#### Untitled Test Box

1. Screws come in packets of 30. Each bracket needs four screws. What will one packet of screws be enough for?

A: 6 brackets with 3 screws left over; B: 7 brackets with 2 screws left over; C: 7 brackets with 3 screws over; D: 8 brackets exactly

2. Hasran has planned a new TV cupboard. A TV is 40cm wide and will sit in the middle of a shelf that is 900mm wide. How wide is the gap on each side of the TV?

A: 10cm; B. 25cm; C. 43cm; D. 50cm

3. Match these discounts (1-3) with the following labels, A-D:

1. £300 reduced to £180

2. £240 reduced to £160

3. £350 reduced to £280

A. Amazing 1/3 off! B. Massive 20% off! C. Slashed by 30%! D. Reduced by 40p in the £

The level of numeracy in the adult population of Britain is dire.

I do not confuse numeracy with maths, which is a bigger subject. I do not think quadratic equations are part of numeracy, nor geometry, algebra, trigonometry, topology, set theory, number theory and calculus. I do think competence at reading and precision of understanding are part of—or a requirement for competence in—numeracy. I see numeracy as being among the topics at the centre of what we assume is general competence, what we accept as adequate education. I do not think we are achieving this.

Evidence at [4] says in 2012 we had 49% of the adult population, some 17 million people, with no better than the numeracy expected of an 11-year old. Does numeracy decay, I wonder? Could it be that failing to practise any facility with numbers makes the situation worse? Is it fashionable to be 'bad at maths' and *therefore* incompetent with number? Not that I agree with the 'therefore' at all, you understand: I continue to see the problem as an imprecision with thinking, consequently imprecision in speech and from there an acceptance that this means numbers are not used to express any idea, simply because that would require a level of precision on framing the thought (concept, idea, even just sentence) that is several steps too far.

A poll carried out for the new charity of 2,000 adults by YouGov found that while 80 per cent would be embarrassed to tell someone they were bad at reading and writing, only slightly more than half (56 per cent) would feel ashamed to say they were bad at maths. [4]

Would you be put off by a job description that includes something suggesting that handling data and an assumption that you can cope with the associated numbers? What level of maths (including numeracy) do you think a would-be primary school teacher must have to join a course? Would you assume that yours is at least as good as that? How could the school system have served you better? I found a you.gov survey that drew conclusions from asking whether as a parent you were or would be proud of your child if it was good at English or good at Maths (and by the ages indicated, they meant numeracy). Try it:

Which makes you prouder as a parent, being told that your child is good at English or good at Maths?

But the survey didn't allow you to simply expect, or to reflect that opinion based on how hard the child had worked at it, nor did it ask if your opinion was based on your own competence or lack of such. As a definitely numerate person I too would have chosen English of the forced choices; as parents we demanded clarity of thought from our children and all of us spent more time working on having the best command of language we could than we did on our assumed competence with number. For us, numeracy was equivalent to something like spelling; of course we could do it. As for meaning *maths *rather than numeracy, all of us have quite enough to run our lives with success plus enough sense to know when there might be need to take a problem to someone with better maths.

For a first pass at thinking about changing maths at school, look at [3]. I don't think it goes far enough, nor do I think it provides a route that continues to supply us with engineers, but I do think it points at the opportunity that we have (essay 291 *et al*) to rethink what we want as the minimum acceptable education.

I do think—and please recognise I taught a lot of maths, mostly at the 'hard' extreme, but also trying to stimulate Y8-10 kids into seeing some point in being able to sort out issues with numbers included—we could dramatically change what we expect in terms of precision of reading. What is often labelled critical thinking but really means precision *reading* is so easily recognised as the same set of difficulties as many people have with what is called school mathematics but mostly is precision reading attached to some number handling. We might even recognise that the use of number in such a context is what provides the recognition of a 'right' answer, where words so often fail to provide the same simplicity.

Page 6 of [2] starts You are paid £9/hour and receive a 5% pay rise. What is your new rate of pay? I think, at about the same time as I see the ? symbol, £9 x 1.05 = (tiny pause) £9.45, but that answer is followed by "What causes this to be expressed as a percentage?" and other consequential imaginings, when someone being given a rise probably wants to work out if 5% will make an appreciable difference. But my fast answer demonstrates a load of buried knowledge, not least knowing what to do with 5% (add it to the 100% given, to make 105%, which means a multiplier of 105/100=1.05) and then, for all those whose 'maths is bad', where's a phone to do the arithmetic?

