Why exams mean nothing out of context

What are the chances that the kids are good at calculating prices because the sample space of possible total costs of products and offered money is quite small? In this case, they could imitate good mental arithmetic simply by memorising the most common combinations.

If you sell only two products - sunscreen and gum - at a fixed price and most people are unlikely to buy more than a couple of each, you can draw up an easily memorisable table of all likely total costs. Assuming a finite number of notes in "normal" denominations (i.e. not a 8063 cruzeiro note) then it is probably also relatively straightforward to memorise all possible combinations of products and proffered notes. This memorisation might not happen consciously, but through endless repetition.

So if you buy a pack of gum for 300 cruzeiros and pay with a 1000 cruzeiro note, just like everybody else did that day, the kid will know that it's 700 in change from memory. Bring that same kid into a classroom, introduce a suite of new products at different prices and ask him/her to perform the same computations and it is quite understandable that he/she will not perform as well.

Now I'm not saying the classroom setting doesn't have an effect such as making the kids nervous, just that it would be important to control for this kind of memorisation. I couldn't access a full copy of the paper cited, so I don't know if it was taken into account...

I can confirm this result from personal experience. In teaching basic algebra, I found people who couldn't multiply 0.8 by 20 without a calculator could easily tell me how much something that cost $20 would be if a store was having a 20%-off sale. Some of them could even compute the amount with sales tax.

The problem with the kids in the private schools is that they are taught to memorize a procedure to attain an answer to a pre-constructed question. For them it's different to ask if x is 3.56 and y is 4, what is the product of x times y, in contrast to asking them to multiply a the 3.56 per item cost of four burgers.

In my opinion the problem is not what is taught or how, but the direction teaching as a whole has always had. It's fine to teach kids that the product of x and y is z, as long as you've also spent time explaining the actual uses something might have in the children's life. Kids and teenagers always say "Why do I have to study this if it has no use in real life?", and it's the school's and teacher's job to teach this children that they're wrong.

From the research paper linked from the article, here are how the kids scored in different contexts:

  calculating prices in the street      98%
  solving word problems on an exam      74%
  solving abstract problems on an exam  34%

This would suggest that applying concepts is more important, physical context less so.

Mind you, this is an extremely difficult experiment to carry out scientifically and is open to many interpretations. I would at least want to see it reproduced before giving it much consideration.

This might just be why you're an entrepreneur: it's way better doing it than learning about it out of context ;)