I recently asked this question of my Year 7 class. We were working on measurement and I thought it’d be a fairly easy introduction to the world of units of measurement.
“no, no no. 7 metres?”
Yikes. Clearly my students hadn’t really grasped the visualisation of units before this point. They seemed OK with telling me how many this were in that, and even which units to use for different distances. But actually picturing a metre? Not so great.
So I gave them a starting point : the height of a door is just over 2 metres.
“Do i have to stoop to get through the door?”
Nobody really noticed, so I went through the door again.
“ooooh, OK, 2 metres”
“Did my head nearly touch the top of the door frame?”
“maybe a bit less than 2 metres”
Close enough. I’m 1.88m tall. This whole exercise really struck me, and had me really re-evaluate what I prioritise in teaching. I’ve often spent a lot of time on conceptual understanding, and embedding skills, which will never change, but what I don’t do nearly enough is get students to estimate.
I’m not even sure I know why. When I think back to all the really, REALLY silly answers I see sometimes from students in any year group, and I found myself saying “can’t you SEE that your answer cannot be even nearly right??” I should really have done a little more self reflection. Classic examples like negative perimeters, negative areas, the mean of a data set that is over 30 times larger than any value in the data set, single angles inside triangles that go way over 180 degrees, pretty much any calculation involving a negative number, I could go on and on.
I accept that part of the problem is that students get so engrossed in the calculation, that when they get to the answer they’ve completely forgotten the context of the answer, and therefore the sensibility of the answer.
But there’s a lot more going on here too.
How often do we get students to answer questions such as
“what will the answer look like?”
“will the answer be bigger or smaller than x?”
“which of these answers is likely and why?”
“how do I know that the answer will not be more than y?”
“which direction will that go in and why?”
This exploration of where the answer will likely take us, and a narrowing down of the area in which it will reside, is crucial to aid our students. I don’t do it enough.
Since that day I have started to incorporate estimation questions in worksheets and class discussions for a whole range of topics. Not just measurement, where it sits quite comfortably, but also areas, algebra, plotting, you name it. I’m trying to enhance their general number sense and reduce the amount of ridiculous answers that seep into lessons.
A great example is when working with circles. Put those calculators away, but don’t put your answer in terms of pi. Give me an estimate.
I fully recommend the website estimation180.com to use in starters / morning registration time to help aid student visualisation and general estimation skills. Here are a couple of questions from that site: