[Maths-Education] Fw: Mathematics education and Covid

[Ernest, Paul]

Dear Colleagues

This (below) might seem trivial  --  and you will have spotted it - but I think it is still worth saying and provides us with educational opportunities

Best wishes to all - and keep safe

Paul

_________
Paul Ernest
Emeritus Professor, Education, Exeter University, Exeter, EX1 2LU, UK
Homepage <https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.people.ex.ac.uk%2FPErnest%2F&data=02%7C01%7CP.Ernest%40exeter.ac.uk%7Cbc8f81cc9a2d46864bdf08d7f9b8da7c%7C912a5d77fb984eeeaf321334d8f04a53%7C0%7C1%7C637252444661410045&sdata=9sTsuvQGwQT45kk%2BPYBObCGRciOXnCz6aNnFi%2BhdGQc%3D&reserved=0> http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/<https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fsocialsciences.exeter.ac.uk%2Feducation%2Fresearch%2Fcentres%2Fstem%2Fpublications%2Fpmej%2F&data=02%7C01%7CP.Ernest%40exeter.ac.uk%7Cbc8f81cc9a2d46864bdf08d7f9b8da7c%7C912a5d77fb984eeeaf321334d8f04a53%7C0%7C1%7C637252444661410045&sdata=EphmMfdz0VCAg9e2iDm%2F98yGp5%2FrIhptnM89Lngrkw4%3D&reserved=0> The Philosophy of Mathematics Education Journal
Memories of a misspent youth  https://sites.google.com/site/witchescauldron60s/home<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fsites.google.com%2Fsite%2Fwitchescauldron60s%2Fhome&data=02%7C01%7CP.Ernest%40exeter.ac.uk%7Cbc8f81cc9a2d46864bdf08d7f9b8da7c%7C912a5d77fb984eeeaf321334d8f04a53%7C0%7C1%7C637252444661420041&sdata=lZD7JGxkFX2IFW9IZGood40qhFHEQo7Gnk7b1sx3vLA%3D&reserved=0>




Why the maths behind covid alert levels makes no sense<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Ftheconversation.com%2Fcoronavirus-why-the-maths-behind-covid-alert-levels-makes-no-sense-138634&data=02%7C01%7CP.Ernest%40exeter.ac.uk%7Cbc8f81cc9a2d46864bdf08d7f9b8da7c%7C912a5d77fb984eeeaf321334d8f04a53%7C0%7C1%7C637252444661420041&sdata=u%2F517przcCATT5NEt1pDiMDbrYez9s2RnOG9ndWicPE%3D&reserved=0>

Will de Freitas, has written a piece explaining why the maths behind covid alert levels makes no sense<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Ftheconversation.com%2Fcoronavirus-why-the-maths-behind-covid-alert-levels-makes-no-sense-138634&data=02%7C01%7CP.Ernest%40exeter.ac.uk%7Cbc8f81cc9a2d46864bdf08d7f9b8da7c%7C912a5d77fb984eeeaf321334d8f04a53%7C0%7C1%7C637252444661430036&sdata=x8CfD9FdMmOL%2FMb2XsvslJglPJPltNaP4jLD227RPTs%3D&reserved=0>. He critiques the Government’s ‘mathematical models' of Corona Virus. He shows that there are problems with the meanings of the 3 slides used to model the dangers of  Covid-19, and our response to it. In the Government’s slides, there is a central equation CAL = R + N.

As Will de Freitas, correctly points out – the units on the LHS and the RHS do not match up.  CAL is a discrete number in the range 1 – 5, so it is a non parametric statistic. Whatever R + N is, it is not of the same kind, being mostly made up of a (large) number of persons. But there is a deeper problem and misunderstanding in this equation. Rates are fundamentally multiplicative terms, so if the RHS of the equation was RxN it would mean something. If 100,000 people are infected (N = 100,000), and R = 1.5 (or 0.5)  then RxN = 150,000 (or 50,000) meaning that 100,000 people each infect 1.5 (or 0.5. persons, respectively) each leading to 150,000 (or 50,000) new cases.

But as it stands the value of R + N  has a value (for large N)  about that of N (100,001.5 or 100,000.5  respectively). To misunderstand rates as additive rather than multiplicative is elementary and widely noted among  young children who have not made the step to Logical Reasoning, in Piagetian terms. It is rather alarming coming with the full authority of HM Government and the NHS.

The misleading use of mathematics to back up the presentation of the Government's Covid Strategy was termed “number theatre” by David Spiegelhalter. My point here is not a political one, just that it is worrying that no one in No. 10 either spotted the errors, or if they did, did not care for their inaccuracy. For it is well within the grasp of a normal school child to identify the errors and absurdities in the presentation. This provides us with an opportunity that can be exploited in education.  The concept of R, the rate of spread of the infection indeed presents a useful concretisation of ratio and proportions which can be exploited in the teaching of these ideas.

References

Will de Freitas, why the maths behind covid alert levels makes no sense<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Ftheconversation.com%2Fcoronavirus-why-the-maths-behind-covid-alert-levels-makes-no-sense-138634&data=02%7C01%7CP.Ernest%40exeter.ac.uk%7Cbc8f81cc9a2d46864bdf08d7f9b8da7c%7C912a5d77fb984eeeaf321334d8f04a53%7C0%7C1%7C637252444661430036&sdata=x8CfD9FdMmOL%2FMb2XsvslJglPJPltNaP4jLD227RPTs%3D&reserved=0>, In The Conversation at https://theconversation.com/coronavirus-why-the-maths-behind-covid-alert-levels-makes-no-sense-138634<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Ftheconversation.com%2Fcoronavirus-why-the-maths-behind-covid-alert-levels-makes-no-sense-138634&data=02%7C01%7CP.Ernest%40exeter.ac.uk%7Cbc8f81cc9a2d46864bdf08d7f9b8da7c%7C912a5d77fb984eeeaf321334d8f04a53%7C0%7C1%7C637252444661440031&sdata=R0qUb8QvNWiSCMTMEeAEeaHgAWhAy6ls%2B30gnbda3po%3D&reserved=0>, retrieved 16 May 2020.

Anjana Ahuja, Boris Johnson’s Covid-19 threat alert system is a parody of mathematical precision, New Statesman online, at https://www.newstatesman.com/science-tech/coronavirus/2020/05/boris-johnson-s-covid-19-threat-alert-system-parody-mathematical<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.newstatesman.com%2Fscience-tech%2Fcoronavirus%2F2020%2F05%2Fboris-johnson-s-covid-19-threat-alert-system-parody-mathematical&data=02%7C01%7CP.Ernest%40exeter.ac.uk%7Cbc8f81cc9a2d46864bdf08d7f9b8da7c%7C912a5d77fb984eeeaf321334d8f04a53%7C0%7C1%7C637252444661440031&sdata=Bu1yapgDw7YDJHWEdZMF0FoXjlyIE1VmLvmRGauDXZA%3D&reserved=0>, retrieved 16 May 2020.

 [cid:d2d99efa-e54e-42da-b56d-64d37c7124a3] [cid:1364c71c-162e-40a3-b2cb-39b0721c0990]

________________________________
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Cornona 1.jpg
Type: image/jpeg
Size: 27243 bytes
Desc: Cornona 1.jpg
URL: <http://lists.nottingham.ac.uk/pipermail/maths-education/attachments/20200516/a73d8e38/attachment-0004.jpg>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Cornona 2.jpg
Type: image/jpeg
Size: 14629 bytes
Desc: Cornona 2.jpg
URL: <http://lists.nottingham.ac.uk/pipermail/maths-education/attachments/20200516/a73d8e38/attachment-0005.jpg>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Cornona 1.jpg
Type: image/jpeg
Size: 27243 bytes
Desc: Cornona 1.jpg
URL: <http://lists.nottingham.ac.uk/pipermail/maths-education/attachments/20200516/a73d8e38/attachment-0006.jpg>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Cornona 2.jpg
Type: image/jpeg
Size: 14629 bytes
Desc: Cornona 2.jpg
URL: <http://lists.nottingham.ac.uk/pipermail/maths-education/attachments/20200516/a73d8e38/attachment-0007.jpg>