Q1 If you do 2000 hours a year, how much more money does that 5% above represent? (how many would shy away from such a question?) A 2017 you.gov survey showed that close to a quarter of adults got the above question wrong, even with a calculator on offer. ¹

A study I reference at [5] looked at *financial* literacy and the UK rates below the average, notably in knowledge (they were not that bad in behaviour or attitude). Much of the poor response (only 56% of all participating scored the acceptable minimum five or more out of seven). Questions here in blue, where words were changeable for national context and I've shifted to sterling:

Q2 Imagine that five siblings are given a gift of £1000 in total. If they are to share this equally, how much does each one get?

Q3 Now imagine the <siblings> (children, brothers, sisters) have to wait for one year to get their share and inflation stays at x% then <range of multiple choice positions>. Your Q3; They have to wait a year for their share at 5% per annum inflation; how much does one share represent right now to the nearest £10?

Q4 You lend a friend £25 and he gives you £25 back tomorrow, How much interest has he paid on the loan?

Q5a You put £100 into a savings account (no fee, no tax) which has a guaranteed return of 2% a year. If you make no further transactions in or out, how much will there be in a year after the interest is paid?

Q5b ... and how much at the end of five years? Multiple choice responses include £110, £110.41, £110.25, £127.63 and 'something else'.

Q6a An investment with a high return is likely to be high risk. True or false?

OR Q6a' If someone offers you the chance to make a lot of money it is likely that there is also a chance you will lose a lot of money. T/F

Q6b High inflation means the cost of living is increasing rapidly True/false?

Q6c It is usually possible to reduce the risk of investing in the stock market by buying a wide range of stocks and shares. T/F

You are less likely to lose all your money if you save it in more than one place. T/F [7 questions: Q2,3,4,5, 6a, 6b, 6c]

Source [6] is an (the?) OECD 2019 report on Adult Skills and is well worth reading in its entirety if you're in adult education. It is pretty damning about current youth too, since most other countries show a marked improvement in (all sorts of) skills with age. It is not good that UK numeracy is the same in the 55-65 bracket as it is in the 25-35 bracket. That's two groups unequal in education and a generation apart: for the UK the older group has about 30% with any tertiary education and 35% without proper secondary education (so they left school at 16 or earlier), while for the younger group those figures are dramatically better, close to 50% and about 15%. Yet their numeracy is very similar; that is awful.

The OECD report divides literacy into five levels, which read to me very like standard deviations from the mean, such that 2 and 3 are -1σ and +1σ, levels 1 and 4 are 2σ from the mean and levels 0 and 5 are more than 2σ from the mean. This makes levels 4 and 5 definitely competent in language and in differentiating subtleties, recognising rhetorical clues and able to make high-level inferences. I may fail to reach level 5 myself, though I hope not. Within this scale, England rates a little above the OECD average, adjacent to the USA. Table shown to the right; read the OECD average (mean) line as showing half of people at levels 3 and upwards and 10% at levels 4&5. See pages 43-47 of [6].

Numeracy is rated in a similar way, pp48-53. Here, England is very similar to the OECD average (not good). Now it is quite clear that a low ability to read will affect any ability to score on numeracy testing, so it is well worth looking extensively at those who score badly in both skills. Again, England is pretty typical (i.e., close to the OECD average, with something over 25% at or below level 1 in numeracy and perhaps 15% at or below level 1 in both literacy and numeracy. Japan has around 9% only below level 1 at anything. These people are referred to as 'low performing'.

There is a third category, proficiency in technology-rich environments. Around 25% of people failed or opted out of the computer-based assessment and the remainder was divided much as before across four levels 0-3 such that level 3 is 5% (>2σ) of the whole; the description of the content leaves me feeling I might not qualify, simply by not being current with whatever software is deemed 'expected'. However, England (separated from UK) as a whole scored very well, with what seems to me to be 35% (fig 2.16) of its population scoring at the top two levels, 2 and 3, maybe 15% in the 'failed or rejected' category. Note that this leaves 50% at and below whatever level 1 indicates. This is one occasion where Japan, so very good on the other measures, looks not at all good. Finland scored very well in all categories.

