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# Padrões Common Core: números negativos

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so here again with Bill McCollum one of
the authors of the Math Standards of the Common Core and I thought today we could
think about how the the Common Core thinks about negative numbers and like always I guess it would
be interesting as an overview, Bill, you can tell us um how how the Common Core thinks about
it especially relative to your sense of previous standards. Well..negative numbers are introduced in a way that is fairly straightforward and unconventional the only comment I would make is that
because we've had that emphasis on the number line throughout starting from there I'm
putting a whole numbers and by fractions on the number line it's a
it's a natural thing to extend that number line where some point and think about what
would happen it got numbers that were less than zero and so I think this set up a number line
with us all up I Sunday a representation at the member system picture in good
shape for representing negative numbers we do start out with this idea that you
are negative numbers to have some sort of and motivation exactly what qualities in
service that scared about um thinking about parties that have
opposite direction tho values I'm such as your temperature below to
the wrong things like that right I often say that I have three
children a 5-year-old a three year old and a negative
three-month-old a my real real-life context clues to the
at this point in my life and and because the very high level way that it
seems to be split is that in 6th grade you do what you just talk about you you
think about the number line you you you associates a meaning with
negative numbers like things long temperature thanks to the right or left
or something things above and below something to these are all the sixth grade
standard right over here and then in at in 7th Grade you actually start to
compute with right and your I mean the operations with negative
numbers um addition is really a very natural um
extension addition on the underlying with positive
numbers a when if you have a very solid mutual understanding but additional
numbers on the number line additional positive numbers is about putting links
together at a edits foundational level that that anytime you want to add two numbers
is just like measuring to a certain point on the line when
you're measuring it for a good distance to add a second number then it's a pretty easy chip from there
to understand that with native number to just go in the opposite direction but
it's still a model %uh adding numbers right where you put lakes together
except the lights now have a have a positive or a negative writer
kinda was more like one dimensional vectors or something exactly that exactly if I could probably
use the word vector in seventh grade but it's good it's a
good foundation thinking when kids get the high school
are probably about vector addition right and you know one one question
exist I miss has been curious and even before the
concourses and I've always been curious that you know the the idea haven't you know that I have a number line is
obviously I'm you choose to children when they're alright but quite young and and a notice what I've turned out
that the vid cousins there is a negative numbers don't seem
that daunting to them you know specific us decide if directionality you going to
the left now that many to the left what's your sense of why his previous standards and also the
comic or wait until six great you know why not introduce it in first-grader second well you care I mean the main reason it I think I i think at
a sort of just as basic idea of going below zero kids will not really think
about you know they're all these videos are
capable working with kids in much earlier grades with negative
numbers um the main reason not to I would say is
that there's a lot of work to be done with fractions its people get find difficult and part
of the principal a problem call was to focus on what was most important thing
at grade level in the league if that understanding the time to mature and
develop I'm not clutter of early grade levels
with things that were not necessary at night by a double so I think the main reason to hold
office to make sure you have a really solid understanding a positive numbers
particularly rack your fractions firm before you stop
caring about negative numbers right now that's it there's no harm in
having it come up earlier as an extension popping as long as it's not
getting any in in in the way of a major work it very
I see the senses a.m. you're right I I've observed this
with with people earning a fractions is one of those big things
in elementary school that your many middle school student even don't
have for mastery of it and so you're saying you know especially when their first getting
exposed ideas fractions dude in and also simplest way possible so they
don't have to worry about you know were hard by the nato numbers and and whatever I mean no sometimes these
might think your DVD topics like negative numbers um become an excuse not do the hard work up a great it's a
little bit like you know when you're supposed to be getting
bitchy helping you find any excuse but bum I mean it so I think we didn't wanna
provide those excuses we wanted to say look at the far post a raise case your kid who is getting addition down the focus here great
injured by but getting modification infractions down when you know once you done that anything stop the about
negative numbers I see is it's like that I think now what is a
little bit difficult but the people start to get a hang up his winnings are
multiplying all the rules multiplying positive and
negative numbers those are very mysterious to some people yup yup yep absolutely and just I guess
that at the time we have %remaining% you just pick looking at a couple EastEnders that but
don't tell me when I when I first look at the Standard & you know this this idea that recognize
opposite sign for the number as indicating locations on opposite
sides of the other number I'm probably make sense of a coru単a
positive three and you have -3 just like that then there's this kind of implicit are
emphasis on recognizing that the that the opposite over numbers is that
so you have seen some items and even from the we put on
Academy were you know we use the word opposite in I remember the first time
that I review look at those items or what thats that's
not my natural word to use are you know so with the
negative on this number what's black so what's your sense of this you know
using the word opposite ha how important it is that is it for people to outnumber that we are well as with all of these
language issues if you understand what you mean it
doesn't matter what already it is but light which can cause
misunderstandings and misunderstanding that can arise from or eating or negative his kids get to college and
we'll see negative X mmm and don't think that's native cora
alright right chipped a and across Texas native
a negative and positive mindset thats gets that word negative
used indicate taking the officer classes with the word negative as many actually
negative here at the very bottom but he said that the point xxx the main
reason from now you know that said if you
understand negative x could also be positive then
there's no I'm using the word I wouldn't want teachers are
instructional materials to speak that way because I think using at work in
court this misconception used to use negative into you would
prefer that pursuant to more familiarity with the word you know the opposite in a mathematical context
at least we were talking about sign is Rai I opposite side and I and goes but you want to go to replace
the officer to Parliament negative number of 78 number the parking officer
putting that native sorry I'm could right bro number
changes its sign right now that that that that make sense
the other thing that happens in in six grade is and I guess what is this
happening generally aren't we there looking at you know SNC look not
only plotting on a on a kind of a one-dimensional number
line but flooding in two dimensions is that
happening in general in sixth grade at that point and this is a speech senator
has that happened already in fifth grade only be parting in corner playing with
just the positive quadrant before in fifth grade he wakes getting
back to the other up a four-point gain sang israeli
preparation for graphing functions I'm for analytic geometry it's a white
paper reaching for Obama but you want kids to start getting
used to the idea but you can plot are up to conventional coordinate system
where I did for me to be negative and my sis is that is al.'s relative to
what I remember from school that is earlier than what was to be done arm you know I think it varies I didn't
have a solid sense of what the average was I'm and again I guess I would say a I bad it's not you don't want to get
carried away with his plate level mmm for example we're not plotting functions
arming I I anything except the first quarter
and we're not really very naughty going to get a great seven
let me start I'm thinking about proportional
relationships which is sorta thats you know no credits so to the
function concept but was still grapple reporting
relationships as relates it been positive qualities just came out first walking I see I C and then there's more is kinda under Settings order that I'm
it's a wonderful things in general design principles of the Common Core is you'll see standards in a great
double what you really just like thin streams live beginning on that then wiping out into larger
rivers in later grade levels and that's an example this is a seed standard if you like arm people aren't
always used to thinking that way that stands at RCS terribly only got have to
do like every day right now where it's not
really that it's just that it's just me you see ID you might as well do it at
the same time we've introduced the negative part of a member Lauren model introduced negative I'm axes in a
two-dimensional system as well yup make sense and I'm see also in six
grade ordering in the idea absolute value is gonna distance to the
the right to the left of over up zero and then and of course in seventh grade that's
when it really is just all about computation and it's about me it's about extending
the operation it's only operations your very cool thanks a bunch okay
thanks