Name: The Number Sense
ISBN: 9780199753871

The Number Sense

Dehaene, a mathematician turned cognitive neuropsychologist, begins with the eye-opening discovery that animals, including rats, pigeons, raccoons, and chimpanzees, can perform simple mathematical calculations. He goes on to describe ingenious experiments that show that human infants also have a rudimentary number sense. Dehaene shows that the animal and infant abilities for dealing with small numbers and with approximate calculations persist in human adults and have a strong influence on the way we represent numbers and perform more complex calculations later in life. According to Dehaene, it was the invention of symbolic systems for writing and talking about numerals that started us on the climb to higher mathematics. He traces the cultural history of numbers and shows how this cultural evolution reflects the constraints that our brain architecture places on learning and memory. Dehaene also explores the unique abilities of idiot savants and mathematical geniuses, asking whether simple cognitive explanations can be found for their exceptional talents. In a final section, the cerebral substrates of arithmetic are described. We meet people whose brain lesions made them lose highly specific aspects of their numerical abilities - one man, in fact, who thinks that two and two is three! Such lesion data converge nicely with the results of modern imaging techniques (PET scans, MRI, and EEG) to help pinpoint the brain circuits that encode numbers.

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omginternetsSep 2020

If you're interested in Numerical Cognition, I can't recommend Stanislas Dehaene's The Number Sense enough.

It's fantastic.

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ChaitanyaSaiFeb 2015

It might also help to know what parts of math are intuitive and what parts aren't. Our brains just can't visualize tensors, but we can visualize quantities. Trying to relate tensors to the spatial geometry of the world around us -- the world we can perceive -- may not lead to much.

I found this book helpful

http://www.amazon.com/Number-Sense-Creates-Mathematics-Revis...

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aethertapNov 2013

I have been researching this for a couple of years and can recommend a couple of books that I thought were particularly good:

* Good questions for math teaching (http://amzn.com/0941355519)

* Young Mathematicians at Work (http://amzn.com/032500353X)

* Number Sense Routines (http://amzn.com/1571107908)

* Dr Wright's Kitchen Table Math book (there are three) - http://amzn.com/0982921128

I haven't finished these next two, but they look promising:

* Fostering Geometric Thinking (http://amzn.com/0325011486)

* Fostering Algebraic Thinking (http://amzn.com/0325001545)

I also like the approach of the Art of Problem Solving curriculum, though it doesn't currently have elementary school material. I haven't used it on my own kids yet because they're still too young, but I did buy the set and I think it looks good. If you read "Good Questions for Math Teaching" you will probably modify the way the problems are presented to make them more open-ended, but I like that topics are introduced with a problem that is later explained, instead of explaining then drilling.

http://www.artofproblemsolving.com/Store/curriculum.php

Finally, I thought that this online course was a nice introduction to the approach. It's a pretty short course, but I just put the audio on an mp3 player so I could listen while working on other things and there were only a couple of places where I couldn't tell what was happening in the video.

* https://class.stanford.edu/courses/Education/EDUC115N/How_to...

For a more general book about early childhood education, I really liked

* "Engaging Children's Minds - the Project Approach" (http://amzn.com/1567505015)

* Making Thinking Visible (http://amzn.com/047091551X)

* Learning Intelligence: Cognitive acceleration...(http://amzn.com/0335211364)

Sadly, most of these books are pretty pricey for the page count, but the material I thought was quite good. If you were to get only two, I'd say go with "Young Mathematicians at Work" and "Good Questions for Math Teaching" because they will probably give you the quickest jump start, especially if you can get the "How to Learn Math" course.

If you're interested in where my evidence for the approach outlined here comes from, my main sources are the following books:

* Effectiveness In Learning (cognitive load theory) http://amzn.com/0787977284

* Visible Learning (synthesis of 800 meta-analyses) - http://amzn.com/0415476186

Edited because I put some of them in the wrong spots and forgot links...

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grosalesMar 2010

If you'd like to understand a little bit about how our brain might process and understand numbers, get "The Number Sense" by Stanislas Dehaene

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nsrivastJun 2008

Most of Stanislas Dehaene's papers are excellent, if you're into that sort of thing:

http://www.unicog.org/biblio/Author/DEHAENE-S.html

#4, "The Number Sense", is particularly good.

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agumonkeyAug 2012

My anecdote is a chapter called 'Piaget errors' in 'The number sense' http://www.amazon.com/The-Number-Sense-Creates-Mathematics/d... a book from Stanisla Dehaene. You can check out the preview but it skips a part of the piaget chapter though.

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