Adult numeracy in Britain is measured [7] using levels in, I think, the standard European meaning, such that level 2 is an accepted 'good' GCSE pass grade 4 and better or, on older units, grade C and better. Level 1 is then grades 3-1 and D-G. But this, please note well, is grades from testing in *maths*, not *numeracy*. Below this we have three 'entry levels' where No1 is equivalent to age 5-7, No2 fits ages 7-9 and No3 fits ages 9-11. [7] shows this. Visit [2] to explore; I found this a bit tabloid, but maybe that is necessary. [8] gets you to the National Numeracy 2019 Impact report. 49% of of British adults classify as entry level; I see that as terrifyingly bad.

So what could we do about this? In primary school we need to focus on numeracy without drifting off to secondary maths, At least, where that occurs we must cease thinking this 'maths' is still numeracy; numeracy is not a substitute label for mathematics. What we clearly need is for the standards of numeracy to be very much higher, such that perhaps secondary education does not need to repeat that work as extensively as it has need to; we do not make very much progress when forever repeating content. Yes, there are topics within secondary numeracy—such as estimation, precision and error handling—that might have a better place with older students simply because of being better readers, but since we have such a high proportion of the population who are provably awful at anything involving number, this has to be improved. So I am not saying that numeracy is something that is only done at primary level, nor am I saying that no maths (yes, I meant *maths*) should be done at primary level; I am saying these need to be recognised as different, even as they overlap. Heavens, the overlap in requiring reading to be precise doesn't demand that we call "maths' English, does it?

Outside school we must offer all sorts of routes to improved numeracy. As a nation we set targets in 1999 and in 2019 had made no appreciable progress. None. The 2019 report at [8] provides several uncomfortable findings. Here are three such, awful comments:

• A quarter of adults have 'acceptable numeracy', while a half match those of primary children. Awful.

• The cost of poor numeracy is valued at £388 million, while business leaders estimated this at £7 million.

Read that again: The cost of poor numeracy is valued at* £388 million*, while business leaders estimated this fifty times less. Wait for it; £388 million? once? No: those are *weekly* figures. ²

• Confidence with numbers is the dominant factor in scoring at numeracy. I am surprised; I expect the dominant factor to be sloppy reading. Believing that you can improve is [shown to be, repeatedly] the biggest factor in actually showing improvement. Again, hard to believe.

[A] lack of numeracy skills has in the past been linked to lower wages, higher unemployment, social problems, school exclusions, truancy and crime. [10, p10]. That's ammunition for any politician; detail, perhaps? I'll let you look.

Looking further at costs, the cost of having poor numeracy, via [10], costs can be considered in the areas of employment, health, crime, financial planning, and skills transfer from parents to children. The financial planning topic is nicely covered by the financial literacy report.

DJS 20200315

small edits, mostly typos, 20200403

Subsequently, during Covid-19 lockdown, I came across a campaign (keywords Wolfram, Mathematica) for a change in our approach to maths teaching. This argues for a lot more computing power and a lot more context as persuasion that this is worth understanding. It reads as such a commercial application (a piece of marketing) that one is (was, has been repeatedly) largely put off exploring further, in the sense that one needs to be committed to change before exploring further, where my perception is that we (all) need to be persuaded first that change is necessary and desirable. Sources after [10] apply. The more I read of this, the more I felt that algebra was going to become a specialist skill, rather than hold the central place it has at the moment. But this has happened to (geometric) proof within my lifetime and we don't seem to have noticed the lack. Or, if we have, not enough to bring it back.

