The rounding pandemic
Today, during my further maths AS class, I had an extremely worrying experience. One of the students made a glaring error in rounding, but had been taught that way!
The student in question is in Y13, and has picked up Further Maths as an extra AS level. She is averaging an A over her first 3 modules (C1, C2, and D1) so is certainly bright and good at maths, so what was the problem?
The question they were solving was a mechanics question and required them to round the answer to 1dp. The answer they had to round was 6.14463. The student wrote 6.2. Obviously I said, “just check your rounding there,” so she did. And replied “I have, still 6.2”. To say I was surprised would be an understatement so on asked her how she had got her answer.
She said: “6.14463 you look at the 3, it’s under 5 so you leave the 6, that’s over 5, so the 4 rounds up, that puts that to a 5, so the next 4 rounds up which makes that a five so the 1 rounds up giving 6.2 to 1 decimal place.”
I was aghast and open mouthed, as were the entirety of the class. She asked “what?” I asked if she was sure that hoew you rounded, and she told me yes, that’s definitely how she’d been taught. (Not at our school, I hasten to add, she joined at the start of Y12).
I calmly stated, “but rounding to 1dp is the same as rounding to the nearest tenth,” I saw the lightbulb come on in her eyes, she looked at her page and exclaimed “oh, how could I be so stupid?!” I then asked how she thought people rounded pi as there was an infinite number of digits, at which point she just said, “I have no answer, I can’t believe I never questioned that, it is so obvious.” I didn’t even need to prove it via basic subtraction.
This worried me, I knew that one of my KS4 pupils had attended that school, so I sought him out and asked if he’d been taught to round there. He had, and the same way as the yr13 had. This in itself was very worrying, I mentioned it in the staffroom and was met by shock and disgust, but one of the supply staff told me that earlier in his career he’d taught it wrong and that everyone in the school he had worked in at the time had done it that way. Another member of staff said her daughter had been taught wrong at a different local school, another said they’d seen a resource online that had it that (the wrong) way and a Y12 student had been taught wrong at her previous school which was out of the area.
The whole episode has left me with a few thoughts. How have so many maths teachers entered the profession with an inability to round? Why hasn’t this been picked up? Why are pupils blindly learning this without question? We need to be creating independent thinkers! Are there any other areas of maths being taught wrong on this sort of scale?
If you are ever looking for a topic to give for an interview lesson, do yourself a favour- choose rounding!
cavmaths 
First time I ever corrected a teacher! Launton Primary School, ca. 1989. He was doing it WRONG (like your students), I tell you. Lucky I didn’t know the Mathematical Ninja back then, Mr Hawkins wouldn’t have known what hit him.
I actually can’t fathom how educated people can get it wrong!
Carelessness, thoughtlessness. The twin enemies of the Mathematical Ninja!
Reblogged this on The Echo Chamber.
Is anybody going to raise the obvious issue here that a lot of maths teachers don’t have maths degrees? In recent years the rise of “conversion courses” means that many have a background that isn’t in the least mathematical.
I wholeheartedly agree that more maths teachers should have maths degrees. I have one, and I remember while training being shocked that there were only two of us on a PGCE course of 30+ that had maths degrees. Some of the degrees you see have maths involved (ie Engineering, OR etc) and that makes sense, but some seem to have none at all (there were some with straight language degrees…) however, in this case I’m not sure that is the issue, I would expect any teacher, Maths or not, to be able to round. Surely it’s a fundamental skill?!
Just to play devil’s advocate: I’m pretty sure one wouldn’t need to know how to round to get a maths degree – in my arbitrary system for dividing topics, it’s a numeracy skill rather than a mathematical one, and I’m sure one could get through a maths degree without ever having to touch a decimal point. (Thinking about it: my real introduction to teaching – say – trig was in the physics classroom, not the maths one.)
I think there’s such a gap between academic maths and GCSE that I’m not sure a maths degree is necessarily /that/ much of a help in the classroom, and certainly no more help than a quantitative science one.
Indeed, quantative scince ones would be fine, it’s the ones with no maths elements at all that are worrying. Especially when often teacher have only chosen maths as there is a bigger bursary, and they really don’t like the subject!
I don’t think it’s ‘that’ surprising. The whole profession is littered with tricks and shortcuts that are shown to students to get them to pass exams. It is bound to end up in a massive game of Chinese whispers.
I was teaching my A2 class just today and they were revising Partial Fractions and when get the common denominator of the A and B terms they blindly used that annoying cross multiplication trick a lot of students seem to have been taught when working with numbers. All 7 of them did exactly the same thing and had notated the X on their work as their method.
No substitute for teaching the why along with the how, or even trying to contextualise it in some way ala ‘tenths’.
Still your example is pretty heinous by any standards.
Aye, I certainly agree with you on all points, I’d love to see this obsession with tricks wiped out. I often see that problem with year 13, when the denominators is quadratic and the other is linear and a factor, they blindy do it and miss the fact that one is a factor of another and enf up with cubic denominators.