Could seeing Word Problems as transactions actually help?
Every teacher will have come face-to-face with this from their students, and most likely on a very regular basis during maths lessons. I am working with a few children at the moment for whom this seems to be the default setting – almost as though they look for something not to understand, which is a sign of maths anxiety, but that’s a whole other blog.
Over the years I’ve tried a variety of responses to this, but like the tide the question keeps coming, no matter what I try. Recently I’ve been trying a new technique. But before I tell you about it, here are a few of the traditional strategies you may have come across.
Ask a Friend: Allowing children to work in pairs has significant benefits. Since no two children are identical, it is likely that they will both have different insights into a problem.
Draw a Picture or Diagram: often a picture can help make sense of something better than words can. Topics such as fractions, percentages and ratios lend themselves particularly well.
Read it out: Sometimes the mere act of saying something out loud can add understanding. This may well be because the brain then has another source of information – the ear – from which to try to make sense of the problem.
Act It Out: this week I was amazed to find a Y6 child could not answer the following question:
58 + 73 = 131, so what is 131 – 58 ?
A part-part-whole diagram didn’t work, so I went with a ‘hands of rice’ approach. “Hold out your left hand as though it contains 58 grains of rice“, I told him, modelling this with my own left hand. “Now hold out your right hand, and imagine that it contains 73 grains of rice.” Again, we both did so.
“Now, let’s put our hands together: can you see that we are adding the grains?” We did so, he nodded.
“So using what the question tells us, how many grains are there altogether?” (He got to 131, but interestingly if took a few seconds for him to make the connection.)
I pointed to his hands in turn. “Good. 131 in total, made from 58 here, and 73 here, yes?” Affirmative response.
“If you take your left hand away, with its 58 grains, how many remain?” The response was somewhat hesitant but there was less of a pause – “73?”
“Well done. So, we have 131 in total, made from 58 and 73. We take away the 58 from the 131; what do we have left?” “73!“. (This time with no hesitation, and it sounded like more of a joyful exclamation than a question.)
So I can definitely recommend ‘Act it Out’ as an effective strategy. It is particularly effective in the case of word problems, where children are frequently to be found loudly declaring their stuck-ness.
There are a few reasons for this, but I suspect one of them is a lack of regular practice at unpicking anything that has both words and numbers. Finding a calculation amidst the net curtains of obfuscatory noise can prove a challenge that feels simply too big, and children give up. So resilience needs building, for sure. But perhaps also we can be forensic in the way we look at word problems.
Find The ‘One Thing‘: My friend the late Richard Dunne used to emphasise that hidden in every word problem, however embellished it may be, was a maths story that was only ever about one thing. That thing might be pounds, candles, miles, or whatever, but whatever it might be then becomes the units with which to work, and everything not connected with that is irrelevant. This is an approach that really helps children ‘find the maths’, and one that I have drawn on in my Bar Modelling books and tabletop word-problem cards.
As Zig Ziglar said, and many have copied, “The main thing is to keep the main thing as the main thing.”
Children can then focus just on the information about that one thing, and ignore everything else (rather than the overly simplistic approach advocated by the R.U.C.S.A.C. method of simply ‘underlining key information’ without helping children to decide WHICH information is actually relevant).
Often when I ask children specifically what it is they don’t understand, and get them to read each sentence to me, they understand everything they’ve read. It’s as if they’ve just made an assumption that they don’t get it, and this becomes a self-fulfilling prophecy. So over the past few days I’ve been working on a new theory to address why else children might find word problems so tricky. It boils down to the following observation.
In essence, every word problem contains just two distinct things:
|INFORMATION GIVEN||INFORMATION REQUIRED (THE QUESTION)|
And that’s all. So, my hypothesis is that if we can train children to look at a worded question and then either mentally, or with highlighters, or just with a pencil – that bit doesn’t matter – sort everything into ‘what they’re telling me’ (information given) and ‘what they’re asking me’ (answer required) this might offer a way into “I’m stuck“.
I’m hoping that this way children will habitually begin to see such questions as a transaction between the setter and them, as if the setter is saying: “First I’ll give you some information, and then I want you to give me some information.” Of course, not all the information given may be relevant, (those pesky net curtains of obfuscation again) but at least children will be clearer about the transaction that is expected.
So for the next couple of weeks my response to ‘I’m stuck” is going to be – “Sort first, then if you’re still stuck, ask me again.“
Will it work? I honestly don’t know, but I think it’s an interesting enough idea to explore further, particularly if you have a child or group of children with a strong sense of learned helplessness.
I’d love to hear your most effective strategies for tackling this most frustrating of questions- please leave them in the comments below.