[1] https://www.kcl.ac.uk/policy-institute/assets/national-numeracy-day-2019.pdf

[2] https://www.nationalnumeracy.org.uk/sites/default/files/nn124_essentials_numeracyreport_for_web.pdf

[3] https://www.tes.com/news/we-should-give-students-choice-numeracy-gcse-even-if-it-replaces-maths-some

[5] https://www.oecd.org/finance/oecd-infe-survey-adult-financial-literacy-competencies.htm

[6] https://read.oecd-ilibrary.org/education/skills-matter_1f029d8f-en#page9 to read *Skills Matter *online

[7] https://www.nationalnumeracy.org.uk/what-do-adult-numeracy-levels-mean

[8] https://www.nationalnumeracy.org.uk/sites/default/files/nn180_2019_impact_report.pdf

[9] https://www.nationalnumeracy.org.uk/numerate-nation full report https://www.nationalnumeracy.org.uk/sites/default/files/building_a_numerate_nation_report.pdf

[10] https://www.nationalnumeracy.org.uk/cost-outcomes-associated-low-levels-adult-numeracy-uk-2014

full report 2014 t https://www.nationalnumeracy.org.uk/sites/default/files/pbe_national_numeracy_costs_report_11mar.pdf

[11] https://www.wired.com/2016/10/meet-new-math-unlike-old-math/

[12] https://www.theguardian.com/education/2014/feb/23/maths-teaching-revolution-needed-conrad-wolfram

[13] https://www.nousgroup.com/uk/insights/magic-maths-future-nous-conrad-wolfram/

1 YouGov June 2017. 23% of respondents answered incorrectly or ‘don’t know’. Three everyday maths questions were asked and 5 out of 6 respondents (83%) failed to answer all three correctly.

2 Where did these numbers come from? The 7 million from a YouGov survey, the £388m/week was from In 2014, Pro Bono Economics estimated the cost of poor numeracy to the UK economy to be £20.2bn per annum. This is £388m per week. The thinking assumes that the wage penalty for being below the Level 2 group (GCSE D-G) is about 9%. This leads to £20.2 billion not generated and so lost to the economy each year. So that assumption excludes those who cannot reach grade G; it assumes that the maths grade is a measure of numeracy (definitely not true), it implies that all of this group could have been moved to the higher classification, not that the grades themselves would move. This does not define a minimum acceptable standard, it does not measure numeracy and indeed it serves to confuse the issue by not being clear what the problem is. The National Numeracy campaign suggests that the underlying problem is to do with confidence with numbers, quite possibly a problem created way back at primary levels, possibly (my thought) because this is so easily categorised as having binary states, right and wrong. If Wrong=Failure rather than some part of a learning process requiring testing and adjustment (what a lot of learning is), then this is Wrong Process and Bad Teaching.

Writing essay 310 I found a better source explaining numeracy decay.

**Untitled test box** (not a text box) answers: 1. B 30=4x7+2 2. B mixed cm and mm 3. C doesn't apply (1-D; 2-A; 3-B) [4]

**Q1** We know from the previous answer that 5% of £9 is an extra 45p per hour, (9x.05=0.45) 2000 hours@£0.45 = £900. I'll bet some wonder if I have the zeroes right; roughly half a £ per hour, so about £1000, so £900 is right.

**Q2** £1000/5=£200 (not included in the 2016 score, treated as a warm-up question.)

**Q3** £200 / 1.05 = £190.48. An adequate method is to say the £1000 goes up to £1050, so the current value of £1000 in a year is close to £950. So one share is £190. Objective to show that inflation affects purchasing power. UK 38%

**Q4** Duh, none. In some countries interest is forbidden, hence why the question is so framed. UK 83%

**Q5**a Duh again, £102. Multiply by (100%+2%) = 102% = 102/100 = 1.02

and **Q5**b £100 x 1.02⁵= £110.41 5% for two years is £110.25, 5% for 5 years is £127.63, rounding up. Multiple choice options only require the recognition that the answer is a little more than the* simple interest *answer of £110. Maybe (my additional) offering £110.25 as a possible answer is wrong? UK 36% for a&b together, 57% on just 5a, 52% on just 5b

**Q6** a) true, true, b) true. c) true and true. Establishes an understanding of a relationship between risk and return, of inflation as a term, of the benefits of diversification. UK: 74%, 80%, 52%.

Yes, I got all of these right 6 (and 13) weeks later in a very short time and needing no calculator. So the brains haven't rusted all *that* much. I just wish my typing was more accurate; my fingers are dyslexic. The missus, on the other hand, cannot understand or do Q3 at all and misread Q1 and Q6 though she only got 6c wrong. So she got 5/7 as 'expected', but followed my expectation that it was the reading that was the problem, nothing about confidence or knowing what to do with numbers.