[Numeracy 206] Re: manipulatives
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Mon Feb 22 13:56:46 EST 2010
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Manipulative materials, I think have most value in the early
grades.... when developing early concepts of place value, addition and
subtraction, etc. I think the 'scanty understanding" of place value
is at the root of many problems adults have with math. Most
elementary math books, and certainly adult books, seem to devote mere
paragraphs to the topic, although schools seem to be doing better at
this more recently. Usually, I spend a considerable amount of time
making sure students (even adults) understand this fundamental
concept (place value) which is needed throughout the math curriculum.
Decimals, exponential notation, powers of ten, etc. are concepts that
build on place value. I use some base ten blocks, stories, and things
like "straw bundles" , toooth picks, money, etc. to establish the hook
for the basic concept. I spend considerable time demonstrating how
the "decimal system" works, with 10 digits, 0-9 being the only symbols
use to represent quantities. Once we have gone through the decimal
system, I challenge the students to create values in the binary
system, using only 2 digits, 0 and 1, and having them generate the
values according to the same pattern. They usually are successful
doing so, and I know they get the idea. When we get to "algebra", I
review the basic concrete ideas (using concrete manipulative materials
if necessary) to review what underlies the new learning, and then make
the leap into the abstract. I do this each and every time we begin a
topic where the prior knowledge required can be demonstrated with
manipulative materials or real life examples.... the idea is to
proceed from what is known/familiar to what is unknown/unfamiliar.
When introducing equations in algebra, I start with the expamples of
"real life" concepts , such as area,, perimeter, volume, etc. as
examples of algebraic equations that serve as "formulas" that apply to
certain types of problems. We can "solve" for any of the missing
components of the equation. I also talk about "pi" by wrapping a
string ( equal in length to the diameter) around many different size
circles, such a plates, cups, etc.... noticing that on each occasion,
it is "a little more than 3 times the diameter of the circle, no
matter its size". I do a lot of "story telling" about the "geeky
Greeks" and what they noticed about natural occurrences that still
holds in math and upon which even today's computer scientists still
build. ( Of course, it was more than the Greeks.... but it cuts to
the chase without taking up too much diversionary time... the "geek"
part is for an "emotional zap" and may not work with all groups / I
follow it with: "I am proud to be a geek". You need to know your
group).
For those interested in the Making Math Real Curriculum, the
curriculum uses manipulative materials extensively in the early stages
of math, (moving from concrete, to semi-concrete, to semi-abstract to
abstract) but by Pre-Algebra, holds that the concepts need to be
well established and manipulated mentally. The bridge needs to be
made from concrete to abstract, and some things to "automaticity"
before algebra.
Maureen Carro, MS, ET
Academic Learning Solutions
Alamo, CA
mcarro at lmi.net
On Feb 19, 2010, at 10:34 AM, Jacqueline Kiefer wrote:
> Susan, I too am interested in what you learn from Making Math Real.
>
> I understand what you mean about manipulatives becoming one more
> layer of confusion. When I used algebra tiles to explain algebra, I
> BOMBED BIG TIME.
> However, when I used them to explain integers, there were light
> bulbs coming on all over the classroom. A deck of cards and a game
> of Integer Showdown is also great.
> Jackie
>
> From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov]
> On Behalf Of Leslie Hunten
> Sent: Friday, February 19, 2010 7:39 AM
> To: The Math and Numeracy Discussion List
> Subject: [Numeracy 198] Re: manipulatives
>
> Susan, please do share what you learn from Making Math Real!
>
> Leslie
>
>
> On Thu, Feb 18, 2010 at 3:00 PM, Susan Jones <SUJones at parkland.edu>
> wrote:
> Nobody uses manipulatives here, which I think is a shame.
>
> Hard to make the bridge from concrete to abstract without the
> concrete, though we sometimes can anyway.
>
> We do use some visuals -- but not much of that, either.
>
> I wish I could say that the folks working with the more basic than
> pre-algebra did, but I'm 99 44/100% sure they don't either. We
> explain and wish and wonder why students don't connect math to the
> real world...
>
> That said, there's not a lot of evidence (either formal research or
> anecdotal) to say manipulatives help... I've seen them be one more
> layer of confusion, if the connection between the concrete to the
> symbols isn't solidified. One reason I'm really looking forward to
> the Making Math Real overview is that I have a feeling this does
> that (or at least makes a good effort;)) and would give me the tools
> to try.
>
>
>
> Susan Jones
> Academic Development Specialist
> Center for Academic Success
> Parkland College
> Champaign, IL 61821
> 217-353-2056
> sujones at parkland.edu
> Webmastress,
> http://www.resourceroom.net
> http://bicyclecu.blogspot.com
>
>
> >>> Jaye Luke <flipfloprun at gmail.com> 2/18/2010 11:52 AM >>>
> I haven't taught a math class for adult learners...yet:) But I am
> curious
> 1- Are you using manipulatives?
> 2- If you are using manipulatives are they specifically for math
> (cuisenaire
> rods) or more generalizable (tokens/tiles)?
> 3- Do you think the manipulatives are beneficial and why?
>
>
> Cheers
> jaye
>
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