors I have found has turned the tide of confidence in the room. The pupils ultimately do want to get “correct” answers to pass exams etc but are more willing to trial different methods and talk about their maths now we have said it’s ok (in fact great for their learning) to be wrong. I also tweet these mistakes out on twitter and many students enjoy this twist on learning.
Time needs to be built into curriculum design to allow students to master the above skills and practice and work on them regularly. I don’t believe that for most children just because they “get” something in class one day they will remember it in six months time. Time needs to be factored in to allow pupils to practise these fundamental skills regularly so that they can remember and master them and they move from their short term to longer term memory.
I want to end on this point. I know there is a debate in education going on at the moment between quality instruction and independent learning (and there are various names and shades of grey for these ideas). I don’t want to get into that but in my opinion just want to say that I believe that quality instruction of maths can help students immensely in their mathematical confidence. For me quality maths instruction is comprised of the following ideas:
– Ordering of the scheme of work
– Links to other maths
– Picture representations
– Positivity and humour
by Colin Hegarty @hegartymaths