Picked up a copy of Alex Bellos’ book, *Alex’s Adventures in Numberland*. Readable, observant, well-written.

I learned some new terms …

If I focus on a group of 5 carrots, I’d be thinking in **Cardinal** terms. If I were counting from 1 to 20 , I’d be thinking in **Ordinal** terms. (p23)

*pug – xep xep – ebapug – ebadipdip – pug pogbi*

*The Munduruku count ‘one’, ‘two’, ‘threeish’, ‘fourish’, ‘fiveish’. (p34)
Their words for the numbers one to five have as many syllables as the number up to four, then drop off – does 5 become a handful? A bunch? A pinch?*

**Logarithmic** **thinking** is the ability to compare ratios rather than quantities, figure out best odds in a survival situation, and linear thinking – the kind of thinking we use when we contemplate numbers in sequence. We think differently when counting and comparing. (Bellos, pp 19 FN ref to p 190) Wow!

It reminds me of *38 Parrots, *a classic Russian cartoon featuring a group of jungle friends – a snake, a monkey, a parrot and an elephant . In one episode, the elephant asks, ‘how many nuts do I need to pick to make a huge pile?’ … after some ordinal / cardinal to-ing and fro-ing, the monkey provides the definitive answer .. ‘lots’. It’s not so much the words, but the complete conviction with which they are uttered that makes the statement so compelling.

*We put so much emphasis on training cardinal and ordinal perceptions of number yet we instinctively use logarithmic thinking to get through our daily lives – time passes slowly when we’re bored, it rushes when we’re having fun. It ceases to exist when we’re in the zone / groove. Perspective changes the size of objects, although the distance between them is the same. We can process this without a problem. I can tell without counting the floors in a building whether I want to take the stairs or the lift and estimate how long it’ll probably take. *

*I think this explains the success behind many advertising and marketing strategies – they target the logarithmic parts of our brain, bypassing the cardinal / ordinal functions. Wow!*

*Would an awareness of and increased familiarity with these thought modes make us less gullible? I believe it might – just have to devise a few exercises to address this.*

Bellos points to a recent study (Only referenced as a 2008, John Hopkins University and Kennedy Krieger Institute collaborative study and not listed in the bibliography. It really annoys me that editors are paid good money to edit books and get away with substandard work in so many books that are published nowadays) that shows ‘a strong correlation between a talent at reckoning [logarithmic thinking – guessing whether there are more blue or yellow dots in different groupings] and success in formal maths. The better one’s approximate number sense, it seems, the higher one’s chance of getting good grades. This might have serious consequences for education. If a flair for estimation fosters mathematical aptitude, maybe maths classes should be less about times tables and more about honing skills at comparing sets of dots.’ (p 33)

*Not so much of a wow – what would the use of that be if no connection is being made at a functional, internal level?*

*Can you give the answer to 7 x 7 or 8 x 7 as fast as you can 5 x 10 or 6 x 4?
*

*How do you work out the sums?*

What’s going on inside your mind?

What’s going on inside your mind?

In Munduruku mode, we find it easy to think of 1, 2, 3 – even 4. This is borne out by Lawrence Potter (Mathematics Minus Fear, Marion Boyars publishing, London 2006, pp 34-40) in terms of his observation of relative difficulty of multiplication / times table retention and recall. 1, 2, 3, 4, 5 are fine. 6, 8, 10 are easy – double the relevant proportional sums in the lower groups. 9 works back from 10, but 7 seems the hardest to recall. It certainly checks out in my own mind.

In Munduruku mode, we find it easy to think of 1, 2, 3 – even 4. This is borne out by Lawrence Potter (Mathematics Minus Fear, Marion Boyars publishing, London 2006, pp 34-40) in terms of his observation of relative difficulty of multiplication / times table retention and recall. 1, 2, 3, 4, 5 are fine. 6, 8, 10 are easy – double the relevant proportional sums in the lower groups. 9 works back from 10, but 7 seems the hardest to recall. It certainly checks out in my own mind.

Bellos mentions Dyscalculia – it seems that Dyscalculics can be very good at logic and geometry that ‘prioritize [sic] (I hate the cultural infiltration of American spellings in the UK edition of a book that is published by a UK-based publisher with offices also in the States) deductive reasoning or spatial awareness rather than dexterity with numbers or equations.’ (p 39)

A final observation – I’m observing a selective function operating here – filtering out things which don’t interest me – traffic cones in the introduction (pp 8-9); experiments with animals (pp 21-28); experiments with kids; perceptions of mathematical processes (pp 28-30). Logarithmic processes working as I read … and comparison and recall as well. On p 30, Bellos outlines similarities between visual depictions of quantity in Roman, Chinese Indian number systems. He doesn’t mention Arabic numbers (ie written in Arabic script). There was a better expose’ of the correlation between script and number which went up to 10 displayed as part of the *1,001 Inventions *exhibition of Islamic culture at the Science Museum earlier this year. Mental note to contact them to get the information. When I do I’ll add it to this post.

happyseaurchin(07:04:53) :zone

got to try the dots recognition system with my students

I think it has been monopolized by kumon maths…

and dyscalculia…

I never liked dyslexia so have been reluctant to adopt this category…

but I will see if i can come up with other ways to circumnavigate such perceived problems…

I am tutoring someone who is definitely doing something odd in their heads

and I have got close to putting my finger on it

but haven’t come up with a solution…

yet….

thanks for the post :)

Leon Conrad(18:39:52) :David – put the dots exercise on your intentions list on the wiki. It’s an important test for the book project I think.

I’m loath to discuss your comments on dyslexia, as it’s really chasing down an alleyway and I know you well enough to know that thoughts jotted down quickly, which appear superficial come from a considered stance within you – even though clarity of communication is compromised for sake of speed.

Back to the book, though, please can you work on a chapter which addresses diversity in mindsets / wiring / physiology eg your understanding / experience of Dyscalculia, dyspraxia, dyslexia, in relation to thinking and teaching the art of thinking (now there’s a title for a book for another sector – The Art of Thinking).

happyseaurchin(23:03:39) :hehe

the art of thinking

yes

there’s a time lag with these comments

because i often see you and hear your ideas before i read them here!

happyseaurchin(18:50:32) :upon reading your comments after a two year gap

i am amazed at how bad i am at reading….

your comments are insightful

eg drawing my attention to logarithmic thinking and ratio

connecting this to advertising and bypassing linear thinking

eg dyscalculia seems related to the “language” side of maths or algebra

and i look forward to seeing if this appears in my mind

as i approach advertising bods