Wednesday, September 13, 2017

More Than One Way to Crack an Egg

Last week I posted this photo onto my Twitter account and it received a lot of interest:
I often am asked to help out with the initial Math assessment for students who have come from different countries into our board. These were two solutions from two different students, both from Vietnam. The first thing that struck me was that these methods were completely new to me:
Many folk agreed. Others still wondered why these methods were chosen. I agreed with Matt Dunbar that my preferred method would be this: 
My mantra has always been: 'First, isolate the variable'. Yet this is not what these students did. Other folk wondered, in the case of the student on the right, what the student was thinking:
So this week, I happened to see this student again and asked him if we would be happy to do some more questions for me. Fortunately, he was happy to help! Here's the first question I gave:
OK, so this tells me that his very first solution wasn't a one off: this 'first get-a-common-denominator' approach is a go-to strategy for him. I next gave him this question:
So now I see he is also paying attention to the numerator of the fraction in the first line. But still, he uses the 'first get-a-common-denominator' approach. I was now curious as to what he would do with a simpler equation:
So in this case, he does isolate the variable first: verrrry interrrresting! But now I want to see what he does when there is more than one denominator:
At this point, I am grinning like a Cheshire cat. What a neat way of solving this! When I asked him if everyone learns this method in his Vietnamese school, he replied that they did. So I showed him how I would have solved these (isolate first, then get rid of the denominators) and it was nice to see him smile and nod and say "Cool!"
I love it when I see something new like this. It reminds me that what we take for 'standard' here might not be standard everywhere. That doesn't mean to say that I will change the way I do these types of questions myself (I still like 'my' way!) but knowing that there is more than one way to crack an egg will help me as a teacher help students who might not get 'my' way.


  1. Although alternative methods are of merit & interest (as long as pupils are correctly applying inverse operations) ... I would discourage pupils (like this one has) from reducing their number lines of working ... this is how errors may occur with + or - signs/operations. Also a method that undoes the equation in the order in which it was constructed is IMHO best practice. Bear in mind that these alternative methods may become their method of choice and when we move onto problem solving or into higher topics (eg solving simultaneous equations) these alternative approaches may not be the most apt ... which is why I recommend encourage pupils master the method I supplied an image of ... which you have kindly reproduced. Matt Dunbar

  2. Thanks ver much for our comments Matt. You've got me thinking about situations in higher topics when this method would not be the most apt and also when 'our' method might not be the most apt: i haven't got the answers yet but I am thinking;-)! As for showing your working out I certainly am in favour of this being shown clearly as in your example especially when students are beginning to learn these techniques. That being said, once this has been mastered (as this student clearly has) I myself feel that the work he has shown is sufficient. But I would be interested to know what other people think.
    Thanks again,