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Re: Some important demonstrations on negative numbers > a MACS syllabus
Posted:
Dec 17, 2012 7:57 PM
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On Dec 17, 2012, at 1:17 PM, Joe Niederberger <niederberger@comcast.net> wrote:
>> Most of the popular modern math textbooks have stopped telling the story. No plot development. No character development. No formal development.
>
> Here's an antidote to what I consider your simple dichotomies:
> http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/chapter1_about_this_book.pdf
>
> One not agree with it entirely, but it represents a serious investigation.
>
> Cheers,
> Joe N
So, if it was based on concrete evidence like you suggest, then why do so few actually get it? This is my point, and my proof. It isn't based on concrete evidence at all. It isn't simply an extension of our senses. It is an altogether new sense. I never claimed that students reach a mostly formal state of thinking by 8. I stated that by the end of algebra 2, the transformation is mostly done. And I base that on performance, not appreciation.
Bob Hansen
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