[Numeracy 210] Re: manipulatives
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Tue Feb 23 00:16:45 EST 2010
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True enough!
Maureen Carro, MS, ET
Academic Learning Solutions
Alamo, CA
mcarro at lmi.net
On Feb 22, 2010, at 1:04 PM, Carolyn Dickinson wrote:
> Maureen,
>
> In the interest of creating less antagonism between the "Western"
> world and the "Muslim" world, you might also mention that a very
> large part of algebra (including its name) came from the Arabic world.
>
> Carolyn
>
> On Mon, Feb 22, 2010 at 11:56 AM, Maureen Carro <mcarro at lmi.net>
> wrote:
> 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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>
>
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