My main concern is in the graphic. If this is one of the examples they used it’s no wonder the concrete group did little better than guessing. When one uses a “real world” example, one needs to make sure it conforms to the “real world,” otherwise it simply causes more cognitive dissonance. I personally have never experienced 2/3 cups and 2/3 cups being combined to make 1/3 cup in the “real world.” As an asside, I did have a student insist that 1/4+1/4 was 2/8 until we went into the kitchen and poured water into measuring cups.

I remember reading something, I forget where it was, about how the times tables are not so much problems of arithmetic, but of language. We are having to manipulate the words “seven times six equals forty two” which bear very little relation to numbers as such. This is why most people, even those of high intelligence, can struggle with them, and often descend into savage self-criticism. Whereas if we see the numbers as a pattern, it is much easier to arrive at the correct answer.

In regards to “Dehaene conjectured that, when we see numerals or hear number words, our brains automatically map them onto a number line that grows increasingly fuzzy above 3 or 4. He found that no amount of training can change this” does this mean that no amount of “Brain Training” programmes out there – such as the one for the Nintendo DS – are actually any good? lol

Stefan
(http://shoptilltheydrop.wordpress.com)

Thanks for the great ideas!!!!