This blog post is an attempt to sift through and lay out the spider diagram in my head of how to send up a child into year 7 smiling, focused and ready to impress their future maths teacher. It would be great if all children left primary school with the following attributes: quick recall of maths facts, being quick at deciphering a problem, choosing and ordering a calculation process and then being damn quick and accurate in calculating an answer, using all the formal methods, spotting those numbers-within-numbers and asking poignant questions or explaining their own thought processes with aplomb.
1.Seating: just face the front
Children seem increasingly averse to looking at a human face and the current cohorts of children who have grown up looking at iPads in addition to not having dinner table conversations etc are yet to transfer to secondary school. Group seating is also the norm and this means that children not only instinctively turn away from the teacher, but also struggle to decipher the more subtle display of emotion of an adult. This is a situation that will not miraculously right itself during the 6 week holiday between year 6 and 7 but actually needs an act of kindness from decision makers in primary education; children need to be trained to listen and concentrate on what the adult is teaching from an early age and this will only happen if children are all facing the front! This would also facilitate better back-and-forth questioning that is the norm in places like Shanghai, for example.
2. Textbooks: use them and stop feeling so guilty about it
Worked examples, sequenced learning trajectory worked out by experts, containing useful vocabulary and giving children a sense of progression, of getting better at maths and a chance to have a sneaky peek at what is coming up or remind selves of what was done last week. How can a worksheet ever compare? I also rather like the Eastern idea of having the odd page devoted to information about famous mathematicians. I don’t understand the guilt and hand-wringing that goes with, ‘Oh we must spend thousands of hours producing personalised worksheets’. Even when people admit to the usefulness of textbooks, there is always this caveat thrown in about how it is best to just use them sparingly, like some health worker talking about the dangers of salt on chips. Let’s face it, we all know chips taste great with lots of salt.
3. Pre-learning and catch up, daily
Children with SEN don’t need the teacher to facilitate their falling behind by allowing them to do fewer and easier calculations combined with less thinking every lesson, what they need is more time to over-learn and do extra practice. This can only happen in addition to the usual maths classes rather than during them, otherwise we have this weird situation where children are both catching up and falling behind at the same time. I have yet to get my head round the logistics of how exactly pre-learning and catch up could happen every day because I don’t have time or access to the plethora of information needed to make effective planning decisions on this matter. Oh how I would love to do a serious bit of management accounting with this issue in mind.
4. Frequent testing and competition: feel good factor for children and vital information to engage parents
We do arithmetic and times tables tests every week and then we come together to go through the various ways of finding the answer. I also encourage the children to be honest and say when they have got something wrong and they know they will get lots of appreciation from me when they say exactly why they got something wrong and how they’re going to remember to do X, Y and Z for the next test. Basically, mistakes are good and nothing to be ashamed of, so long as you learn from them. Also, the weekly tests are a chance for children to practise recall of various mathematical bits and bobs they have learned over the last few weeks. The children tot up their scores and go for a ‘PB’ (personal best) which is a term I have borrowed from my coaching days that seems to be massively motivational for everyone. After we have totted up scores I draw a big PB bubble on a flipchart and the children get to put their initials and a smiley face in it if they’ve got a PB. Honestly, just being able to use a teacher’s poster pen and draw a silly face is enough to give a child a little extra push in terms of making an effort. We celebrate also those who have made a massive PB jump and the hard-working children who have got full marks; I make a point of letting children know that full marks don’t happen by accident and that they are the result of effort, focus and always trying to do extra practice. Just as any sensible parent would, I ban sulking, whining and bad sportsmanship (we don’t allow it in other subjects, so why should we in maths?). I noticed recently that some of the boys are challenging each other and that there is a subtle change in social pecking order: it is not the silly, loud comedians who are ruling the roost because the hard working children are being given more ‘airtime’ as it were.
As you have gathered, the above situation described is something I do actually have some autonomy and control over. However, what I think would be even better is if termly results of maths tests were reported to parents in an open and honest way. Most, if not all, primary schools shy away from this, seeking to reserve test results for internal progress meetings, instead reporting to parents on progress or ‘effort’. What are we afraid of? That parents find out their child is behind and realises that the teacher is a mere human being? No. I’m a parent and I know that most parents want to know, regardless of how much of a shock it might be, where exactly their child is. Also, most parents want their children to do well and a low result will mostly cause parents to have stern words with their own child as well as galvanise said parents into sitting down with their child to go over times tables etc.
5. Less distracting walls
This is a difficult subject because I can understand the urge to fill up every conceivable space with vocabulary etc. However, it is distracting, particularly for children with SEN and I also don’t like the short-term solution of outsourcing children’s memories to the walls; not learning times tables or number bonds for example inhibits access to maths lessons in upper KS2 and KS3 (actually, forever). All information that is needed must be permanently inside the child’s head and if it isn’t, then we need to help that child to memorise it, rather than let the child carry on to a maths cul-de-sac a couple of years down the line.
Lots of practice helps children to memorise maths facts and become automatic in terms of performing certain calculations. Practice also helps a child become more confident because they have instant feedback that they’re getting quicker and more accurate. Further, the discipline of individual practice helps a child to develop focus, concentration and thinking. Being able to focus and think does not come naturally and a teacher who values practice is being kind to the child rather than lazy.
7. Being able to read well
This aspect is about how children can engage with the language the teacher is using when he or she is explaining and demonstrating. Children need to be fluent readers in order to comprehend questions and they need to be given a wider vocabulary so that they can speak and listen to an adult. Daily reading practice to the point where a child is a truly fluent reader and listening to the clear voice of the teacher (whilst also facing the teacher to see mouth movement) rather than wading through the limited vocabulary of multiple children’s voices would help a child to be a better mathematician.
8. The teacher actually teaching
How would you like to discover how to bake a cake? I could provide you with some ingredients and then you could experiment until you end up with a nice cake. Would you like that? No. Somebody who already knows a little bit about baking, about the combinations of ingredients and ratios might be able to enjoy the challenge, but the complete novice will end up frustrated, wasting time and ingredients and probably not ending up with a cake. Judging from the many, many cookbooks that grace the shelves of WHSmith I assume that we prefer clear, simple instructions to follow, maybe with a diagram or a picture. We also like a glossary of terms to refer to. With lots of practice of following instructions and set procedures, we start to memorise the common ratios, temperatures, ingredients and procedures. Eventually, we are able to bake a cake off by heart. A teacher can be that clear set of instructions as well as providing motivation, a human touch, a ‘Well done’ at the end.
I’m sure I will think of a few more ingredients that would help make a confident year 7 mathematician, so I will probably return to this post a bit later to change it a bit. In the meantime,
Who’s with me?