Interesting view from Peter Atkins at the RSC Historial Group - don't tell students that there's a lot of hard maths in chemistry.
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@HGourlayUCL @martinvermeer But jsut to continue with this thought, there is so much confusion over significant figures. Schools need to get a grip on this because different subjects/boards put the focus on sig figs or decimal places. Many teachers too are not confident about this, in my view, or rather the deeper meaning of the digits quoted.
These are crucial components of critical thinking that need to be built in very early and not left for university teachers to sort out.@sellathechemist @martinvermeer Experience from school suggests that even where teachers are confident, there's sometimes a 'receptiveness' barrier with students. In one school a student regularly referred to my 'obsession with significant figures' and did not act on advice!
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@HGourlayUCL @martinvermeer Maybe they were thinking of Elon Musk's mole of satellites.
@sellathechemist @HGourlayUCL But seriously, in aerial mapping I have run into the situation where there are two solutions for the location of the mapping aircraft that the iterative (gradient descent) solving of the observation equations converges to, where one of them is underground. One should be able to notice that and choose only the physically realistic alternative...
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@sellathechemist @martinvermeer Experience from school suggests that even where teachers are confident, there's sometimes a 'receptiveness' barrier with students. In one school a student regularly referred to my 'obsession with significant figures' and did not act on advice!
@HGourlayUCL @martinvermeer Yes. I get that and that is because there is little joining of the dots at exam board level. Physics, chemistry and maths all seem to do things slightly different. Maths focuses on decimal places all the time while SF are never properly grounded in the sense of confidence - how much money/chocolate would you bet on the last, the penultimate, the penpenultimate, and so on, figures being correct!
I worry that it's a zombie problem that will keep recurring… -
@HGourlayUCL @martinvermeer Yes. I get that and that is because there is little joining of the dots at exam board level. Physics, chemistry and maths all seem to do things slightly different. Maths focuses on decimal places all the time while SF are never properly grounded in the sense of confidence - how much money/chocolate would you bet on the last, the penultimate, the penpenultimate, and so on, figures being correct!
I worry that it's a zombie problem that will keep recurring…@sellathechemist @martinvermeer I think there are two ideas coming up in this discussion. One is about having a feel for the approximate size of the value calculated. Does this seem about the right size? The second is about certainty/uncertainty. How sure can we be that this value is correct?
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@HGourlayUCL I think one of the most important things we should resurrect and develop is the idea of solving problems by estimation; the Fermi approach. It is a skill for life that needs to sit alongside making up solutions and concentrations.
It's not very sexy but you can take articles out of the newspaper every day and try to make sense of chemistry, physics and more just by running some arithmetic and powers of ten.
Accuracy and precision can then follow further down the road.THIS!! So much!
When I was ~11, our teacher was sick one day and our vice-principal subbed in for her. He said that he had no idea about our lesson plan, so he was going to teach us how to estimate and why.
Probably the most useful hour in maths of my life. -
@sellathechemist @martinvermeer I think there are two ideas coming up in this discussion. One is about having a feel for the approximate size of the value calculated. Does this seem about the right size? The second is about certainty/uncertainty. How sure can we be that this value is correct?
1/ @HGourlayUCL @martinvermeer You've hit on the head one of the things I puzzled with for a long time. How to devise a practical that had "epistemic doubt/uncertainty" (to be as pompous as possible
) built into it. For a long time the response from people was "how will you mark it?" because we assessment looms so large in our thinking these days (KPIs, innit!). It puts the focus on the numerical value of the answer in a perverse and binary way (right vs wrong). -
@HGourlayUCL I think one of the most important things we should resurrect and develop is the idea of solving problems by estimation; the Fermi approach. It is a skill for life that needs to sit alongside making up solutions and concentrations.
It's not very sexy but you can take articles out of the newspaper every day and try to make sense of chemistry, physics and more just by running some arithmetic and powers of ten.
Accuracy and precision can then follow further down the road.@sellathechemist @HGourlayUCL
Had an 'orders of magnitude' exercise in my #carbonliteracy courses for just this reason (didn't call it that! But a shockingly useful recap of units, tens, hundreds and so forth in a picturecard sorting game:) -
1/ @HGourlayUCL @martinvermeer You've hit on the head one of the things I puzzled with for a long time. How to devise a practical that had "epistemic doubt/uncertainty" (to be as pompous as possible
) built into it. For a long time the response from people was "how will you mark it?" because we assessment looms so large in our thinking these days (KPIs, innit!). It puts the focus on the numerical value of the answer in a perverse and binary way (right vs wrong).@sellathechemist @HGourlayUCL @martinvermeer I have senior (~17yo) students help out with my technicianing. I always encourage them to have a rough idea of the result before they calculate. "Dilute this 3.85M acid down to 1.2M. Well, that's basically 4M down to 1M, so we know it should be in the 25% ballpark." Catches so many order of magnitude slips etc.
I also tell them that being 10/100/1,000 out is great, there's probably a simple decimal place error. There always is. -
@geomannie @gemlog @sellathechemist @HGourlayUCL
There is an OCW MIT course about estimation: https://ocw.mit.edu/courses/18-098-street-fighting-mathematics-january-iap-2008/
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THIS!! So much!
When I was ~11, our teacher was sick one day and our vice-principal subbed in for her. He said that he had no idea about our lesson plan, so he was going to teach us how to estimate and why.
Probably the most useful hour in maths of my life.@gemlog @sellathechemist @HGourlayUCL We were taught to estimate so as to check our "properly" calculated answers for sanity. The idea was to prevent the kids from turning the handle and writing down a calculated answer that was an order of magnitude out without noticing that there was anything wrong with it.
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