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**Even Pigeons Can Do Maths**

This is a really interesting study from a couple of years ago, which shows that even pigeons can deal with numbers as abstract quantities – in the study the pigeons counted groups of objects in their head and then classified the groups in terms of size. From the New York Times Article:

*“Given groups of six and nine, they could pick, or peck, the images in the right order. This is one more bit of evidence of how smart birds really are, and it is intriguing because the pigeons’ performance was so similar to the monkeys’. “I was surprised,” Dr. Scarf said.*

*He and his colleagues wrote that the common ability to learn rules about numbers is an example either of different groups — birds and primates, in this case — evolving these abilities separately, or of both pigeons and primates using an ability that was already present in their last common ancestor.*

*That would really be something, because the common ancestor of pigeons and primates would have been alive around 300 million years ago, before dinosaurs and mammals. It may be that counting was already important, but Dr. Scarf said that if he had to guess, he would lean toward the idea that the numerical ability he tested evolved separately. “I can definitely see why both monkeys and pigeons could profit from this ability,” he said.”*

To find mathematical ability amongst both monkeys and pigeons therefore raises two equally interesting possibilities. Perhaps basic numeracy is a rare trait, but such a fundamentally important skill for life that it emerged hundreds of millions of years ago. Or perhaps basic numeracy is a relatively common trait – which can evolve independently in different species.

Either way, it is clear that there must be an evolutionary benefit for being able to process abstract quantities – most likely in terms of food. A monkey who can look at two piles of coconuts and count 5 in one pile and 6 in the other and know that 6 is a bigger quantity than 5 can then choose the larger pile to sit alongside and eat. Perhaps this evolutionary benefit is the true origin of our ability to do maths.

Another similar experiment looked at the ability of chimpanzees to both count numbers, and also demonstrated their remarkable photographic memory.

On the screen the monkeys are given a flash of 10 number for a fraction of a second, before the numbers are covered up, and they then proceed to correctly show the position of all numbers from 1-10. They are much better at this task than humans. This is a good task to try at school using the online game here and would also make a good IB investigation. Can you beat the chimps?

This all ties into the question about where mathematical ability comes from. If there had been no evolutionary ability for such abstract abilities with numbers, then perhaps today our brains would be physically incapable of higher level mathematical thinking.

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Essential resources for IB students:

Revision Village has been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams. I would strongly recommend students use this as a resource during the course (not just for final revision in Y13!) There are specific resources for HL and SL students for both Analysis and Applications.

There is a comprehensive Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and then provides a large bank of graded questions. What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial. Really useful!

The Practice Exams section takes you to a large number of ready made quizzes, exams and predicted papers. These all have worked solutions and allow you to focus on specific topics or start general revision. This also has some excellent challenging questions for those students aiming for 6s and 7s.

Each course also has a dedicated video tutorial section which provides 5-15 minute tutorial videos on every single syllabus part – handily sorted into topic categories.

2) Exploration Guides and Paper 3 Resources

I’ve put together four comprehensive pdf guides to help students prepare for their exploration coursework and Paper 3 investigations. The exploration guides talk through the marking criteria, common student mistakes, excellent ideas for explorations, technology advice, modeling methods and a variety of statistical techniques with detailed explanations. I’ve also made 17 full investigation questions which are also excellent starting points for explorations. The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.