Mark Twain once wrote:
I’ve always read that quote and was troubled by the ignorance part, which I, being a firm advocate in meritocracy with all things in life, like to believe is not the case. But in so far as applying this quote to success for a pupil in school maths I would alter the ignorance part and keep the second part to it to say
“To succeed in school maths, you need two things: knowledge and confidence”
I believe that 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 and hard-to-break down cycle for many pupils that can go something like this
I get things wrong in maths. I experience what I deem is failure. This happens repeatedly. I believe I am rubbish at maths. I can’t do maths and have no confidence in myself mathematically. I now give up and don’t try anymore. I actually then become actually bad and unsuccessful at maths.
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
Even though maths is an unbelievably creative subject often with numerous answers to solutions, some elegant and even beautiful, 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, praised and ultimately sought, students will work hard to get the correct answer and be happy when this is achieved. For students who struggle, they will experience an incorrect answer which by contrast to the praise for correctness will essentially be failure. If that moment of “failure” is dealt with incorrectly by student, teacher or parent this can start off the cycle mentioned above which ultimately leads to a loss of confidence in maths and disengagement.
When I first started teaching I was terrible for only praising the correct answers. I saw many happy faces (the students who gave correct answers) but also saw numerous unhappy faces. Over time I realised what was going on, especially for the pupils who were becoming low in maths confidence and worked hard to turn this around.
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). 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
Use of Mini-Whiteboards in lesson
If I could only have one piece of equipment in my maths classroom would I have 30 x iPads, the interactive whiteboard, 30 x fancy graphical calculators? No! I would turn them all down for a class set of mini-whiteboards and pens (the A4 ones blank on one side and with an x-y axis on the other) and this is why…
Linked in with the above idea of being right or wrong I find in many cases two things happen in a “normal” classroom situation. If students learn a new piece of maths some pick it up quicker than others (this could be a factor of the explanation, activity, topic, mood of child etc) but too often students are asked to practise straight away in their maths books. Some pupils are hesitant to write down something which they know they might make mistakes on in their books. This can lead to them plodding along, making a lot of mistakes, they deem they’ve ruined their book with red crosses and the cycle of confidence loss may start again.
If before they are asked to go to their books to practise, teachers jump around the room with hands up whole class questioning. Either a student is caught off guard, hates being put on the spot with a right/wrong/black/white scenario and feels under time pressure and tries an answer or often students who have picked up the topic quickly pounce on the questioning and can dominate. Either way for a student struggling it’s not a pleasant experience. Even if they get the answer correct, they breathe a sigh of relief and hope they have bought some time from the next pounce. Worst case they get it wrong and feel ashamed and embarrassed. Close to worst case they slip under the radar and get away without answering and the teacher can’t effectively help them improve.
Mini-whiteboards allow me to have a conversation with every single pupil in that class and check they can do the new maths before I ask them to do some practice. Also often the mistake in maths can often just be “I forgot the negative sign” and the great moment when a student looking around the class at correct answers just sees that if they wipe their finger over a small vertical line in a positive sign error in their working they would have got it fully correct is liberating for them. I let pupils make their mistakes on mini-whiteboards first, celebrate and share that but then try and bring a bit of serious focus and method in committing to exercise book practice.
Growth vs fixed mindset
I read a book called Bounce by Matthew Syed two years ago and for me it was one of the best teaching books I had ever read even though it was about sport. It talked about the idea of a Fixed vs Growth mindset and the work of Carol Dweck in this regard (whom I have read more extensively since). I could write a whole piece on this but suffice to say I work hard on creating a Growth mindset in any maths class I teach from the very first day I meet them to any opportunity I get (in marking, class discussion, at the door on entry to my room). In essence the message is with hard work and effort you can be successful in anything you turn your hand at. There is no such thing as being innately rubbish at maths and this is a lie society has fed to you as a student and you have fallen hook line and sinker for it - shame on you for believing it but you’re not going to believe that anymore. With hard work you will be successful in maths.
My room is covered with famous people talking about how hard work has got them to where they are and debunking the natural talent myth. I refer to those posters in my room every day and praise students all the time for hard work and effort.
- Home learning
I do a lot of work also on making maths tutorials videos for my students. With some classes I run a fully flipped learning model and others I make the videos for them to revise from. This use of technology has greatly impacted student confidence. If they didn’t quite get something I was talking about in class they can go to www.hegartymaths.com and work on it at home. As homework (when running classes not doing a flipped learning model) I often just get students to rewatch a video of what we did in class today and do 5 questions on that. I find repetition and time to practise are keys to confident and successful students.
- Fun/creativity in maths
I try my hardest to bring the joy and excitement to maths I see to my students and often a bit of fun and creativity can help with maths confidence too. Open and rich tasks that require students to work collaboratively have often proved successful in bringing a “buzz” to the classroom. I have to admit I tend to do this at the end of a block of learning (I know other teachers teach like this all the time) but I find it has worked well in the maths classrooms I am trying to build when we have worked hard to secure the basic skills.
- Quality instruction
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 a scheme of work
Maths is built on some foundations which mathematicians call axioms. In a similar vein, the maths a student needs to learn at school are build on only a few fundamental idea and skills and almost all the rest of maths is mere extrapolation or generalisation of these ideas. These ideas/skills include (this is not an exhaustive list) understanding of number (number bonds to 10, 100), place value, arithmetic with numbers of all place values, times tables (multiplication and division) negative numbers, proportional reasoning, simplifying algebra, rearranging formulae, substituting into formulae and solving equations. Almost all the rest of the maths curriculum are extensions of these ideas so for me a scheme of work needs to start at these fundamental ideas and work with children until these skills are mastered and solid before trying to move on. All too often for me, pupils do not have these skills to a sufficiently good level and are battling through their maths journey (a 11/12 year battle) in which all crossroads requires these skills. The cycle of failure to lack of confidence can start at this point so it is our duty as teachers to ensure these fundamental gaps are filled and made right.
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.
- Links to other maths
For me its important to choose the maths explanations for a cohort that fit in with the point and wider picture of maths. For example,
If teaching students to simplify fractions e.g.
You can teach them to "halve it and halve it again" to get 3 / 4 or you could ask them to use a skill you have enabled them to master previously in their maths journey i.e. write the numerator and denominator as a product of primes to get
For me in the long run this is a better method although maybe in the short term a bit longer. The reasons I say this are
1) it gives a need to use that product of prime factors thing you were going on about last month
2) it reinforces a skill you spent time on teaching previously
3) and most important it allows pupils to experience a skills which they will need in later maths when they are asked to simplify (x^2 + 5x + 6/ (x^-4) where factoring is the only way of doing this.
- Picture representations
For me use of box modelling especially for arithmetics, fractions and percentages and worded functional skills questions has been a great way bring the abstract maths in a question alive on the page and actually explain why some of the algorithms are at work. I would strongly recommend using bar modelling to teach fractions and percentages - it has been super especially for pupils who lacked confidence in this area before.
- Positivity and humour
Along with clear, precise and well thought-out instruction if you can bring your maths classroom alive with some analogies I feel this only adds to the atmosphere in the room and allows students to connect better and hence improve in their maths confidence. Here is an example of a way I thought to explain factors and multiples using Marshal Mathers aka “Eminem”. (Marshal Mathers has 2 split personalities - Slim Shady and Eminem - these are the things that make him up - they are his factors. In the Real Slim Shady video there are loads of identical eminems in the room - there are many copies of eminem in the room, this is a multiple of eminem).
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