I read The Number Sense in French so I have to hope that the English version is close to it… The book recaps a large number of studies on how our brains work with numbers in a lively and easily readable style (in other words, it’s written by a psychologist, not a mathematician, and is easily accessible to non-mathematicians and even math phobics).
What I found most interesting is the contrast between the innate mathematical talents of babies, who can easily tell differences between small numbers and who are pretty good at number matching on the one hand, and the fundamental lack of inborn mental structure to support abstract math. This means that we are all astonishingly good at estimating, matching, and pattern recognition, but only a few weird people can be very good at exact calculations while many of us struggle with relatively basic tasks such as subtractions with carries. We simply don’t have brains meant to deal with them. So let’s all agree that calculators (machines, that is) are our friends and we should just use them and focus our energies and school hours to learning something else.
The chapter about math savants and those poor brain-damaged people who get dragged into any discussion about the functioning of the brain can be safely skipped. And enjoy the wonderful quotes at the beginning of each chapter!