So today I had a bit of a moment in my bottom set year 10 class.
It was our second lesson together, ever, and we were multiplying and dividing by powers of 10. Together, we constructed a place value grid on the board and worked out that if you divide by 100, the numbers move to the right, two columns. During the utterly thrilling session of Multiplying & Dividing by Powers of Ten Bingo, I noticed that some pupils were moving the numbers in the opposite direction to what we had decided on.
They were so used to moving the decimal point that, when we had discussed what direction they go in when you multiply or divide, they applied the direction to the decimal point instead.
At that moment I thought to myself “am I doing the right thing?”.
This class will always find maths a challenge. They will take their linear foundation GCSE at the end of year 10 in order to give them an early bash at it, followed by a re-sit in November of year 11 and then again in June of year 11. I have two years to help them get to grips with the subject and, here’s the crucial bit, I have the opportunity to help them attempt to get a C in Maths.
Should I teach them that the decimal point stays put and the numbers move? Or should I teach them to move the decimal point?
This throws up a massive question over the way I decide to teach these pupils for the next two years. I know that I could teach a ‘certain’ way in order to train them to answer exam questions, but this will be purely instrumental, tricks, rules, methods to follow.
My instinct was to teach relationally, especially as I have two years with them (for the past couple of years I have got yr11 bottom set when they arrived in yr11, so only had one year with them). However, when I realised they were so used to moving the decimal point, I wondered whether I wasn’t just making their life harder by insisting on drawing out the place value grid.
Or can I have a combination? Can I teach them about multiplication and division using a place value grid and then finish off with a “now you know how it works, here’s a quick trick to make your life easier”?
This decimal point dilemma has really got me thinking. What do I want? Pupils with a relational understanding, although this may take longer to achieve and therefore slow down the pace with which we cover content, or pupils who can follow methods and rules who may be able to answer exam questions through training and therefore be more likely to get a C and, thus, more likely to have choices in life. (I am torn, by the way, between ‘helping pupils to get a C in order to improve their opportunities in life’ and ‘not devaluing a C grade by training pupils to achieve it through following rules when they may not really understand it’. Some may say those pupils do not deserve to pass maths, but others may say it is those pupils who need our help more than anyone.)
It makes me uncomfortable and I’m not sure what I want. I know I want to do the best I can for them, so I’ll focus on building their confidence in maths and building trust and rapport with the class. I think I’ll have to work out what is right for them and what is right for us.